From 9873de670bb899f6e75986a4ff5972e69e92478f Mon Sep 17 00:00:00 2001 From: marcelolooser Date: Fri, 2 May 2025 14:53:30 +0200 Subject: [PATCH 1/3] chore: clarify user input convention for multiorbital non-reciprocal models --- .../NonReciprocalAbelianBlochHamiltonian.nb | 487 ++++++++++++---- ...procalAbelianBlochHamiltonianExpression.nb | 522 ++++++++++++++---- .../Symbols/NonReciprocalTBHamiltonian.nb | 508 ++++++++++++----- 3 files changed, 1177 insertions(+), 340 deletions(-) diff --git a/Paclet/Documentation/English/ReferencePages/Symbols/NonReciprocalAbelianBlochHamiltonian.nb b/Paclet/Documentation/English/ReferencePages/Symbols/NonReciprocalAbelianBlochHamiltonian.nb index c1197e4..452a3aa 100644 --- a/Paclet/Documentation/English/ReferencePages/Symbols/NonReciprocalAbelianBlochHamiltonian.nb +++ b/Paclet/Documentation/English/ReferencePages/Symbols/NonReciprocalAbelianBlochHamiltonian.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 125486, 3068] -NotebookOptionsPosition[ 111822, 2774] -NotebookOutlinePosition[ 112628, 2800] -CellTagsIndexPosition[ 112547, 2795] +NotebookDataLength[ 139628, 3365] +NotebookOptionsPosition[ 124878, 3049] +NotebookOutlinePosition[ 125684, 3075] +CellTagsIndexPosition[ 125603, 3070] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -453,10 +453,10 @@ AbelianBlochHamiltonianExpression"]], "InlineSeeAlsoFunction", "40a5967c-b2d7-4ad4-bb67-87cb6c247423"], DynamicModuleBox[{$CellContext`nbobj$$ = NotebookObject[ "ca524783-33ba-4436-a7c7-e9b68abdb844", - "1d6237b8-b6b5-aa41-9799-963dcbf87367"], $CellContext`cellobj$$ = + "7c289219-9f2e-6046-ab73-6e12af829af9"], $CellContext`cellobj$$ = CellObject[ "f192ff71-19a1-4a57-b3cc-520a4f08fea8", - "2a83925f-ce99-6648-adfa-5266ca5294db"]}, + "37d6b5d7-23f1-b44f-9000-fdd70011d409"]}, TemplateBox[{ GraphicsBox[{{ Thickness[0.06], @@ -484,8 +484,8 @@ AbelianBlochHamiltonianExpression"]], "InlineSeeAlsoFunction", CellChangeTimes->{{3.906081385224657*^9, 3.906081393032315*^9}, { 3.906081431010906*^9, 3.906081446001929*^9}, {3.93450616595286*^9, 3.93450624807312*^9}, {3.9345063104834785`*^9, 3.934506330963293*^9}, { - 3.9374049102532196`*^9, 3.937404915982052*^9}, {3.9400952283675175`*^9, - 3.9400952383173943`*^9}, {3.940095303675123*^9, 3.940095309225073*^9}}, + 3.937404910253219*^9, 3.937404915982052*^9}, {3.940095228367518*^9, + 3.940095238317395*^9}, {3.940095303675123*^9, 3.940095309225073*^9}}, CellID->381155944,ExpressionUUID->"dbc05f00-cfba-473e-bc6d-ca3adf85f088"] }, Open ]], @@ -547,8 +547,8 @@ Cell[BoxData[ CellID->287190428,ExpressionUUID->"d2f8cf66-026c-48d5-a784-375f28f06a2d"], Cell[TextData[{ - "Construct the Abelian Bloch Hamiltonian of an elementary nearest-neighbor \ -hopping model defined on an ", + "Construct the non-reciprocal Abelian Bloch Hamiltonian of an elementary \ +nearest-neighbor hopping model defined on an ", Cell[BoxData[ ButtonBox["HCModelGraph", BaseStyle->"Link", @@ -562,7 +562,7 @@ in canonical and opposite to the canonical direction, respectively:" 3.9060287922921596`*^9, 3.906028807134487*^9}, {3.9345071774232864`*^9, 3.9345071795629616`*^9}, {3.934507342442824*^9, 3.93450742533321*^9}, { 3.934507810362931*^9, 3.934507819672989*^9}, {3.9345080614427013`*^9, - 3.934508103447901*^9}}, + 3.934508103447901*^9}, {3.955167704822487*^9, 3.955167708322012*^9}}, CellID->82755364,ExpressionUUID->"ebb1feb3-0056-4f70-a821-cb75db877955"], Cell[CellGroupData[{ @@ -2655,6 +2655,8 @@ Cell[BoxData[ $Line = 0; Null]], "ExampleSection", CellID->317484403,ExpressionUUID->"5d9c66a9-2524-477e-bda4-777d86e71207"], +Cell[CellGroupData[{ + Cell[BoxData[ InterpretationBox[Cell[ "Properties & Relations", "ExampleSection",ExpressionUUID-> @@ -2662,6 +2664,279 @@ Cell[BoxData[ $Line = 0; Null]], "ExampleSection", CellID->298852093,ExpressionUUID->"b34fadbf-53bf-4c0f-a2c9-b944d3b156e0"], +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell[TextData[Cell[BoxData[ + InterpretationBox[Cell[ + "Multiple orbitals", "ExampleSubsection",ExpressionUUID-> + "cba59b7a-5e0e-cf44-b6db-ac80d486eccb"], + $Line = 0; Null]], + CellChangeTimes->{{3.9060313294514136`*^9, 3.906031330419829*^9}, { + 3.9374005375764217`*^9, 3.937400540021569*^9}},ExpressionUUID-> + "4f180156-c70d-1940-870b-45d9ee9bddc5"]], "ExampleSubsection", + ExpressionUUID->"1231e9d3-b771-724d-99f0-0109afa16c72"], + $Line = 0; Null]], "ExampleSubsection", + CellChangeTimes->{{3.9060313294514136`*^9, 3.906031330419829*^9}, { + 