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:1806.07634 · Physical review. B./Physical review. B

Chiral topological states in Bose-Fermi mixtures

Ying-Hai Wu

Published Mar 7, 2019• 3 citations
arXivHTMLPDF

Abstract

Topological states were initially discovered in solid state systems and have generated widespread interest in many areas of physics. The advances in cold atoms create novel settings for studying topological states that would be quite unrealistic in solid state systems. One example is that the constituents of quantum gases can be various types of bosons, fermions, and their mixtures. This paper explores interaction-induced topological states in two-dimensional Bose-Fermi mixtures. We propose a class of topological states which have no fractionalized excitations but possess maximally chiral edge states. For previously known topological states, these two features can be found simultaneously in the integer quantum Hall states of fermions and the ${E}_{8}$ state of bosons. The existence of some proposed states in certain continuum and lattice models is corroborated by exact diagonalization and density matrix renormalization group calculations. This paper suggests that the Bose-Fermi mixture is a very appealing platform for studying topological states.

DOI
10.1103/physrevb.99.125108

Related papers

Topological properties of one-dimensional hardcore Bose—Fermi mixture

Yongfei Jia, Huaiming Guo, Jihong Qin +2 more

We study the topological properties of a one-dimensional (1D) hardcore Bose—Fermi mixture using the exact diagonalization method. We firstly add a hardcore boson to a fermionic system and by examining the edge states we find that the quasi-particle manifests the topological properties of the system. Then we study a mixture with 7 fermions and 1 boson. We find that the mixture also exhibits topological properties and its behaviors are similar to that of the corresponding fermionic system. We present a qualitative explanation to understand such behaviors using the mapping between a hardcore boson and a spinless fermion. These results show the existence of topological properties in a 1D hardcore Bose—Fermi mixture and may be realized using cold atoms trapped in optical lattices experimentally.

Chinese Physics B•Sep 1, 2013•2 citations

Fractional quantum Hall effect of Bose-Fermi mixtures

Tian-Sheng Zeng

Multicomponent quantum Hall effect, under the interplay between intercomponent and intracomponent correlations, leads us to new emergent topological orders. Here, we report the theoretical discovery of fractional quantum hall effect of strongly correlated Bose-Fermi mixtures classified by the $\mathbf{K}=\left(\begin{array}{cc}m& 1\\ 1& n\end{array}\right)$ matrix (even $m$ for boson and odd $n$ for fermion), using topological flat band models. Utilizing the state-of-the-art exact diagonalization and density-matrix renormalization group methods, we build up the topological characterization based on three inherent aspects: (i) topological $(mn\ensuremath{-}1)$-fold ground-state degeneracy equivalent to the determinant of the $\mathbf{K}$ matrix; (ii) fractionally quantized topological Chern number matrix equivalent to the inverse of the $\mathbf{K}$ matrix; and (iii) two parallel-propagating chiral edge branches with level counting 1,2,5,10 consistent with the conformal field theory description.

arXiv:2012.08203•Physical review. B./Physical review. B•May 21, 2021•6 citations

Emergent Topological Order in Interacting Bose-Fermi Mixtures.

Revista, Zen, PHYSICS, 10

The exploration of novel quantum states of matter remains a central theme in condensed matter physics. Among these, topological order stands out for its robust properties against local perturbations and its potential applications in quantum information processing. While considerable progress has been made in understanding topological order in purely bosonic or fermionic systems, the interplay between different quantum statistics in interacting Bose-Fermi mixtures offers a rich platform for discovering new forms of topological order. This paper investigates the theoretical conditions and characteristic signatures for the emergence of topological order in these hybrid quantum systems. We propose that tunable interspecies interactions, combined with appropriate lattice geometries or synthetic gauge fields, can drive Bose-Fermi mixtures into exotic phases exhibiting non-trivial topological properties. Specifically, we explore scenarios where bosonic particles mediate effective interactions between fermions, or where bosonic condensation leads to a modification of the fermionic band structure, thereby inducing topological phases. Our analysis focuses on identifying key experimental observables, such as fractionalized excitations, robust edge modes, and entanglement properties, which can serve as hallmarks of emergent topological order. The theoretical framework incorporates mean-field approaches, variational methods, and numerical simulations to characterize the phase diagram of interacting Bose-Fermi mixtures, providing a pathway for experimental realization and verification of these fascinating quantum states.

