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:1810.03673 · Physical review. B./Physical review. B

Families of gapped interfaces between fractional quantum Hall states

Julian May-Mann, Taylor L. Hughes

Published Apr 19, 2019• 13 citations
arXivHTMLPDF

Abstract

Some interfaces between two different topologically ordered systems can be gapped. In earlier work it was shown that such gapped interfaces can themselves be effective one-dimensional topological systems that possess localized topological modes in open boundary geometries. Here we focus on how this occurs in the context of an interface between two single-component Laughlin states of opposite chirality, with filling fractions ${\ensuremath{\nu}}_{1}=1/p$ and ${\ensuremath{\nu}}_{2}=1/p{n}^{2}$. While one type of interface in such systems was previously studied, we show that allowing for edge reconstruction effects opens up a wide variety of possible gapped interfaces depending on the number of divisors of $n.$ We apply a complementary description of the ${\ensuremath{\nu}}_{2}=1/p{n}^{2}$ system in terms of Laughlin states coupled to a discrete gauge ${\mathbb{Z}}_{n}$ field. This enables us to identify possible interfaces to the ${\ensuremath{\nu}}_{1}$ system based on complete or partial confinement of this gauge field. We determine the tunneling properties, the ground-state degeneracy, and the nature of the non-Abelian zero modes of each interface in order to physically distinguish them.

DOI
10.1103/physrevb.99.155134

Related papers

Abelian origin of ν=2/3 and 2+2/3 fractional quantum Hall effect

Liangdong Hu, W. Zhu

We investigate the ground-state properties of the fractional quantum Hall effect at the filling factor $\ensuremath{\nu}=2/3$ and $2+2/3$, with a special focus on their typical edge physics. Via a topological characterization scheme in the framework of the density matrix renormalization group, the nature of the $\ensuremath{\nu}=2/3$ and $2+2/3$ states is identified as an Abelian hole-type Laughlin state, as evidenced by the fingerprint of entanglement spectra, central charge, and topological spin. Crucially, by constructing an interface between the $2/3$ $(2+2/3)$ state and different integer quantum Hall states, we study the structures of the interfaces from many aspects, including charge density and dipole moment. In particular, we demonstrate the edge reconstruction by visualizing edge channels comprised of two groups: the outermost $1/3$ channel and the inner composite channel made of a charged mode and neutral modes.

arXiv:2109.00781•Physical review. B./Physical review. B•Apr 22, 2022•4 citations

Fractional quantum Hall states with gapped boundaries in an extreme lattice limit

Zhao Liu, Emil J. Bergholtz

We present a detailed microscopic investigation of fractional quantum Hall states with gapped boundaries in a coupled bilayer lattice model featuring holes whose counterpropagating chiral edge states are hybridized and gapped out. We focus on an lattice limit for cold-atom experiments, in which each hole just consists of a single removed site. Although the holes distort the original band structure and lead to in-gap remnants of the continuum edge modes, we find that the lowest nearly flat band representing a higher-genus system may naturally form by controlling the local hopping terms that gap out the boundaries. Remarkably, local interactions in this new flat band lead to various Abelian and non-Abelian fractional quantum Hall states with gapped boundaries residing on emergent higher-genus surfaces, which we identify by extracting the nontrivial topological ground-state degeneracies and the fractional statistics of quasiparticles. These results demonstrate the feasibility of realizing novel fractional quantum Hall states with gapped boundaries even in the extreme lattice limit, thus enabling a possible new route towards universal topological quantum computation.

arXiv:1901.05119•Physical review. B./Physical review. B•May 13, 2019•4 citations

Fractional quantum Hall bilayers at half filling: Tunneling-driven non-Abelian phase