3.937405053908352*^9, 3.937405065322071*^9}, {3.9551680429373455`*^9, + 3.95516805009239*^9}}, + CellID->296669070,ExpressionUUID->"3390a96f-2b13-6344-bd3a-88875f42664b"], + +Cell[TextData[{ + "Non-reciprocal Abelian Bloch Hamiltonians are constructed through a \ +generalization of the function ", + Cell[BoxData[ + ButtonBox["AbelianBlochHamiltonian", + BaseStyle->"Link", + ButtonData-> + "paclet:PatrickMLenggenhager/HyperBloch/ref/AbelianBlochHamiltonian"]], + "InlineFormula",ExpressionUUID->"2bb6ddac-3982-b04e-9f5e-0c72bceb16db"], + ". As such, the onsite potential and the hopping amplitudes are specified \ +analogously. Crucially, the following convention is imposed:" +}], "ExampleText", + CellChangeTimes->{{3.906027105777158*^9, 3.906027175428211*^9}, { + 3.9060285881964235`*^9, 3.90602860227144*^9}, {3.9060288129869814`*^9, + 3.906028831115154*^9}, {3.906028997135098*^9, 3.906029000923377*^9}, + 3.9345103390559063`*^9, {3.937421005016327*^9, 3.9374210159177094`*^9}, { + 3.9551673567773075`*^9, 3.955167361081892*^9}, {3.955168934862646*^9, + 3.9551689986790257`*^9}, {3.9551691386825943`*^9, + 3.9551691946723156`*^9}, {3.955169256152302*^9, 3.9551694931826744`*^9}, { + 3.955169586572748*^9, 3.9551697126776447`*^9}, {3.955169791552847*^9, + 3.9551697986726894`*^9}, {3.955169850973112*^9, 3.9551698519929733`*^9}, { + 3.9551699271128254`*^9, 3.955170211827799*^9}, {3.955170242038122*^9, + 3.955170255833084*^9}, {3.955170301413376*^9, 3.9551703913169937`*^9}, { + 3.955170445563442*^9, 3.9551705987731857`*^9}, {3.95517525090296*^9, + 3.955175264852995*^9}}, + CellID->105689035,ExpressionUUID->"fd9c54f6-8d5c-7445-b2b0-bc2558b8ccf2"], + +Cell[TextData[{ + "To specify the hopping matrix for the hopping amplitudes ", + Cell[BoxData[ + StyleBox["hoppingsOpposite", "TI"]], "InlineFormula",ExpressionUUID-> + "83bd0532-97da-f248-8b17-51a00579e4fb"], + " appropriately, the positions of the matrix entries for each pair of \ +orbitals is inherited from the hopping matrix ", + Cell[BoxData[ + StyleBox["hoppingsCanonical", "TI"]], "InlineFormula",ExpressionUUID-> + "9966380f-fb2b-ba4d-9f24-ab65e5d9d312"], + ". 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{3.9551712636836224`*^9, 3.9551712747634583`*^9}, { + 3.9551714818336887`*^9, 3.9551715032236137`*^9}, {3.955172112773716*^9, + 3.955172113753664*^9}, {3.955172958744713*^9, 3.9551729998145275`*^9}, { + 3.9551738888346024`*^9, 3.955174072975092*^9}}, + CellID->135010306,ExpressionUUID->"8426917f-e9a1-9b4a-b254-015f536580c5"], + +Cell[TextData[{ + "Note, for the specification of the hopping matrix ", + Cell[BoxData[ + StyleBox["hoppingsOpposite", "TI"]], "InlineFormula",ExpressionUUID-> + "7e156c0c-aa14-144e-80b9-0e46027671bf"], + " it is instructive to think of constructing an Abelian Bloch Hamiltonian \ +with adjusted hopping amplitudes. The location of the matrix entries, \ +signifying which orbitals are couped, are not to be adjusted." +}], "ExampleText", + CellChangeTimes->{{3.906027105777158*^9, 3.906027175428211*^9}, { + 3.9060285881964235`*^9, 3.90602860227144*^9}, {3.9060288129869814`*^9, + 3.906028831115154*^9}, {3.906028997135098*^9, 3.906029000923377*^9}, + 3.9345103390559063`*^9, {3.937421005016327*^9, 3.9374210159177094`*^9}, { + 3.9551673567773075`*^9, 3.955167361081892*^9}, {3.955169884838175*^9, + 3.955169900892893*^9}, {3.9551712636836224`*^9, 3.9551712747634583`*^9}, { + 3.9551714818336887`*^9, 3.9551715032236137`*^9}, {3.9551715785834274`*^9, + 3.955171787968336*^9}, {3.9551718215979214`*^9, 3.955171921880068*^9}, { + 3.955171980553753*^9, 3.95517204996364*^9}, {3.9551721380934505`*^9, + 3.955172210473549*^9}, {3.955172312600815*^9, 3.95517231343186*^9}, { + 3.955172798924677*^9, 3.9551728555947685`*^9}}, + CellID->359104851,ExpressionUUID->"353ad895-6faf-2643-85a6-a8331bb20202"] +}, Open ]] +}, Open 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b/Paclet/Documentation/English/ReferencePages/Symbols/NonReciprocalAbelianBlochHamiltonianExpression.nb index 700004d..967b4da 100644 --- a/Paclet/Documentation/English/ReferencePages/Symbols/NonReciprocalAbelianBlochHamiltonianExpression.nb +++ b/Paclet/Documentation/English/ReferencePages/Symbols/NonReciprocalAbelianBlochHamiltonianExpression.