•Nov 28, 2025•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

Exotic topological density waves in cold atomic Rydberg-dressed fermions

Xiaopeng Li, S. Das Sarma

Versatile controllability of interactions in ultracold atomic and molecular gases has now reached an era where quantum correlations and unconventional many-body phases can be studied with no corresponding analogues in solid-state systems. Recent experiments in Rydberg atomic gases have achieved exquisite control over non-local interactions, allowing novel quantum phases unreachable with the usual local interactions in atomic systems. Here we study Rydberg-dressed atomic fermions in a three-dimensional optical lattice predicting the existence of hitherto unheard-of exotic mixed topological density wave phases. By varying the spatial range of the non-local interaction, we find various chiral density waves with spontaneous time-reversal symmetry breaking, whose quasiparticles form three-dimensional quantum Hall and Weyl semimetal states. Remarkably, certain density waves even exhibit mixed topologies beyond the existing topological classification. Our results suggest gapless fermionic states could exhibit far richer topology than previously expected.

arXiv:1501.05320•Nature Communications•May 14, 2015•48 citations

Bulk-edge correspondence in (2 + 1)-dimensional Abelian topological phases

Jennifer Cano, Meng Cheng, Michael Mulligan +3 more

The same bulk two-dimensional topological phase can have multiple distinct, fully chiral edge phases. We show that this can occur in the integer quantum Hall states at $\ensuremath{\nu}=8$ and 12, with experimentally testable consequences. We show that this can occur in Abelian fractional quantum Hall states as well, with the simplest examples being at $\ensuremath{\nu}=\frac{8}{7},\frac{12}{11},\frac{8}{15},\frac{16}{5}$. We give a general criterion for the existence of multiple distinct chiral edge phases for the same bulk phase and discuss experimental consequences. Edge phases correspond to lattices while bulk phases correspond to genera of lattices. Since there are typically multiple lattices in a genus, the bulk-edge correspondence is typically one-to-many; there are usually many stable fully chiral edge phases corresponding to the same bulk. We explain these correspondences using the theory of integral quadratic forms. We show that fermionic systems can have edge phases with only bosonic low-energy excitations and discuss a fermionic generalization of the relation between bulk topological spins and the central charge. The latter follows from our demonstration that every fermionic topological phase can be represented as a bosonic topological phase, together with some number of filled Landau levels. Our analysis shows that every Abelian topological phase can be decomposed into a tensor product of theories associated with prime numbers $p$ in which every quasiparticle has a topological spin that is a ${p}^{n}$th root of unity for some $n$. It also leads to a simple demonstration that all Abelian topological phases can be represented by $\mathrm{U}{(1)}^{N}$ Chern-Simons theory parameterized by a $K$ matrix.

