Spin Structures and Exact Dualities in Low Dimensions

Radicevic, Djordje

doi:10.48550/arxiv.1809.07757

Cited by 21 publications

(24 citation statements)

References 40 publications

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“…We note that such issues have been discussed in a number of excellent references, say Ref. 13, and so we will not repeat the discussion here. As a small digression, we also sketch below how the classic transformation in 1D can also be understood in our framework.…”

Section: Appendix A: 1d Recapmentioning

confidence: 99%

“…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].…”

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confidence: 99%

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Symmetric Jordan-Wigner transformation in higher dimensions

2021

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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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Section: Appendix A: 1d Recapmentioning

confidence: 99%

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confidence: 99%

Symmetric Jordan-Wigner transformation in higher dimensions

2021

Preprint

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“…It is worth mentioning that such kind of mapping is possible in any dimension, generically requiring some factors of σ x in the definition of Z r,η on properly chosen neighboring links. The only exception is one spatial dimension, where no extra operators σ x are needed [30,32,53,54].…”

Section: The Limit H → ∞: Resonating Quantum Dimers and Clusteringmentioning

confidence: 99%

Quantum phases of two-dimensional $\mathbb{Z}_2$ gauge theory coupled to single-component fermion matter

Borla,

Jeevanesan,

Pollmann

et al. 2020

Preprint

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We investigate the rich quantum phase diagram of Wegner's theory of discrete Ising gauge fields interacting with U (1) symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits the model reduces to (i) pure Z2 even and odd gauge theories, (ii) free fermions in a static background of deconfined Z2 gauge fields, (iii) the kinetic Rokhsar-Kivelson quantum dimer model at a generic dimer filling. We develop a local transformation that maps the lattice gauge theory onto a model of Z2 gauge-invariant spin 1/2 degrees of freedom. Using the mapping, we perform numerical density matrix renormalization group calculations that corroborate our understanding of the limits identified above. Moreover, in the absence of the magnetic plaquette term, we reveal signatures of topologically ordered Dirac semimetal and staggered Mott insulator phases at half-filling. At strong coupling, the lattice gauge theory displays fracton phenomenology with isolated fermions being completely frozen and dimers exhibiting restricted mobility. In that limit, we predict that in the ground state dimers form compact clusters, whose hopping is suppressed exponentially in their size. We determine the band structure of the smallest clusters numerically using exact diagonalization.

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“…If the other isolated bosonic anyon (say e) is kept dynamically immobile, these constructions can be viewed as a form of Z 2 charge-flux attachment implementing a type of local 2D Jordan-Wigner transformation. 4,5,[8][9][10][11][12][13][14][15][16] In this case, and in contrast to the bosonic case, any local fermion Hamiltonian always respects parity. Therefore the state lacks any form of long-range parity-phase rigidity, and distant immobile anyons that are seen as a πfluxes by the fermions can be inserted with a finite energy cost.…”

Section: Introductionmentioning

confidence: 99%

Theory of weak symmetry breaking of translations in $\mathbb{Z}_2$ topologically ordered states and its relation to topological superconductivity from an exact lattice $\mathbb{Z}_2$ charge-flux attachment

Rao,

Sodemann

2020

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We study Z2 topologically ordered states enriched by translational symmetry by employing a recently developed 2D bosonization approach that implements an exact Z2 charge-flux attachment in the lattice. Such states can display 'weak symmetry breaking' of translations, in which both the Hamiltonian and ground state remain fully translational invariant but the symmetry is 'broken' by its anyon quasi-particles, in the sense that its action maps them into a different super-selection sector. We demonstrate that this phenomenon occurs when the fermionic spinons form a weak topological superconductor in the form of a 2D stack of 1D Kitaev wires, leading to the amusing property that there is no local operator that can transport the π-flux quasi-particle across a single Kitaev wire of fermonic spinons without paying an energy gap in spite of the vacuum remaining fully translational invariant. We explain why this phenomenon occurs hand-in-hand with other previously identified peculiar features such as ground state degeneracy dependence on the size of the torus and the appearance of dangling boundary Majorana modes in certain Z2 topologically ordered states. Moreover, by extending the Z2 charge-flux attachment to open lattices and cylinders, we construct a plethora of exactly solvable models providing an exact description of their dispersive Majorana gapless boundary modes. We also review the Z × (Z2) 3 classification of 2D BdG Hamiltonians (Class D) enriched by translational symmetry and provide arguments on its robust stability against interactions and self-averaging disorder that preserves translational symmetry.

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Spin Structures and Exact Dualities in Low Dimensions

Cited by 21 publications

References 40 publications

Symmetric Jordan-Wigner transformation in higher dimensions

Symmetric Jordan-Wigner transformation in higher dimensions

Quantum phases of two-dimensional $\mathbb{Z}_2$ gauge theory coupled to single-component fermion matter

Theory of weak symmetry breaking of translations in $\mathbb{Z}_2$ topologically ordered states and its relation to topological superconductivity from an exact lattice $\mathbb{Z}_2$ charge-flux attachment

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