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 89178, 2322] -NotebookOptionsPosition[ 78212, 2085] -NotebookOutlinePosition[ 78992, 2110] -CellTagsIndexPosition[ 78912, 2105] +NotebookDataLength[ 103841, 2636] +NotebookOptionsPosition[ 91801, 2377] +NotebookOutlinePosition[ 92579, 2402] +CellTagsIndexPosition[ 92499, 2397] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -21,7 +21,7 @@ Notebook[{ Cell[CellGroupData[{ Cell["NonReciprocalAbelianBlochHamiltonianExpression", "ObjectName", - CellChangeTimes->{{3.9345316829462395`*^9, 3.9345316910471287`*^9}}, + 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The location of the matrix entries, \ +signifying which orbitals are couped, are not to be adjusted." +}], "ExampleText", + CellChangeTimes->{{3.906027105777158*^9, 3.906027175428211*^9}, { + 3.9060285881964235`*^9, 3.90602860227144*^9}, {3.9060288129869814`*^9, + 3.906028831115154*^9}, {3.906028997135098*^9, 3.906029000923377*^9}, + 3.9345103390559063`*^9, {3.937421005016327*^9, 3.9374210159177094`*^9}, { + 3.9551673567773075`*^9, 3.955167361081892*^9}, {3.955169884838175*^9, + 3.955169900892893*^9}, {3.9551712636836224`*^9, 3.9551712747634583`*^9}, { + 3.9551714818336887`*^9, 3.9551715032236137`*^9}, {3.9551715785834274`*^9, + 3.955171787968336*^9}, {3.9551718215979214`*^9, 3.955171921880068*^9}, { + 3.955171980553753*^9, 3.95517204996364*^9}, {3.9551721380934505`*^9, + 3.955172210473549*^9}, {3.955172312600815*^9, 3.95517231343186*^9}, { + 3.955172798924677*^9, 3.9551728555947685`*^9}}, + CellID->359104851,ExpressionUUID->"5e0470fd-1dee-c445-84c1-352ca10dd65d"] +}, Open ]] +}, Open 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CellChangeTimes->{{3.9060313294514136`*^9, 3.906031330419829*^9}, { + 3.9374005375764217`*^9, 3.937400540021569*^9}},ExpressionUUID-> + "fa407eb2-e3fb-834d-b730-075cf680ad3f"]], "ExampleSubsection", + ExpressionUUID->"f6a17426-13e8-0d4e-ae7a-af443e905c25"], + $Line = 0; Null]], "ExampleSubsection", + CellChangeTimes->{{3.9060313294514136`*^9, 3.906031330419829*^9}, { + 3.937405053908352*^9, 3.937405065322071*^9}, {3.9551680429373455`*^9, + 3.95516805009239*^9}}, + CellID->296669070,ExpressionUUID->"998b3398-46d9-a441-93a4-7718f68d2e53"], + +Cell[TextData[{ + "Non-reciprocal tight-binding Hamiltonians are generalizations of \ +tight-binding Hamiltonians, which can be constructed with the function ", + Cell[BoxData[ + ButtonBox["TBHamiltonian", + BaseStyle->"Link", + ButtonData->"paclet:PatrickMLenggenhager/HyperBloch/ref/TBHamiltonian"]], + "InlineFormula",ExpressionUUID->"62876ae4-7e52-2d42-bf86-3739faa21ea6"], + ". As such, the onsite potential and the hopping amplitudes are specified \ +analogously. Crucially, the following convention is imposed:" +}], "ExampleText", + CellChangeTimes->{{3.906027105777158*^9, 3.906027175428211*^9}, { + 3.9060285881964235`*^9, 3.90602860227144*^9}, {3.9060288129869814`*^9, + 3.906028831115154*^9}, {3.906028997135098*^9, 3.906029000923377*^9}, + 3.9345103390559063`*^9, {3.937421005016327*^9, 3.9374210159177094`*^9}, { + 3.955167356777308*^9, 3.955167361081892*^9}, {3.955168934862646*^9, + 3.955168998679025*^9}, {3.9551691386825943`*^9, 3.955169194672315*^9}, { + 3.955169256152302*^9, 3.955169493182674*^9}, {3.955169586572748*^9, + 3.955169712677645*^9}, {3.955169791552847*^9, 3.9551697986726894`*^9}, { + 3.955169850973112*^9, 3.9551698519929743`*^9}, {3.955169927112825*^9, + 3.955170211827799*^9}, {3.955170242038122*^9, 3.955170255833084*^9}, { + 3.955170301413376*^9, 3.955170391316994*^9}, {3.955170445563442*^9, + 3.9551705987731857`*^9}, {3.955176636663025*^9, 3.955176641047663*^9}, { + 3.9551768148026085`*^9, 3.9551768275227795`*^9}, {3.955176863612985*^9, + 3.955176863612985*^9}, {3.9551786603626556`*^9, 3.9551787363078537`*^9}}, + CellID->105689035,ExpressionUUID->"7fae03ca-b5ec-1445-82d3-872a8360a200"], + +Cell[TextData[{ + "To specify the hopping matrix for the hopping amplitudes ", + Cell[BoxData[ + StyleBox["hoppingsOpposite", "TI"]], "InlineFormula",ExpressionUUID-> + "d620aeb9-e007-6740-8547-245f6bb362a6"], + " appropriately, the positions of the matrix entries for each pair of \ +orbitals is inherited from the hopping matrix ", + Cell[BoxData[ + StyleBox["hoppingsCanonical", "TI"]], "InlineFormula",ExpressionUUID-> + "3e355822-8ee9-f54c-98e7-6530749b9e2b"], + ". 