W. Zhu, Zhao Liu, F. D. M. Haldane +1 more

Multicomponent quantum Hall systems with internal degrees of freedom provide a fertile ground for the emergence of exotic quantum liquids. Here, we investigate the possibility of non-Abelian topological order in the half-filled fractional quantum Hall (FQH) bilayer system driven by the tunneling effect between two layers. By means of the state-of-the-art density-matrix renormalization group, we unveil ``fingerprint'' evidence of the non-Abelian Moore-Read Pfaffian state emerging in the intermediate-tunneling regime, including the ground-state degeneracy on the torus geometry and the topological entanglement spectroscopy (entanglement spectrum and topological entanglement entropy) on the spherical geometry, respectively. Remarkably, the phase transition from the previously identified Abelian (331) Halperin state to the non-Abelian Moore-Read Pfaffian state is determined to be continuous, which is signaled by the continuous evolution of the universal part of the entanglement spectrum, and discontinuities in the excitation gap and the derivative of the ground-state energy. Our results not only provide a ``proof-of-principle'' demonstration of realizing a non-Abelian state through coupling different degrees of freedom, but also open up a possibility in FQH bilayer systems for detecting different chiral $p\text{\ensuremath{-}}\text{wave}$ pairing states.

arXiv:1608.07761•Physical review. B./Physical review. B•Dec 30, 2016•41 citations

Microscopic Identification of Fractional Quantum Hall States on Higher-Genus Surfaces Induced by Gapped Boundaries on Lattices

Zhao Liu, Emil J. Bergholtz

We present a detailed microscopic investigation of fractional quantum Hall states on effective higher-genus surfaces emerging in a coupled bilayer lattice model featuring holes whose counter propagating chiral edge states are hybridized and gapped out. Although the holes distort the original band structure and lead to ingap remnants of the continuum edge modes, we find that a lowest nearly flat band representing a higher-genus system may naturally form by controlling the local hopping terms that gap out the boundaries. Remarkably, even in the extreme lattice limit where each hole consists of just a single removed site, local interactions in this new flat band lead to various Abelian and non-Abelian fractional quantum Hall states on the emergent higher-genus surfaces which we identify by extracting the non-trivial topological ground-state degeneracies and the fractional statistics of quasiparticles. These results demonstrate that our microscopic lattice model is a promising platform to realize novel fractional quantum Hall states with gapped boundaries, thus enabling a possible new route towards universal topological quantum computation.

•Jan 15, 2019•0 citations

Parafermionic Wires at the Interface of Chiral Topological States

Luiz H. Santos, Taylor L. Hughes

We explore a scenario where local interactions form one-dimensional gapped interfaces between a pair of distinct chiral two-dimensional topological states-referred to as phases 1 and 2-such that each gapped region terminates at a domain wall separating the chiral gapless edge states of these phases. We show that this type of T junction supports pointlike fractionalized excitations obeying parafermion statistics, thus implying that the one-dimensional gapped interface forms an effective topological parafermionic wire possessing a nontrivial ground state degeneracy. The physical properties of the anyon condensate that gives rise to the gapped interface are investigated. Remarkably, this condensate causes the gapped interface to behave as a type of anyon "Andreev reflector" in the bulk, whereby anyons from one phase, upon hitting the interface, can be transformed into a combination of reflected anyons and outgoing anyons from the other phase. Thus, we conclude that while different topological orders can be connected via gapped interfaces, the interfaces are themselves topological.

arXiv:1609.06714•Physical Review Letters•Mar 27, 2017•25 citations

Boundary degeneracy of topological order

Juven Wang, Xiao-Gang Wen

We introduce the concept of boundary degeneracy, as the ground state degeneracy of topologically ordered states on a compact orientable spatial manifold with gapped boundaries. We emphasize that the boundary degeneracy provides richer information than the bulk degeneracy. Beyond the bulk-edge correspondence, we find the ground state degeneracy of the fully gapped edge modes depends on boundary gapping conditions. By associating different types of boundary gapping conditions as different ways of particle or quasiparticle condensations on the boundary, we develop an analytic theory of gapped boundaries. By Chern-Simons theory, this allows us to derive the ground state degeneracy formula in terms of boundary gapping conditions, which encodes more than the fusion algebra of fractionalized quasiparticles. We apply our theory to Kitaev's toric code and Levin-Wen string-net models. We predict that the ${Z}_{2}$ toric code and ${Z}_{2}$ double-semion model [more generally, the ${Z}_{k}$ gauge theory and the $U{(1)}_{k}\ifmmode\times\else\texttimes\fi{}U{(1)}_{\ensuremath{-}k}$ nonchiral fractional quantum Hall state at even integer $k$] can be numerically and experimentally distinguished, by measuring their boundary degeneracy on an annulus or a cylinder.

