Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1510.05972 · Physical review. B./Physical review. B

Monte Carlo study of phase transitions out of symmetry-enriched topological phases of bosons in two dimensions

Jong Yeon Lee, Scott Geraedts, Olexei I. Motrunich

Published Jan 4, 2016• 8 citations
arXivHTMLPDF

Abstract

We study a statistical mechanics model of two species of bosons with mutual statistics $\ensuremath{\theta}=2\ensuremath{\pi}/n$ in (2+1) dimensions. This model realizes a fractionalized topological phase of bosons, which is a fractionalized version of the boson integer quantum Hall effect. The model can be studied with sign-free Monte Carlo simulations. We study the phase transitions between the fractionalized topological phase and a trivial insulator, and between different topological phases. We find that these transitions are continuous, and we measure their critical exponents.

DOI
10.1103/physrevb.93.035103

Related papers

Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases

Scott Geraedts, Olexei I. Motrunich

We study a topological phase of interacting bosons in (3 þ 1) dimensions that is protected by charge conservation and time-reversal symmetry.We present an explicit lattice model that realizes this phase and that can be studied in sign-free Monte Carlo simulations.The idea behind our model is to bind bosons to topological defects called hedgehogs.We determine the phase diagram of the model and identify a phase where such bound states are proliferated.In this phase, we observe a Witten effect in the bulk whereby an external monopole binds half of the elementary boson charge, which confirms that it is a bosonic topological insulator.We also study the boundary between the topological insulator and a trivial insulator.We find a surface phase diagram that includes exotic superfluids, a topologically ordered phase, and a phase with a Hall effect quantized to one-half of the value possible in a purely two-dimensional system.We also present models that realize symmetry-enriched topologically ordered phases by binding multiple hedgehogs to each boson; these phases show charge fractionalization and intrinsic topological order as well as a fractional Witten effect.

arXiv:1408.1096•Physical Review X•Dec 22, 2014•19 citations

Bosonic topological phase in a paired superfluid

Snir Gazit, Ashvin Vishwanath

We study an effective model of two interacting species of bosons in two dimensions, which is amenable to sign problem free Monte Carlo simulations. In addition to conventional ground states, we access a paired superfluid which is also a topological phase, protected by the remaining $U(1)\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry. This phase arises from the condensation of a composite object, the bound state of vortices and antivortices of one species, to a boson of the second species. We introduce a bulk response function, the Ising analog of the quantized Hall effect, to diagnose the topological phase. The interplay of broken symmetry and topology leads to interesting effects such as fractionally charged vortices in the paired superfluid. Possible extensions towards realistic models of cold atomic bosons are discussed.

arXiv:1510.05007•Physical review. B./Physical review. B•Mar 30, 2016•4 citations

Numerical Studies of Topological Phases

Scott Geraedts

iii The topological phases of matter have been a major part of condensed matter physics research since the discovery of the quantum Hall effect in the 1980s. Recently, much of this research has focused on the study of systems of free fermions, such as the integer quantumHall effect, quantum spin Hall effect, and topological insulator. Though these free fermion systems can play host to a variety of interesting phenomena, the physics of interacting topological phases is even richer. Unfortunately, there is a shortage of theoretical tools that can be used to approach interacting problems. In this thesis I will discuss progress in using two different numerical techniques to study topological phases. Recently much research in topological phases has focused on phases made up of bosons. Unlike fermions, free bosons form a condensate and so interactions are vital if the bosons are to realize a topological phase. Since these phases are difficult to study, much of our understanding comes from exactly solvable models, such as Kitaev’s toric code, as well as Levin-Wen and Walker-Wang models. We may want to study systems for which such exactly solvable models are not available. In this thesis I present a series of models which are not solvable exactly, but which can be studied in sign-freeMonte Carlo simulations. The models work by binding

•Jan 1, 2015•0 citations

Theory and classification of interacting integer topological phases in two dimensions: A Chern-Simons approach