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CellID->709734105,ExpressionUUID->"f0c703c0-675d-604c-b432-3e835efa8bb9"], + +Cell[TextData[{ + "For example, the non-reciprocal Abelian Bloch Hamiltonian of a hopping \ +model defined on an ", + Cell[BoxData[ + ButtonBox["HCModelGraph", + BaseStyle->"Link", + ButtonData->"paclet:PatrickMLenggenhager/HyperBloch/ref/HCModelGraph"]], + "InlineFormula",ExpressionUUID->"dce7542b-9b3a-de46-920c-19d9a2c1cc9e"], + " (here the primitive cell of the {8,8} tessellation) with hopping \ +amplitudes ", + Cell[BoxData[ + StyleBox["hoppingsCanonical", "TI"]], "InlineFormula",ExpressionUUID-> + "bcc92f37-c462-4b47-bf90-40deea9f78ca"], + " in the canonical directions and ", + Cell[BoxData[ + StyleBox["hoppingsOpposite", "TI"]], "InlineFormula",ExpressionUUID-> + "cd32a374-d5b7-f04b-a01b-bacdbd048c9f"], + " in the opposite directions and two orbitals per site, using symbolic \ +arguments, is:" +}], "ExampleText", + CellChangeTimes->{{3.906027105777158*^9, 3.906027175428211*^9}, { + 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terms of the orbitals to zero, the \ +intra-site coupling to -t1 in the canonical direction and t1 in the opposite \ +direction and the inter-site coupling to -t2 in the canonical direction and \ +t2 in the opposite direction.\ +\>", "ExampleText", + CellChangeTimes->{{3.906027105777158*^9, 3.906027175428211*^9}, { + 3.9060285881964235`*^9, 3.90602860227144*^9}, {3.9060288129869814`*^9, + 3.906028831115154*^9}, {3.906028997135098*^9, 3.906029000923377*^9}, + 3.9345103390559063`*^9, {3.937421005016327*^9, 3.9374210159177094`*^9}, { + 3.9551673567773075`*^9, 3.955167361081892*^9}, {3.955169884838175*^9, + 3.955169900892893*^9}, {3.9551712636836224`*^9, 3.9551712747634583`*^9}, { + 3.9551714818336887`*^9, 3.9551715032236137`*^9}, {3.955172112773716*^9, + 3.955172113753664*^9}, {3.955172958744713*^9, 3.9551729998145275`*^9}, { + 3.9551738888346024`*^9, 3.955174072975092*^9}, {3.955178351427471*^9, + 3.955178362197628*^9}}, + CellID->135010306,ExpressionUUID->"b900a028-a822-464c-b723-e8bfc1d1476e"], + +Cell[TextData[{ + "Note, for the specification of the hopping matrix ", + Cell[BoxData[ + StyleBox["hoppingsOpposite", "TI"]], "InlineFormula",ExpressionUUID-> + "0529fa61-edcd-4442-bb4b-dd3e7bc86909"], + " it is instructive to think of constructing an Abelian Bloch Hamiltonian \ +with adjusted hopping amplitudes. 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a/Paclet/Documentation/English/ReferencePages/Symbols/NonReciprocalTBHamiltonian.nb b/Paclet/Documentation/English/ReferencePages/Symbols/NonReciprocalTBHamiltonian.nb index f917bb4..75f283b 100644 --- a/Paclet/Documentation/English/ReferencePages/Symbols/NonReciprocalTBHamiltonian.nb +++ b/Paclet/Documentation/English/ReferencePages/Symbols/NonReciprocalTBHamiltonian.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 162862, 3854] -NotebookOptionsPosition[ 145528, 3495] -NotebookOutlinePosition[ 146307, 3520] -CellTagsIndexPosition[ 146226, 3515] +NotebookDataLength[ 185448, 4359] +NotebookOptionsPosition[ 166268, 3968] +NotebookOutlinePosition[ 167053, 3993] +CellTagsIndexPosition[ 166972, 3988] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -305,6 +305,109 @@ edge or a number if ", 3.93765740170562*^9, 3.937657430205425*^9}}, CellID->122405462,ExpressionUUID->"916d2e20-f426-4271-9d7c-a98609af83a2"], +Cell[TextData[{ + "For multi-orbital models with ", + Cell[BoxData[ + StyleBox["norb", "TI"]], "InlineFormula",ExpressionUUID-> + "213aa462-443a-5947-b599-20d5c8d9ade2"], + "\[NotEqual]", + StyleBox["1", "InlineCode"], + ", the specification of the hopping matrix for the hopping amplitudes ", + Cell[BoxData[ + StyleBox["hoppingsOpposite", "TI"]], "InlineFormula",ExpressionUUID-> + "e1146ad2-589b-b54f-9880-e912d3a711af"], + " need to follow the same assignment conventions as the hopping amplitudes \ +", + Cell[BoxData[ + StyleBox["hoppingsCanonical", "TI"]], "InlineFormula",ExpressionUUID-> + "34a82d16-daa7-9d4d-9517-77c7d6e13191"], + ". In order to illustrate the used convention it is instructive to consider \ +a general two-orbital ", + StyleBox["{p,q}", "InlineCode"], + "-lattice model with nearest-neighbor interactions on an arbitrary unit cell \ +with two sites specified on a finite flake. Consider the two sites ", + StyleBox["i", "InlineCode"], + " and ", + StyleBox["j", "InlineCode"], + " in a unit cell, each equipped with two orbitals ", + StyleBox["a", "InlineCode"], + " and ", + StyleBox["b", "InlineCode"], + ". Further, let a hopping in the canonical direction be defined as ", + StyleBox["i", "InlineCode"], + " \[Rule] ", + StyleBox["j,", "InlineCode"], + " and ", + StyleBox["j", "InlineCode"], + " \[Rule] ", + StyleBox["i", "InlineCode"], + " in