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Berry Phases of Vison Transport in $\mathbb{Z}_2$ Topologically Ordered States from Exact Fermion-Flux Lattice Dualities
Strongly Correlated Electrons · Submitted 2 Feb 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This map allows to explicitly compute the Berry phases for the transport of fluxes in a large class of symmetry enriched topologically ordered states with emergent $\mathbb{Z}_2$ gauge fields that includes chiral, non-chiral, abelian or non-abelian, that can be perturbatively connected to models where the visons are static and the emergent fermionic spinons have a non-interacting dispersion.
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The abstract, sentence by sentence
We develop an exact map of all states and operators from 2D lattices of spins-$1/2$ into lattices of fermions and bosons with mutual semionic statistical interaction that goes beyond previous dualities of $\mathbb{Z}_2$ lattice gauge theories because it does not rely on imposing local conservation laws and captures the motion of ``charges'' and ``fluxes'' on equal footing. This map allows to explicitly compute the Berry phases for the transport of fluxes in a large class of symmetry enriched topologically ordered states with emergent $\mathbb{Z}_2$ gauge fields that includes chiral, non-chiral, abelian or non-abelian, that can be perturbatively connected to models where the visons are static and the emergent fermionic spinons have a non-interacting dispersion. The numerical complexity of computing such vison phases reduces therefore to computing overlaps of ground states of free-fermion Hamiltonians. Among other results, we establish numerically the conditions under which the Majorana-carrying flux excitation in Ising-Topologically-Ordered states enriched by translations acquires $0$ or $\pi$ phase when moving around a single plaquette.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We develop an exact map of all states and operators from 2D lattices of spins-$1/2$ into lattices of fermions and bosons with mutual semionic statistical interaction that goes beyond previous dualities of $\mathbb{Z}_2$ lattice gauge theories because it does not rely on imposing local conservation laws and captures the motion of ``charges'' and ``fluxes'' on equal footing. | contribution 0.89 | 0.95 | 0.26 | asserted 1.00 |
| s1 | This map allows to explicitly compute the Berry phases for the transport of fluxes in a large class of symmetry enriched topologically ordered states with emergent $\mathbb{Z}_2$ gauge fields that includes chiral, non-chiral, abelian or non-abelian, that can be perturbatively connected to models where the visons are static and the emergent fermionic spinons have a non-interacting dispersion. | contribution 0.63 | 0.80 | 0.34 | asserted 0.98 |
| s2 | The numerical complexity of computing such vison phases reduces therefore to computing overlaps of ground states of free-fermion Hamiltonians. | interpretation 0.44 | 0.72 | 0.17 | asserted 0.99 |
| s3 | Among other results, we establish numerically the conditions under which the Majorana-carrying flux excitation in Ising-Topologically-Ordered states enriched by translations acquires $0$ or $\pi$ phase when moving around a single plaquette. | result 0.99 | 0.95 | 0.17 | asserted 1.00 |
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The paper
Original abstract
We develop an exact map of all states and operators from 2D lattices of spins-$1/2$ into lattices of fermions and bosons with mutual semionic statistical interaction that goes beyond previous dualities of $\mathbb{Z}_2$ lattice gauge theories because it does not rely on imposing local conservation laws and captures the motion of ``charges'' and ``fluxes'' on equal footing. This map allows to explicitly compute the Berry phases for the transport of fluxes in a large class of symmetry enriched topologically ordered states with emergent $\mathbb{Z}_2$ gauge fields that includes chiral, non-chiral, abelian or non-abelian, that can be perturbatively connected to models where the visons are static and the emergent fermionic spinons have a non-interacting dispersion. The numerical complexity of computing such vison phases reduces therefore to computing overlaps of ground states of free-fermion Hamiltonians. Among other results, we establish numerically the conditions under which the Majorana-carrying flux excitation in Ising-Topologically-Ordered states enriched by translations acquires $0$ or $\pi$ phase when moving around a single plaquette.
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How the literature uses it
3 arXiv papers cite this in 24 sentences
Papers citing it · 13 sentences without a confident label
Uses its method or tool 1 paper
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We will now present the “dictionary” that allows to map exactly any local operator acting the underlying physical spin degrees of freedom onto operators acting on the dual vison and spinon degrees of freedom, introduced in Ref. [ref] .
Nature of visons in the perturbed ferromagnetic and antiferromagnetic Kitaev honeycomb models · Vison hoppings from the duality mapping · 0.97
Compares with it 1 paper
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Therefore, as we will see, this phase is in exact agreement with the phase that was computed in Ref. [ref] with a perturbation different from the Zeeman field.
Nature of visons in the perturbed ferromagnetic and antiferromagnetic Kitaev honeycomb models · Kitaev model Perturbed by a Zeeman field · 0.99
Cites it as background 1 paper
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The presence of background anyons, if any, leads to a braiding phase seen by other anyon species on any path that encloses an odd number of the background anyons, with discussions for generic $Z_2$ QSLs in Ref [ref] .
Translation-enriched $Z_2$ spin liquids and topological vison bands: Possible application to $\alpha$-RuCl$_3$ · Introduction · 0.88
What it cites · 1 sentence without a confident label
Compares with 2 papers
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While an earlier version of Ref. [ref] had concluded that the phase of vison in the FM model was $π$ around a unit cell, the updated understanding provided in Refs. [ref] is currently in mutual agreement with the conclusion that the vison acquires zero phase in the FM model and $π$ phase in the AFM model around a unit cell, which is also in agreement with the current study.
Dynamics of visons and thermal Hall effect in perturbed Kitaev models · Kitaev model with a Haldane mass term · 0.88
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While an earlier version of Ref. [ref] had concluded that the phase of vison in the FM model was $π$ around a unit cell, the updated understanding provided in Refs. [ref] is currently in mutual agreement with the conclusion that the vison acquires zero phase in the FM model and $π$ phase in the AFM model around a unit cell, which is also in agreement with the current study.
Nature of visons in the perturbed ferromagnetic and antiferromagnetic Kitaev honeycomb models · Kitaev model with a Haldane mass term · 0.88
Cites as background 2 papers
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The motion of the vison in the ferromagnetic (FM) and antiferromagnetic (AFM) Kitaev models induced by physically realistic perturbations such as the Zeemann field, has also been studied in Refs. [ref] .
Dynamics of visons and thermal Hall effect in perturbed Kitaev models · Kitaev model with a Haldane mass term · 0.95
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The motion of the vison in the ferromagnetic (FM) and antiferromagnetic (AFM) Kitaev models induced by physically realistic perturbations such as the Zeemann field, has also been studied in Refs. [ref] .
Nature of visons in the perturbed ferromagnetic and antiferromagnetic Kitaev honeycomb models · Kitaev model with a Haldane mass term · 0.95
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