Yuan-Ming Lu, Ashvin Vishwanath

We study topological phases of interacting systems in two spatial dimensions in the absence of topological order (i.e., with a unique ground state on closed manifolds and no fractional excitations). These are the closest interacting analogs of integer quantum Hall states, topological insulators, and superconductors. We adapt the well-known Chern-Simons $K$-matrix description of quantum Hall states to classify such ``integer'' topological phases. Our main result is a general formalism that incorporates symmetries into the $K$-matrix description. Remarkably, this simple analysis yields the same list of topological phases as a recent group cohomology classification, and in addition provides field theories and explicit edge theories for all these phases. The bosonic topological phases, which only appear in the presence of interactions and which remain well defined in the presence of disorder, include (i) bosonic insulators with a Hall conductance quantized to even integers, (ii) a bosonic analog of quantum spin Hall insulators, and (iii) a bosonic analog of a chiral topological superconductor, whose $K$ matrix is the Cartan matrix of Lie group ${E}_{8}$. We also discuss interacting fermion systems where symmetries are realized in a projective fashion, where we find the present formalism can handle a wider range of symmetries than a recent group super-cohomology classification. Lastly, we construct microscopic models of these phases from coupled one-dimensional systems.

arXiv:1205.3156•Physical Review B•Sep 14, 2012•507 citations

Phase transitions of bosonic fractional quantum Hall effect in topological flat bands

Tian-Sheng Zeng

We study the phase transitions of bosonic $\ensuremath{\nu}=1/2$ fractional quantum Hall (FQH) effect in different topological lattice models under the interplay of onsite periodic potential and Hubbard repulsion. Through exact diagonalization and density matrix renormalization group methods, we demonstrate that the many-body ground state undergoes a continuous phase transition between bosonic FQH liquid and a trivial (Mott) insulator induced by the periodic potential, characterized by the smooth crossover of energy and entanglement entropy. When the Hubbard repulsion decreases, we claim that this bosonic FQH liquid would turn into a superfluid state with a direct energy level crossing and a discontinuous leap of off-diagonal long-range order.

arXiv:2009.06478•Physical review. B./Physical review. B•Feb 15, 2021•5 citations

Fractionalized conductivity at topological phase transitions

Yan-Cheng Wang, Meng Cheng, William Witczak‐Krempa +1 more

The experimental discovery of the fractionalized Hall conductivity revealed new types of quantum particles beyond bosons and fermions. These anyons are usually studied deep inside a topological phase. But can such fractionalization be detected at the phase transition point to a conventional phase? To answer this question, we study a quantum phase transition between a topological state called a $\mathbb{Z}_2$ spin liquid and a conventional superfluid using large-scale quantum Monte Carlo simulations. Our results show that the conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulator-to-superfluid transition. This opens the door for the experimental detection of anyons in a much broader regime, and has ramifications in the study of quantum materials and ultra-cold atomic gases.