the opposite direction. The following hopping matrices need to be \ +specified, where each matrix entry specifies the corresponding hopping \ +amplitudes between corresponding pairs of orbitals:" +}], "Notes", + CellChangeTimes->{{3.959416241755583*^9, 3.959416242459528*^9}, { + 3.9594167264317684`*^9, 3.959416768108032*^9}, {3.959417246453047*^9, + 3.9594172834939194`*^9}, 3.9594174076191235`*^9, {3.9594180058355064`*^9, + 3.9594180491644745`*^9}, {3.9594184160936623`*^9, 3.959418652769972*^9}, { + 3.9594186847437496`*^9, 3.9594187085016575`*^9}, {3.9594187469976215`*^9, + 3.959418815211241*^9}, {3.959419067188925*^9, 3.959419090362995*^9}, { + 3.9594205426341953`*^9, 3.9594205767974167`*^9}, {3.9594238782360744`*^9, + 3.9594239039424057`*^9}}, + CellID->311370265,ExpressionUUID->"9e832cf1-cb3b-944b-87d7-d59ba8c6c42e"], + +Cell[BoxData[ + RowBox[{ + RowBox[{ + RowBox[{"hoppingsCanonical", "=", + RowBox[{ + RowBox[{"(", GridBox[{ + { + RowBox[{ + SubscriptBox["a", "i"], "\[Rule]", + SubscriptBox["a", "j"]}], + RowBox[{ + SubscriptBox["a", "i"], "\[Rule]", + SubscriptBox["b", "j"]}]}, + { + RowBox[{ + SubscriptBox["b", "i"], "\[Rule]", + SubscriptBox["b", "j"]}], + RowBox[{ + SubscriptBox["b", "i"], "\[Rule]", + SubscriptBox["b", "j"]}]} + }], ")"}], "&"}]}], ";"}], " "}]], "Notes", + CellChangeTimes->{{3.9594190921442356`*^9, 3.9594191869209785`*^9}, { + 3.9594199305607395`*^9, 3.959419942131056*^9}, 3.9594199844307747`*^9, { + 3.959420111086876*^9, 3.9594201114812164`*^9}, 3.959420152732893*^9}, + CellID->207376718,ExpressionUUID->"9d096777-ed38-fa42-a3f0-204ba6b6a912"], + +Cell[TextData[Cell[BoxData[ + RowBox[{ + RowBox[{"hoppingsOpposite", "=", + RowBox[{ + RowBox[{"(", GridBox[{ + { + RowBox[{ + SubscriptBox["a", "i"], "\[LeftArrow]", + SubscriptBox["a", "j"]}], + RowBox[{ + SubscriptBox["a", "i"], "\[LeftArrow]", + SubscriptBox["b", "j"]}]}, + { + RowBox[{ + SubscriptBox["b", "i"], "\[LeftArrow]", + SubscriptBox["b", "j"]}], + RowBox[{ + SubscriptBox["b", "i"], "\[LeftArrow]", + SubscriptBox["b", "j"]}]} + }], ")"}], "&"}]}], ";"}]], + CellChangeTimes->{{3.9594190921442356`*^9, 3.9594191869209785`*^9}, { + 3.9594199305607395`*^9, + 3.959419942131056*^9}},ExpressionUUID->"6a2b9153-008e-0c44-bc72-\ +a9eec9fdfb31"]], "Notes", + CellChangeTimes->{{3.959420522251034*^9, 3.9594205393492985`*^9}}, + CellID->396819643,ExpressionUUID->"ad6e1f75-94fc-a24f-8210-98a92e4ba89d"], + Cell[TextData[{ "The number of orbitals is specified by ", Cell[BoxData[ @@ -474,6 +577,130 @@ edge or a number if ", 3.937649883978386*^9}}, CellID->978527526,ExpressionUUID->"befd335a-f1a3-a742-adb8-bd6148e17917"], +Cell[TextData[{ + "For multi-orbital models with ", + Cell[BoxData[ + StyleBox["norb", "TI"]], "InlineFormula",ExpressionUUID-> + "b470e289-fa16-4a40-9a15-94316920b6bb"], + "\[NotEqual]", + StyleBox["1", "InlineCode"], + ", the specification of the hopping matrix for the hopping amplitudes ", + Cell[BoxData[ + StyleBox["hoppingsOppositePC", "TI"]], "InlineFormula",ExpressionUUID-> + "a266a95f-4ba8-4a4c-a3bb-2a9d821ddcee"], + " need to follow the same assignment conventions as the hopping amplitudes \ +", + Cell[BoxData[ + StyleBox["hoppingsCanonicalPC", "TI"]], "InlineFormula",ExpressionUUID-> + "88b9d73c-ea06-f84a-91f5-e47814cebca1"], + ". In order to illustrate the used convention it is instructive to consider \ +a general two-orbital ", + StyleBox["{p,q}", "InlineCode"], + "-lattice model with nearest-neighbor interactions on an arbitrary unit cell \ +with two sites specified on a finite flake with a disclination defect . \ +Consider the two sites ", + StyleBox["i", "InlineCode"], + " and ", + StyleBox["j", "InlineCode"], + " in a unit cell, each equipped with two orbitals ", + StyleBox["a", "InlineCode"], + " and ", + StyleBox["b", "InlineCode"], + ". Further, let a hopping in the canonical direction be defined as ", + StyleBox["i", "InlineCode"], + " \[Rule] ", + StyleBox["j,", "InlineCode"], + " and ", + StyleBox["j", "InlineCode"], + " \[Rule] ", + StyleBox["i", "InlineCode"], + " in the opposite direction. The following hopping matrices need to be \ +specified, where each matrix entry specifies the corresponding hopping \ +amplitudes between corresponding pairs of orbitals:" +}], "Notes", + CellChangeTimes->{{3.959416241755583*^9, 3.959416242459528*^9}, { + 3.9594167264317684`*^9, 3.959416768108032*^9}, {3.959417246453047*^9, + 3.9594172834939194`*^9}, 