arXiv:1212.4863•Physical Review B•Mar 13, 2015•97 citations
Some interfaces between two different topologically ordered systems can be gapped. In earlier work it was shown that such gapped interfaces can themselves be effective one-dimensional topological systems that possess localized topological modes in open boundary geometries. Here we focus on how this occurs in the context of an interface between two single-component Laughlin states of opposite chirality, with filling fractions \ensuremathν1=1/p{\ensuremath{\nu}}_{1}=1/p\ensuremathν1​=1/p and \ensuremathν2=1/pn2{\ensuremath{\nu}}_{2}=1/p{n}^{2}\ensuremathν2​=1/pn2. While one type of interface in such systems was previously studied, we show that allowing for edge reconstruction effects opens up a wide variety of possible gapped interfaces depending on the number of divisors of n.n.n. We apply a complementary description of the \ensuremathν2=1/pn2{\ensuremath{\nu}}_{2}=1/p{n}^{2}\ensuremathν2​=1/pn2 system in terms of Laughlin states coupled to a discrete gauge Zn{\mathbb{Z}}_{n}Zn​ field. This enables us to identify possible interfaces to the \ensuremathν1{\ensuremath{\nu}}_{1}\ensuremathν1​ system based on complete or partial confinement of this gauge field. We determine the tunneling properties, the ground-state degeneracy, and the nature of the non-Abelian zero modes of each interface in order to physically distinguish them.
We investigate the ground-state properties of the fractional quantum Hall effect at the filling factor $\ensuremath{\nu}=2/3$ and 2+2/32+2/32+2/3, with a special focus on their typical edge physics. Via a topological characterization scheme in the framework of the density matrix renormalization group, the nature of the $\ensuremath{\nu}=2/3$ and 2+2/32+2/32+2/3 states is identified as an Abelian hole-type Laughlin state, as evidenced by the fingerprint of entanglement spectra, central charge, and topological spin. Crucially, by constructing an interface between the 2/32/32/3 (2+2/3)(2+2/3)(2+2/3) state and different integer quantum Hall states, we study the structures of the interfaces from many aspects, including charge density and dipole moment. In particular, we demonstrate the edge reconstruction by visualizing edge channels comprised of two groups: the outermost 1/31/31/3 channel and the inner composite channel made of a charged mode and neutral modes.
We present a detailed microscopic investigation of fractional quantum Hall states with gapped boundaries in a coupled bilayer lattice model featuring holes whose counterpropagating chiral edge states are hybridized and gapped out. We focus on an lattice limit for cold-atom experiments, in which each hole just consists of a single removed site. Although the holes distort the original band structure and lead to in-gap remnants of the continuum edge modes, we find that the lowest nearly flat band representing a higher-genus system may naturally form by controlling the local hopping terms that gap out the boundaries. Remarkably, local interactions in this new flat band lead to various Abelian and non-Abelian fractional quantum Hall states with gapped boundaries residing on emergent higher-genus surfaces, which we identify by extracting the nontrivial topological ground-state degeneracies and the fractional statistics of quasiparticles. These results demonstrate the feasibility of realizing novel fractional quantum Hall states with gapped boundaries even in the extreme lattice limit, thus enabling a possible new route towards universal topological quantum computation.
Multicomponent quantum Hall systems with internal degrees of freedom provide a fertile ground for the emergence of exotic quantum liquids. Here, we investigate the possibility of non-Abelian topological order in the half-filled fractional quantum Hall (FQH) bilayer system driven by the tunneling effect between two layers. By means of the state-of-the-art density-matrix renormalization group, we unveil ``fingerprint'' evidence of the non-Abelian Moore-Read Pfaffian state emerging in the intermediate-tunneling regime, including the ground-state degeneracy on the torus geometry and the topological entanglement spectroscopy (entanglement spectrum and topological