arXiv:2006.16256 · Physical Review Research

Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions

Eyal Leviatan, David F. Mross

Published Dec 29, 2020• 10 citations

Abstract

The authors use non-local transformations to describe spin-chain arrays in terms of partons and emergent gauge fields and use the scheme to produce parent Hamiltonians for gapped phases, including chiral and non-chiral spin liquids.

DOI: 10.1103/physrevresearch.2.043437

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arXiv:2006.16256 · Physical Review Research

Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions

Eyal Leviatan, David F. Mross

Published Dec 29, 2020• 10 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevresearch.2.043437

Related papers

Coupled wire construction of non-Abelian chiral spin liquids

Po-Hao Huang

Jan 1, 20180 citations

Bridging conformal field theory and parton approaches to SU ( n ) k chiral spin liquids

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We employ the $\mathrm{SU}{(n)}_{k}$ Wess-Zumino-Witten (WZW) model in conformal field theory to construct lattice wave functions in both one and two dimensions. The spins on all lattice sites are chosen to transform under the $\mathrm{SU}(n)$ irreducible representation with a single row and $k$ boxes in the Young tableau. It is demonstrated that the wave functions can be reinterpreted as parton states, which enables efficient conversion to matrix product states, such that many physical properties can be evaluated directly. In one dimension, these wave functions describe critical spin chains whose universality classes are in one-to-one correspondence with the WZW models used in the construction. In two dimensions, our constructions yield model wave functions for chiral spin liquids, and we show how to find all topological sectors of them in a systematic way. Using the null vectors of Kac-Moody algebras, parent Hamiltonians of the $\mathrm{SU}{(3)}_{k}$ series are derived. The $\mathrm{SU}{(3)}_{k}$ chiral spin liquids are lattice analogs of non-Abelian spin-singlet fractional quantum Hall states, and the $k=2$ member hosts Fibonacci anyons.We employ the $\mathrm{SU}{(n)}_{k}$ Wess-Zumino-Witten (WZW) model in conformal field theory to construct lattice wave functions in both one and two dimensions. The spins on all lattice sites are chosen to transform under the $\mathrm{SU}(n)$ irreducible representation with a single row and $k$ boxes in the Young tableau. It is demonstrated that the wave functions can be reinterpreted as parton states, which enables efficient conversion to matrix product states, such that many physical properties can be evaluated directly. In one dimension, these wave functions describe critical spin chains whose universality classes are in one-to-one correspondence with the WZW models used in the construction. In two dimensions, our constructions yield model wave functions for chiral spin liquids, and we show how to find all topological sectors of them in a systematic way. Using the null vectors of Kac-Moody algebras, parent Hamiltonians of the $\mathrm{SU}{(3)}_{k}$ series are derived. The $\mathrm{SU}{(3)}_{k}$ chiral spin liquids are lattice analogs of non-Abelian spin-singlet fractional quantum Hall states, and the $k=2$ member hosts Fibonacci anyons.

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We employ the

\mathrm{SU}{(n)}_{k}

Wess-Zumino-Witten (WZW) model in conformal field theory to construct lattice wave functions in both one and two dimensions. The spins on all lattice sites are chosen to transform under the

\mathrm{SU}(n)

irreducible representation with a single row and

k

boxes in the Young tableau. It is demonstrated that the wave functions can be reinterpreted as parton states, which enables efficient conversion to matrix product states, such that many physical properties can be evaluated directly. In one dimension, these wave functions describe critical spin chains whose universality classes are in one-to-one correspondence with the WZW models used in the construction. In two dimensions, our constructions yield model wave functions for chiral spin liquids, and we show how to find all topological sectors of them in a systematic way. Using the null vectors of Kac-Moody algebras, parent Hamiltonians of the

\mathrm{SU}{(3)}_{k}

series are derived. The

\mathrm{SU}{(3)}_{k}

chiral spin liquids are lattice analogs of non-Abelian spin-singlet fractional quantum Hall states, and the

k=2

member hosts Fibonacci anyons.

SO(N)

Kac-Moody Wess-Zumino-Witten algebra at level 1. We focus on the dihedral

D_k

symmetry of

SO(2n)_1

, and its promotion to a gauge symmetry by manipulating the locality of fermion pairs. Gauging the symmetry (sub)group generates the

\mathcal{C}/G

twist liquids, where

G=\mathbb{Z}_2

for

\mathcal{C}=U(1)_l

SU(n)_1

, and

G=\mathbb{Z}_2

\mathbb{Z}_k

D_k

for

\mathcal{C}=SO(2n)_1

. We construct exactly solvable models for all of these topological states. We prove the presence of a bulk excitation energy gap and demonstrate the appearance of edge orbifold conformal field theories corresponding to the twist liquid topological orders. We analyze the statistical properties of the anyon excitations, including the non-Abelian metaplectic anyons and a new class of quasiparticles referred to as Ising-fluxons. We show an eight-fold periodic gauging pattern in

SO(2n)_1/G

by identifying the non-chiral components of the twist liquids with discrete gauge theories.