3.9594174076191235`*^9, {3.9594180058355064`*^9, + 3.9594180491644745`*^9}, {3.9594184160936623`*^9, 3.959418652769972*^9}, { + 3.9594186847437496`*^9, 3.9594187085016575`*^9}, {3.9594187469976215`*^9, + 3.959418815211241*^9}, {3.959419067188925*^9, 3.959419090362995*^9}, { + 3.9594205426341953`*^9, 3.9594205767974167`*^9}, {3.9594209013972054`*^9, + 3.959420903402071*^9}, {3.9594226849460506`*^9, 3.9594227710742455`*^9}, + 3.959422825591652*^9, {3.9594238517981815`*^9, 3.959423864861786*^9}, { + 3.9594239176290054`*^9, 3.959423937512869*^9}}, + CellID->49378578,ExpressionUUID->"14065189-ed9c-344a-85a6-123ab8a4107c"], + +Cell[BoxData[ + RowBox[{ + RowBox[{ + RowBox[{"hoppingsCanonicalPC", "=", + RowBox[{ + RowBox[{"(", GridBox[{ + { + RowBox[{ + SubscriptBox["a", "i"], "\[Rule]", + SubscriptBox["a", "j"]}], + RowBox[{ + SubscriptBox["a", "i"], "\[Rule]", + SubscriptBox["b", "j"]}]}, + { + RowBox[{ + SubscriptBox["b", "i"], "\[Rule]", + SubscriptBox["b", "j"]}], + RowBox[{ + SubscriptBox["b", "i"], "\[Rule]", + SubscriptBox["b", "j"]}]} + }], ")"}], "&"}]}], ";"}], " "}]], "Notes", + CellChangeTimes->{{3.9594190921442356`*^9, 3.9594191869209785`*^9}, { + 3.9594199305607395`*^9, 3.959419942131056*^9}, 3.9594199844307747`*^9, { + 3.959420111086876*^9, 3.9594201114812164`*^9}, 3.959420152732893*^9, { + 3.9594227010783463`*^9, 3.959422701282736*^9}}, + CellID->367081081,ExpressionUUID->"c8bb76f0-24c8-404a-81f9-e75585047e2e"], + +Cell[TextData[Cell[BoxData[ + RowBox[{ + RowBox[{"hoppingsOppositePC", "=", + RowBox[{ + RowBox[{"(", GridBox[{ + { + RowBox[{ + SubscriptBox["a", "i"], "\[LeftArrow]", + SubscriptBox["a", "j"]}], + RowBox[{ + SubscriptBox["a", "i"], "\[LeftArrow]", + SubscriptBox["b", "j"]}]}, + { + RowBox[{ + SubscriptBox["b", "i"], "\[LeftArrow]", + SubscriptBox["b", "j"]}], + RowBox[{ + SubscriptBox["b", "i"], "\[LeftArrow]", + SubscriptBox["b", "j"]}]} + }], ")"}], "&"}]}], ";"}]], + CellChangeTimes->{{3.9594190921442356`*^9, 3.9594191869209785`*^9}, { + 3.9594199305607395`*^9, + 3.959419942131056*^9}},ExpressionUUID->"51d8c5b4-430c-7c43-bcd8-\ +672281462a54"]], "Notes", + CellChangeTimes->{{3.959420522251034*^9, 3.9594205393492985`*^9}, { + 3.9594227034669304`*^9, 3.959422703616144*^9}}, + CellID->285432429,ExpressionUUID->"8d2c174b-0d89-2f4d-93e6-d4ab5843940d"], + +Cell[TextData[{ + "Analogously, the specification of the hopping matrix for the hopping \ +amplitudes ", + Cell[BoxData[ + StyleBox["hoppingsOppositeGluedEdges", "TI"]], "InlineFormula", + ExpressionUUID->"12d4fa68-7c28-0f4d-8ff1-b13b09c92bc9"], + " need to follow the same assignment conventions as the hopping amplitudes \ +", + Cell[BoxData[ + StyleBox["hoppingsCanonicalGluedEdges", "TI"]], "InlineFormula", + ExpressionUUID->"e4c82509-1a14-2d40-b022-d7d1d127ded1"], + ". 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Crucially, the following convention is imposed:" 3.955170301413376*^9, 3.955170391316994*^9}, {3.955170445563442*^9, 3.9551705987731857`*^9}, {3.955176636663025*^9, 3.955176641047663*^9}, { 3.9551768148026085`*^9, 3.9551768275227795`*^9}, {3.955176863612985*^9, - 3.955176863612985*^9}, {3.9551786603626556`*^9, 3.9551787363078537`*^9}}, + 3.955176863612985*^9}, {3.9551786603626556`*^9, 3.9551787363078537`*^9}, { + 3.959424368784218*^9, 3.959424372728924*^9}}, CellID->105689035,ExpressionUUID->"7fae03ca-b5ec-1445-82d3-872a8360a200"], Cell[TextData[{ @@ -3259,7 +3487,7 @@ model defined on an ", BaseStyle->"Link", ButtonData->"paclet:PatrickMLenggenhager/HyperBloch/ref/HCModelGraph"]], "InlineFormula",ExpressionUUID->"dce7542b-9b3a-de46-920c-19d9a2c1cc9e"], - " (here the primitive cell of the {8,8} tessellation) with hopping \ + " (here the primitive cell of the {8,3} tessellation) with hopping \ amplitudes ", Cell[BoxData[ StyleBox["hoppingsCanonical", "TI"]], "InlineFormula",ExpressionUUID-> @@ -3278,7 +3506,7 @@ arguments, is:" 3.9551673567773075`*^9, 3.955167361081892*^9}, {3.955169884838175*^9, 3.955169900892893*^9}, {3.9551712636836224`*^9, 3.9551712747634583`*^9}, { 3.9551714818336887`*^9, 3.9551715032236137`*^9}, {3.955172112773716*^9, - 3.955172113753664*^9}}, + 3.955172113753664*^9}, {3.9594266415751133`*^9, 3.959426641738249*^9}}, CellID->105347582,ExpressionUUID->"e1347469-3698-e04d-b3cd-80a0661f52d5"], Cell[BoxData[{ @@ -3362,7 +3590,7 @@ Cell[TextData[{ Cell[BoxData[ StyleBox["hoppingsOpposite", "TI"]], "InlineFormula",ExpressionUUID-> "0529fa61-edcd-4442-bb4b-dd3e7bc86909"], - " it is instructive to think of constructing an Abelian Bloch Hamiltonian \ + " it is instructive to think of constructing a tight-binding Hamiltonian \ with adjusted hopping amplitudes. The location of the matrix entries, \ signifying which orbitals are couped, are not to be adjusted." }], "ExampleText", @@ -3376,8 +3604,253 @@ signifying which orbitals are couped, are not to be adjusted." 