entanglement entropy) on the spherical geometry, respectively. Remarkably, the phase transition from the previously identified Abelian (331) Halperin state to the non-Abelian Moore-Read Pfaffian state is determined to be continuous, which is signaled by the continuous evolution of the universal part of the entanglement spectrum, and discontinuities in the excitation gap and the derivative of the ground-state energy. Our results not only provide a ``proof-of-principle'' demonstration of realizing a non-Abelian state through coupling different degrees of freedom, but also open up a possibility in FQH bilayer systems for detecting different chiral $p\text{\ensuremath{-}}\text{wave}$ pairing states.
We present a detailed microscopic investigation of fractional quantum Hall states on effective higher-genus surfaces emerging in a coupled bilayer lattice model featuring holes whose counter propagating chiral edge states are hybridized and gapped out. Although the holes distort the original band structure and lead to ingap remnants of the continuum edge modes, we find that a lowest nearly flat band representing a higher-genus system may naturally form by controlling the local hopping terms that gap out the boundaries. Remarkably, even in the extreme lattice limit where each hole consists of just a single removed site, local interactions in this new flat band lead to various Abelian and non-Abelian fractional quantum Hall states on the emergent higher-genus surfaces which we identify by extracting the non-trivial topological ground-state degeneracies and the fractional statistics of quasiparticles. These results demonstrate that our microscopic lattice model is a promising platform to realize novel fractional quantum Hall states with gapped boundaries, thus enabling a possible new route towards universal topological quantum computation.
We explore a scenario where local interactions form one-dimensional gapped interfaces between a pair of distinct chiral two-dimensional topological states-referred to as phases 1 and 2-such that each gapped region terminates at a domain wall separating the chiral gapless edge states of these phases. We show that this type of T junction supports pointlike fractionalized excitations obeying parafermion statistics, thus implying that the one-dimensional gapped interface forms an effective topological parafermionic wire possessing a nontrivial ground state degeneracy. The physical properties of the anyon condensate that gives rise to the gapped interface are investigated. Remarkably, this condensate causes the gapped interface to behave as a type of anyon "Andreev reflector" in the bulk, whereby anyons from one phase, upon hitting the interface, can be transformed into a combination of reflected anyons and outgoing anyons from the other phase. Thus, we conclude that while different topological orders can be connected via gapped interfaces, the interfaces are themselves topological.
We introduce the concept of boundary degeneracy, as the ground state degeneracy of topologically ordered states on a compact orientable spatial manifold with gapped boundaries. We emphasize that the boundary degeneracy provides richer information than the bulk degeneracy. Beyond the bulk-edge correspondence, we find the ground state degeneracy of the fully gapped edge modes depends on boundary gapping conditions. By associating different types of boundary gapping conditions as different ways of particle or quasiparticle condensations on the boundary, we develop an analytic theory of gapped boundaries. By Chern-Simons theory, this allows us to derive the ground state degeneracy formula in terms of boundary gapping conditions, which encodes more than the fusion algebra of fractionalized quasiparticles. We apply our theory to Kitaev's toric code and Levin-Wen string-net models. We predict that the Z2{Z}_{2}Z2​ toric code and Z2{Z}_{2}Z2​ double-semion model [more generally, the Zk{Z}_{k}Zk​ gauge theory and the $U{(1)}_{k}\ifmmode\times\else\texttimes\fi{}U{(1)}_{\ensuremath{-}k}$ nonchiral fractional quantum Hall state at even integer kkk] can be numerically and experimentally distinguished, by measuring their boundary degeneracy on an annulus or a cylinder.