Coupled-wire constructions: a Luttinger liquid approach to topology
@article{Meng2019CoupledwireCA, title={Coupled-wire constructions: a Luttinger liquid approach to topology}, author={Tobias Meng}, journal={The European Physical Journal Special Topics}, year={2019}, volume={229}, pages={527-543} }
Coupled-wire constructions use bosonization to analytically tackle the strong interactions underlying fractional topological states of matter. We give an introduction to this technique, discuss its strengths and weaknesses, and provide an overview of the main achievements of coupled-wire constructions.
21 Citations
Microscopic study of the coupled-wire construction and plausible realization in spin-dependent optical lattices
- Physics
- 2020
Coupled-wire constructions offer particularly simple and powerful models to capture the essence of strongly correlated topological phases of matter. They often rely on effective theories valid in the…
Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions
- PhysicsPhysical Review Research
- 2020
The fractionalization of microscopic degrees of freedom is a remarkable manifestation of strong interactions in quantum many-body systems. Analytical studies of this phenomenon are primarily based on…
Quantum wires, Chern-Simons theory, and dualities in the quantum Hall system
- PhysicsPhysical Review B
- 2022
Over the years, many theoretical frameworks have been developed to understand the remarkable physics of the quantum Hall system. In this work we discuss the interplay among quantum wires,…
Quantum Wires, Chern-Simons, and Dualities in the Quantum Hall System
- Physics
- 2022
Over the years, many theoretical frameworks have been developed to understand the remarkable physics of the quantum Hall system. In this work we discuss the interplay among quantum wires,…
Fractonic topological phases from coupled wires
- PhysicsPhysical Review Research
- 2021
In three dimensions, gapped phases can support "fractonic" quasiparticle excitations, which are either completely immobile or can only move within a low-dimensional submanifold, a peculiar…
Interaction-enabled fractonic higher-order topological phases
- PhysicsPhysical Review B
- 2022
In this work, we present a collection of three-dimensional higher-order symmetry protected topological phases (HOSPTs) with gapless hinge modes that exist only in strongly interacting systems subject…
ZN lattice gauge theory in a ladder geometry
- PhysicsPhysical Review Research
- 2021
Under the perspective of realizing analog quantum simulations of lattice gauge theories, ladder geometries offer an intriguing playground, relevant for ultracold atom experiments. Here, we…
Bosonization for fermions and parafermions
- PhysicsThe European Physical Journal Special Topics
- 2020
Parafermions are fractional excitations which can be regarded as generalizations of Majorana bound states, but in contrast to the latter they require electron-electron interactions. Compared to…
Chiral edge states in (2+1)-dimensional topological phases
- PhysicsInternational Journal of Modern Physics A
- 2019
Chiral edge states of [Formula: see text]-dimensional Abelian and non-Abelian topological phases can be represented by chiral conformal field theories with integer and noninteger values of central…
Strange correlators for topological quantum systems from bulk-boundary correspondence
- Physics
- 2022
”Strange” correlators provide a tool to detect topological phases arising in many-body models by computing the matrix elements of suitably defined two-point correlations between the states under…
References
SHOWING 1-10 OF 165 REFERENCES
From coupled-wire construction of quantum Hall states to wave functions and hydrodynamics
- PhysicsPhysical Review B
- 2019
In this paper we use a close connection between the coupled-wire construction (CWC) of Abelian quantum Hall states and the theory of composite bosons to extract the Laughlin wave function and the h…
Coupled-wire construction of chiral spin liquids
- Physics
- 2015
We develop a coupled wire construction of chiral spin liquids. The starting point are individual wires of electrons in the Mott regime that are subject to a Zeeman field and Rashba spin-orbit…
Quantum Hall hierarchy from coupled wires
- PhysicsPhysical Review B
- 2019
The coupled-wire construction provides a useful way to obtain microscopic Hamiltonians for various two-dimensional topological phases, among which fractional quantum Hall states are paradigmatic…
Parafermions in an interacting nanowire bundle.
- PhysicsPhysical review letters
- 2014
A minimal setup consisting of a bundle of four tunnel coupled nanowires hosting spinless electrons that interact strongly with each other is considered, which relies only on simple one-dimensional wires, a uniform magnetic field, and strong interactions, but does not require the presence of superconductivity or exotic quantum Hall phases.
Fractional topological insulators: From sliding Luttinger liquids to Chern-Simons theory
- Physics
- 2015
The sliding Luttinger liquid approach is applied to study fractional topological insulators (FTIs). We show that a FTI is the low energy fixed point of the theory for realistic spin-orbit and…
Topological Floquet Phases in Driven Coupled Rashba Nanowires.
- PhysicsPhysical review letters
- 2016
We consider periodically driven arrays of weakly coupled wires with conduction and valence bands of Rashba type and study the resulting Floquet states. This nonequilibrium system can be tuned into…
Wire deconstructionism of two-dimensional topological phases
- Physics
- 2014
A scheme is proposed to construct integer and fractional topological quantum states of fermions in two spatial dimensions. We devise models for such states by coupling wires of non-chiral Luttinger…
Three-dimensional fractional topological insulators in coupled Rashba layers
- Physics
- 2017
We propose a model of three-dimensional topological insulators consisting of weakly coupled electron- and hole-gas layers with Rashba spin-orbit interaction stacked along a given axis. We show that…
From Luttinger liquid to non-Abelian quantum Hall states
- Physics
- 2012
We formulate a theory of non-Abelian fractional quantum Hall states by considering an anisotropic system consisting of coupled, interacting one dimensional wires. We show that Abelian bosonization…
Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations
- Physics
- 1983
This Letter presents variational ground-state and excited-state wave functions which describe the condensation of a two-dimensional electron gas into a new state of matter.