3.955171787968336*^9}, {3.9551718215979214`*^9, 3.955171921880068*^9}, { 3.955171980553753*^9, 3.95517204996364*^9}, {3.9551721380934505`*^9, 3.955172210473549*^9}, {3.955172312600815*^9, 3.95517231343186*^9}, { - 3.955172798924677*^9, 3.9551728555947685`*^9}}, - CellID->359104851,ExpressionUUID->"e541d214-04a7-bb47-af31-cfed6716a9fe"] + 3.955172798924677*^9, 3.9551728555947685`*^9}, {3.959427046547167*^9, + 3.959427052733345*^9}}, + CellID->359104851,ExpressionUUID->"e541d214-04a7-bb47-af31-cfed6716a9fe"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell[ + "\t", "ExampleDelimiter",ExpressionUUID-> + "a9fd649d-8453-8548-b449-cf1ed38bc9a1"], + $Line = 0; Null]], "ExampleDelimiter", + CellID->41691713,ExpressionUUID->"90e3572b-3bc2-954e-acdf-2c2209c4376d"], + +Cell[TextData[{ + "Analogously, for disclination (supercell) model graphs the non-reciprocal \ +tight-binding Hamiltonians are generalizations of tight-binding Hamiltonians, \ +the latter can be constructed with the function ", + Cell[BoxData[ + ButtonBox["TBHamiltonian", + BaseStyle->"Link", + ButtonData->"paclet:PatrickMLenggenhager/HyperBloch/ref/TBHamiltonian"]], + "InlineFormula",ExpressionUUID->"9bf61ad6-ad50-5944-bcca-17da799ae99c"], + ". As such, the onsite potential and the hopping amplitudes are specified \ +analogously. Crucially, the following convention is imposed:" +}], "ExampleText", + CellChangeTimes->{{3.906027105777158*^9, 3.906027175428211*^9}, { + 3.9060285881964235`*^9, 3.90602860227144*^9}, {3.9060288129869814`*^9, + 3.906028831115154*^9}, {3.906028997135098*^9, 3.906029000923377*^9}, + 3.9345103390559063`*^9, {3.937421005016327*^9, 3.9374210159177094`*^9}, { + 3.955167356777308*^9, 3.955167361081892*^9}, {3.955168934862646*^9, + 3.955168998679025*^9}, {3.9551691386825943`*^9, 3.955169194672315*^9}, { + 3.955169256152302*^9, 3.955169493182674*^9}, {3.955169586572748*^9, + 3.955169712677645*^9}, {3.955169791552847*^9, 3.9551697986726894`*^9}, { + 3.955169850973112*^9, 3.9551698519929743`*^9}, {3.955169927112825*^9, + 3.955170211827799*^9}, {3.955170242038122*^9, 3.955170255833084*^9}, { + 3.955170301413376*^9, 3.955170391316994*^9}, {3.955170445563442*^9, + 3.9551705987731857`*^9}, {3.955176636663025*^9, 3.955176641047663*^9}, { + 3.9551768148026085`*^9, 3.9551768275227795`*^9}, {3.955176863612985*^9, + 3.955176863612985*^9}, {3.9551786603626556`*^9, 3.9551787363078537`*^9}, { + 3.959424377039385*^9, 3.9594243848944225`*^9}, {3.959426485016968*^9, + 3.9594265234404755`*^9}, {3.9594267259613895`*^9, + 3.9594267550906963`*^9}, {3.959426819278822*^9, 3.9594268987840557`*^9}}, + CellID->626781485,ExpressionUUID->"7879bff2-3886-2a43-9c05-3019887669c4"], + +Cell[TextData[{ + "To specify the hopping matrix for the hopping amplitudes ", + Cell[BoxData[ + StyleBox["hoppingsOppositePC", "TI"]], "InlineFormula",ExpressionUUID-> + "d13d3e1b-e33b-de45-afd6-3421b263fb04"], + " and ", + Cell[BoxData[ + StyleBox["hoppingsOppositeGluedEdges", "TI"]], "InlineFormula", + ExpressionUUID->"c9c2a46c-7fbc-814a-9b2a-26febbd3517b"], + " appropriately, the positions of the matrix entries for each pair of \ +orbitals is inherited from the hopping matrix ", + Cell[BoxData[ + StyleBox["hoppingsCanonicalPC", "TI"]], "InlineFormula",ExpressionUUID-> + "29a80d30-2910-1a47-b76c-7b96e4e3d09d"], + " and ", + Cell[BoxData[ + StyleBox["hoppingsCanonicalGluedEdges", "TI"]], "InlineFormula", + ExpressionUUID->"7e327143-01ee-f541-9dec-a16d889cc8e9"], + ", respectively. 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we have set the mass terms of the orbitals to zero, the \ +intra-site coupling to -t1 in the canonical direction and t1 in the opposite \ +direction and the inter-site coupling to -t2 in the canonical direction and \ +t2 in the opposite direction.