arXiv:1310.5708•Physical Review B•Mar 14, 2014•123 citations
Topological states were initially discovered in solid state systems and have generated widespread interest in many areas of physics. The advances in cold atoms create novel settings for studying topological states that would be quite unrealistic in solid state systems. One example is that the constituents of quantum gases can be various types of bosons, fermions, and their mixtures. This paper explores interaction-induced topological states in two-dimensional Bose-Fermi mixtures. We propose a class of topological states which have no fractionalized excitations but possess maximally chiral edge states. For previously known topological states, these two features can be found simultaneously in the integer quantum Hall states of fermions and the E8{E}_{8}E8​ state of bosons. The existence of some proposed states in certain continuum and lattice models is corroborated by exact diagonalization and density matrix renormalization group calculations. This paper suggests that the Bose-Fermi mixture is a very appealing platform for studying topological states.
We study the topological properties of a one-dimensional (1D) hardcore Bose—Fermi mixture using the exact diagonalization method. We firstly add a hardcore boson to a fermionic system and by examining the edge states we find that the quasi-particle manifests the topological properties of the system. Then we study a mixture with 7 fermions and 1 boson. We find that the mixture also exhibits topological properties and its behaviors are similar to that of the corresponding fermionic system. We present a qualitative explanation to understand such behaviors using the mapping between a hardcore boson and a spinless fermion. These results show the existence of topological properties in a 1D hardcore Bose—Fermi mixture and may be realized using cold atoms trapped in optical lattices experimentally.
Multicomponent quantum Hall effect, under the interplay between intercomponent and intracomponent correlations, leads us to new emergent topological orders. Here, we report the theoretical discovery of fractional quantum hall effect of strongly correlated Bose-Fermi mixtures classified by the K=(m11n)\mathbf{K}=\left(\begin{array}{cc}m& 1\\ 1& n\end{array}\right)K=(m1​1n​) matrix (even mmm for boson and odd nnn for fermion), using topological flat band models. Utilizing the state-of-the-art exact diagonalization and density-matrix renormalization group methods, we build up the topological characterization based on three inherent aspects: (i) topological $(mn\ensuremath{-}1)$-fold ground-state degeneracy equivalent to the determinant of the K\mathbf{K}K matrix; (ii) fractionally quantized topological Chern number matrix equivalent to the inverse of the K\mathbf{K}K matrix; and (iii) two parallel-propagating chiral edge branches with level counting 1,2,5,10 consistent with the conformal field theory description.
The exploration of novel quantum states of matter remains a central theme in condensed matter physics. Among these, topological order stands out for its robust properties against local perturbations and its potential applications in quantum information processing. While considerable progress has been made in understanding topological order in purely bosonic or fermionic systems, the interplay between different quantum statistics in interacting Bose-Fermi mixtures offers a rich platform for discovering new forms of topological order. This paper investigates the theoretical conditions and characteristic signatures for the emergence of topological order in these hybrid quantum systems. We propose that tunable interspecies interactions, combined with appropriate lattice geometries or synthetic gauge fields, can drive Bose-Fermi mixtures into exotic phases exhibiting non-trivial topological properties. Specifically, we explore scenarios where bosonic particles mediate effective interactions between fermions, or where bosonic condensation leads to a modification of the fermionic band structure, thereby inducing topological phases. Our analysis focuses on identifying key experimental observables, such as fractionalized excitations, robust edge modes, and entanglement properties, which can serve as hallmarks of emergent topological order. The theoretical framework incorporates mean-field approaches, variational methods, and numerical simulations to characterize the phase diagram of interacting Bose-Fermi mixtures, providing a pathway for experimental realization and verification of these fascinating quantum states.
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.
Versatile controllability of interactions in ultracold atomic and molecular gases has now reached an era where quantum correlations and unconventional many-body phases can be studied with no corresponding analogues in solid-state systems. Recent experiments in Rydberg atomic gases have achieved exquisite control over non-local interactions, allowing novel quantum phases unreachable with the usual local interactions in atomic systems. Here we study Rydberg-dressed atomic fermions in a three-dimensional optical lattice predicting the existence of hitherto unheard-of exotic mixed topological density wave phases. By varying the spatial range of the non-local interaction, we find various chiral density waves with spontaneous time-reversal symmetry breaking, whose quasiparticles form three-dimensional quantum Hall and Weyl semimetal states. Remarkably, certain density waves even exhibit mixed topologies beyond the existing topological classification. Our results suggest gapless fermionic states could exhibit far richer topology than previously expected.
The same bulk two-dimensional topological phase can have multiple distinct, fully chiral edge phases. We show that this can occur in the integer quantum Hall states at $\ensuremath{\nu}=8$ and 12, with experimentally testable consequences. We show that this can occur in Abelian fractional quantum Hall states as well, with the simplest examples being at $\ensuremath{\nu}=\frac{8}{7},\frac{12}{11},\frac{8}{15},\frac{16}{5}$. We give a general criterion for the existence of multiple distinct chiral edge phases for the same bulk phase and discuss experimental consequences. Edge phases correspond to lattices while bulk phases correspond to genera of lattices. Since there are typically multiple lattices in a genus, the bulk-edge correspondence is typically one-to-many; there are usually many stable fully chiral edge phases corresponding to the same bulk. We explain these correspondences using the theory of integral quadratic forms. We show that fermionic systems can have edge phases with only bosonic low-energy excitations and discuss a fermionic generalization of the relation between bulk topological spins and the central charge. The latter follows from our demonstration that every fermionic topological phase can be represented as a bosonic topological phase, together with some number of filled Landau levels. Our analysis shows that every Abelian topological phase can be decomposed into a tensor product of theories associated with prime numbers ppp in which every quasiparticle has a topological spin that is a pn{p}^{n}pnth root of unity for some nnn. It also leads to a simple demonstration that all Abelian topological phases can be represented by U(1)N\mathrm{U}{(1)}^{N}U(1)N Chern-Simons theory parameterized by a KKK matrix.