•May 15, 2020•1 citation
We study a statistical mechanics model of two species of bosons with mutual statistics \ensuremathθ=2\ensuremathπ/n\ensuremath{\theta}=2\ensuremath{\pi}/n\ensuremathθ=2\ensuremathπ/n in (2+1) dimensions. This model realizes a fractionalized topological phase of bosons, which is a fractionalized version of the boson integer quantum Hall effect. The model can be studied with sign-free Monte Carlo simulations. We study the phase transitions between the fractionalized topological phase and a trivial insulator, and between different topological phases. We find that these transitions are continuous, and we measure their critical exponents.
We study a topological phase of interacting bosons in (3 þ 1) dimensions that is protected by charge conservation and time-reversal symmetry.We present an explicit lattice model that realizes this phase and that can be studied in sign-free Monte Carlo simulations.The idea behind our model is to bind bosons to topological defects called hedgehogs.We determine the phase diagram of the model and identify a phase where such bound states are proliferated.In this phase, we observe a Witten effect in the bulk whereby an external monopole binds half of the elementary boson charge, which confirms that it is a bosonic topological insulator.We also study the boundary between the topological insulator and a trivial insulator.We find a surface phase diagram that includes exotic superfluids, a topologically ordered phase, and a phase with a Hall effect quantized to one-half of the value possible in a purely two-dimensional system.We also present models that realize symmetry-enriched topologically ordered phases by binding multiple hedgehogs to each boson; these phases show charge fractionalization and intrinsic topological order as well as a fractional Witten effect.
We study an effective model of two interacting species of bosons in two dimensions, which is amenable to sign problem free Monte Carlo simulations. In addition to conventional ground states, we access a paired superfluid which is also a topological phase, protected by the remaining $U(1)\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry. This phase arises from the condensation of a composite object, the bound state of vortices and antivortices of one species, to a boson of the second species. We introduce a bulk response function, the Ising analog of the quantized Hall effect, to diagnose the topological phase. The interplay of broken symmetry and topology leads to interesting effects such as fractionally charged vortices in the paired superfluid. Possible extensions towards realistic models of cold atomic bosons are discussed.
iii The topological phases of matter have been a major part of condensed matter physics research since the discovery of the quantum Hall effect in the 1980s. Recently, much of this research has focused on the study of systems of free fermions, such as the integer quantumHall effect, quantum spin Hall effect, and topological insulator. Though these free fermion systems can play host to a variety of interesting phenomena, the physics of interacting topological phases is even richer. Unfortunately, there is a shortage of theoretical tools that can be used to approach interacting problems. In this thesis I will discuss progress in using two different numerical techniques to study topological phases. Recently much research in topological phases has focused on phases made up of bosons. Unlike fermions, free bosons form a condensate and so interactions are vital if the bosons are to realize a topological phase. Since these phases are difficult to study, much of our understanding comes from exactly solvable models, such as Kitaev’s toric code, as well as Levin-Wen and Walker-Wang models. We may want to study systems for which such exactly solvable models are not available. In this thesis I present a series of models which are not solvable exactly, but which can be studied in sign-freeMonte Carlo simulations. The models work by binding
We study topological phases of interacting systems in two spatial dimensions in the absence of topological order (i.e., with a unique ground state on closed manifolds and no fractional excitations). These are the closest interacting analogs of integer quantum Hall states, topological insulators, and superconductors. We adapt the well-known Chern-Simons KKK-matrix description of quantum Hall states to classify such ``integer'' topological phases. Our main result is a general formalism that incorporates symmetries into the KKK-matrix description. Remarkably, this simple analysis yields the same list of topological phases as a recent group cohomology classification, and in addition provides field theories and explicit edge theories for all these phases. The bosonic topological phases, which only appear in the presence of interactions and which remain well defined in the presence of disorder, include (i) bosonic insulators with a Hall conductance quantized to even integers, (ii) a bosonic analog of quantum spin Hall insulators, and (iii) a bosonic analog of a chiral topological superconductor, whose KKK matrix is the Cartan matrix of Lie group E8{E}_{8}E8​. We also discuss interacting fermion systems where symmetries are realized in a projective fashion, where we find the present formalism can handle a wider range of symmetries than a recent group super-cohomology classification. Lastly, we construct microscopic models of these phases from coupled one-dimensional systems.
We study the phase transitions of bosonic $\ensuremath{\nu}=1/2$ fractional quantum Hall (FQH) effect in different topological lattice models under the interplay of onsite periodic potential and Hubbard repulsion. Through exact diagonalization and density matrix renormalization group methods, we demonstrate that the many-body ground state undergoes a continuous phase transition between bosonic FQH liquid and a trivial (Mott) insulator induced by the periodic potential, characterized by the smooth crossover of energy and entanglement entropy. When the Hubbard repulsion decreases, we claim that this bosonic FQH liquid would turn into a superfluid state with a direct energy level crossing and a discontinuous leap of off-diagonal long-range order.
The experimental discovery of the fractionalized Hall conductivity revealed new types of quantum particles beyond bosons and fermions. These anyons are usually studied deep inside a topological phase. But can such fractionalization be detected at the phase transition point to a conventional phase? To answer this question, we study a quantum phase transition between a topological state called a Z2\mathbb{Z}_2Z2​ spin liquid and a conventional superfluid using large-scale quantum Monte Carlo simulations. Our results show that the conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulator-to-superfluid transition. This opens the door for the experimental detection of anyons in a much broader regime, and has ramifications in the study of quantum materials and ultra-cold atomic gases.