\ +\>", "ExampleText", + CellChangeTimes->{{3.906027105777158*^9, 3.906027175428211*^9}, { + 3.9060285881964235`*^9, 3.90602860227144*^9}, {3.9060288129869814`*^9, + 3.906028831115154*^9}, {3.906028997135098*^9, 3.906029000923377*^9}, + 3.9345103390559063`*^9, {3.937421005016327*^9, 3.9374210159177094`*^9}, { + 3.9551673567773075`*^9, 3.955167361081892*^9}, {3.955169884838175*^9, + 3.955169900892893*^9}, {3.9551712636836224`*^9, 3.9551712747634583`*^9}, { + 3.9551714818336887`*^9, 3.9551715032236137`*^9}, {3.955172112773716*^9, + 3.955172113753664*^9}, {3.955172958744713*^9, 3.9551729998145275`*^9}, { + 3.9551738888346024`*^9, 3.955174072975092*^9}, {3.955178351427471*^9, + 3.955178362197628*^9}}, + 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The location of the matrix entries, \ +signifying which orbitals are couped, are not to be adjusted." +}], "ExampleText", + CellChangeTimes->{{3.906027105777158*^9, 3.906027175428211*^9}, { + 3.9060285881964235`*^9, 3.90602860227144*^9}, {3.9060288129869814`*^9, + 3.906028831115154*^9}, {3.906028997135098*^9, 3.906029000923377*^9}, + 3.9345103390559063`*^9, {3.937421005016327*^9, 3.9374210159177094`*^9}, { + 3.9551673567773075`*^9, 3.955167361081892*^9}, {3.955169884838175*^9, + 3.955169900892893*^9}, {3.9551712636836224`*^9, 3.9551712747634583`*^9}, { + 3.9551714818336887`*^9, 3.9551715032236137`*^9}, {3.9551715785834274`*^9, + 3.955171787968336*^9}, {3.9551718215979214`*^9, 3.955171921880068*^9}, { + 3.955171980553753*^9, 3.95517204996364*^9}, {3.9551721380934505`*^9, + 3.955172210473549*^9}, {3.955172312600815*^9, 3.95517231343186*^9}, { + 3.955172798924677*^9, 3.9551728555947685`*^9}, 3.959427031232956*^9, { + 3.959427063103359*^9, 3.9594270660505753`*^9}}, + 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f193d8c..2ec608c 100644 --- a/Paclet/Documentation/English/ReferencePages/Symbols/NonReciprocalAbelianBlochHamiltonian.nb +++ b/Paclet/Documentation/English/ReferencePages/Symbols/NonReciprocalAbelianBlochHamiltonian.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 144163, 3477] -NotebookOptionsPosition[ 129055, 3155] -NotebookOutlinePosition[ 129862, 3181] -CellTagsIndexPosition[ 129781, 3176] +NotebookDataLength[ 144269, 3479] +NotebookOptionsPosition[ 129160, 3157] +NotebookOutlinePosition[ 129967, 3183] +CellTagsIndexPosition[ 129886, 3178] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -283,14 +283,15 @@ Cell[BoxData[ { RowBox[{ SubscriptBox["b", "i"], "\[Rule]", - SubscriptBox["b", "j"]}], + SubscriptBox["a", "j"]}], RowBox[{ SubscriptBox["b", "i"], "\[Rule]", SubscriptBox["b", "j"]}]} }], ")"}], "&"}]}], ";"}], " "}]], "Notes", CellChangeTimes->{{3.9594190921442356`*^9, 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b/Paclet/Documentation/English/ReferencePages/Symbols/NonReciprocalAbelianBlochHamiltonianExpression.nb index d4227f1..84255bf 100644 --- a/Paclet/Documentation/English/ReferencePages/Symbols/NonReciprocalAbelianBlochHamiltonianExpression.nb +++ b/Paclet/Documentation/English/ReferencePages/Symbols/NonReciprocalAbelianBlochHamiltonianExpression.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 108105, 2744] -NotebookOptionsPosition[ 95707, 2479] -NotebookOutlinePosition[ 96491, 2504] -CellTagsIndexPosition[ 96411, 2499] +NotebookDataLength[ 108208, 2746] +NotebookOptionsPosition[ 95810, 2481] +NotebookOutlinePosition[ 96594, 2506] +CellTagsIndexPosition[ 96514, 2501] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -280,14 +280,15 @@ Cell[BoxData[ { RowBox[{ SubscriptBox["b", "i"], "\[Rule]", - SubscriptBox["b", "j"]}], + SubscriptBox["a", "j"]}], RowBox[{ SubscriptBox["b", "i"], "\[Rule]", SubscriptBox["b", "j"]}]} }], ")"}], "&"}]}], ";"}], " "}]], "Notes", CellChangeTimes->{{3.9594190921442356`*^9, 3.9594191869209785`*^9}, { 3.9594199305607395`*^9, 3.959419942131056*^9}, 3.9594199844307747`*^9, { - 3.959420111086876*^9, 3.9594201114812164`*^9}, 3.959420152732893*^9}, + 3.959420111086876*^9, 3.9594201114812164`*^9}, 3.959420152732893*^9, { + 3.9596605259443874`*^9, 3.959660526363762*^9}}, CellID->207376718,ExpressionUUID->"1671ed16-39a8-f84a-a5e7-5d09eddfa739"], Cell[TextData[Cell[BoxData[ @@ -305,7 +306,7 @@ Cell[TextData[Cell[BoxData[ { RowBox[{ SubscriptBox["b", "i"], "\[LeftArrow]", - SubscriptBox["b", "j"]}], + SubscriptBox["a", "j"]}], RowBox[{ SubscriptBox["b", "i"], "\[LeftArrow]", SubscriptBox["b", "j"]}]} @@ -314,7 +315,8 @@ Cell[TextData[Cell[BoxData[ 3.9594199305607395`*^9, 3.959419942131056*^9}},ExpressionUUID->"8ff0a281-19c1-f348-9852-\ 6195910c8754"]], "Notes", - CellChangeTimes->{{3.959420522251034*^9, 3.9594205393492985`*^9}}, + 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