Constraints of kinematic bosonization in two and higher dimensions

Bochniak, Arkadiusz; Ruba, Błażej; Wosiek, J.; Wyrzykowski, Adam

doi:10.1103/physrevd.102.114502

Cited by 14 publications

(26 citation statements)

References 28 publications

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“…This correspondence was then made more precise in [36]. Generalization and new proofs were given in [5,37]. Constraints present in the Γ model were interpreted as the pure gauge condition for a certain Z 2 gauge field.…”

Section: Introductionmentioning

confidence: 99%

“…The fermionization method analogous to the one in [50] was also proposed, at the same time, in [51] and [52]. In the former case the periodic boundary conditions were assumed, so that the role of the analogues of Polyakov lines discussed also in details in [37] began to be important. The role of constraints was discussed, together with the flux-attachment mechanism [53] and the interpretation of modifying the constraints as a coupling to some external Z 2 fields.…”

Section: Introductionmentioning

confidence: 99%

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Bosonization of Majorana modes and edge states

Bochniak,

Ruba,

Wosiek

2021

Preprint

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We present a bosonization procedure which replaces fermions with generalized spin variables subject to local constraints. It requires that the number of Majorana modes per lattice site matches the coordination number modulo two. If this condition is not obeyed, then bosonization introduces additional fermionic excitations not present in the original model. In the case of one Majorana mode per site on a honeycomb lattice, we recover a sector of Kitaev's model. We discuss also decagonal and rectangular geometries and present bosonization of the Hubbard model. For geometries with a boundary we find that certain fermionic edge modes naturally emerge. They are of different nature than edge modes encountered in topological phases of matter. Euclidean representation for the unconstrained version of a spin system of the type arising in our construction is derived and briefly studied by computing some exact averages for small volumes.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bosonization of Majorana modes and edge states

Bochniak,

Ruba,

Wosiek

2021

Preprint

Self Cite

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“…Generally speaking, the fermionic statistics is implemented on the bosonic side using non-local string operators, as is well-known in the classic Jordan-Wigner transformation for onedimensional systems [1]. Generalization of the transformation to higher dimensions using lattice gauge fields have also been proposed [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Such exact bosonization mappings are also important form the quantum simulation perspective, for they address the possibility of simulating a quantum many-body fermionic systems using a bosonic quantum computer [21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Higher-dimensional Jordan-Wigner Transformation and Auxiliary Majorana Fermions

Li¹,

Po²

2021

Preprint

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We discuss a scheme for performing Jordan-Wigner transformation for various lattice fermion systems in two and three dimensions which keeps internal and spatial symmetries manifest. The correspondence between fermionic and bosonic operators is established with the help of auxiliary Majorana fermions. The current construction is applicable to general lattices with even coordination number and an arbitrary number of fermion flavors. The approach is demonstrated on the singleorbital square, triangular and cubic lattices for spin-1/2 fermions. We also discuss the relation to some quantum spin liquid models.

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“…Nevertheless, the possibility of performing a similar transformation in higher than one dimension has fascinated generations of physicists. Indeed, much has been explored from both a field-theory [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and a lattice perspective [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. The intriguing phenomenology of hightemperature superconductors [38] and heavy fermion compounds [39] have also led to the introduction of the slave particle formalism, in which the fermionic electron could be fractionalized into partons with different particle statistics [40][41][42][43][44][45][46][47][48].…”

mentioning

confidence: 99%

Symmetric Jordan-Wigner transformation in higher dimensions

2021

Preprint

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The Jordan-Wigner transformation is traditionally applied to one dimensional systems, but recent works have generalized the transformation to fermionic lattice systems in higher dimensions while keeping locality manifest. These developments could aid the theoretical or even experimental studies of strongly correlated electronic problems through their bosonic counterparts. In this work, we develop a scheme for higher-dimensional Jordan-Wigner transformation which keeps all relevant symmetries manifest on the bosonic side. Our approach connects the discussion of exact lattice bosonization to the familiar notions of fractionalized partons like spinons and chargeons, and works for spin-1/2 fermions-like the physical electrons-on four-coordinated lattices. The construction is applied to fermions defined on the square, kagome and diamond lattices, and we provide explicit expressions for the bosonized versions of well-known models of strongly correlated electrons, like the Hubbard and t-J models.

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Constraints of kinematic bosonization in two and higher dimensions

Cited by 14 publications

References 28 publications

Bosonization of Majorana modes and edge states

Bosonization of Majorana modes and edge states

Higher-dimensional Jordan-Wigner Transformation and Auxiliary Majorana Fermions

Symmetric Jordan-Wigner transformation in higher dimensions

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