Condensate-induced transitions between topologically ordered phases

Bais, F.A.; Slingerland, Joost

doi:10.1103/physrevb.79.045316

Cited by 283 publications

(498 citation statements)

References 113 publications

(222 reference statements)

Supporting

Mentioning

486

Contrasting

Unclassified

Order By: Relevance

“…We shall make heavy use of the technologies studying anyon condensation [20][21][22] . The basic premise of anyon condensation is that certain types of anyons cease to have conserved particle number across a phase transition; they thus effectively condense, exactly as how Cooper pairs condense, in the process breaking some symmetry.…”

Section: Introductionmentioning

confidence: 99%

Ground-State Degeneracy of Topological Phases on Open Surfaces

Hung

Wan

2015

Phys. Rev. Lett.

View full text Add to dashboard Cite

We relate the ground state degeneracy (GSD) of a non-Abelian topological phase on a surface with boundaries to the anyon condensates that break the topological phase to a trivial phase. Specifically, we propose that gapped boundary conditions of the surface are in one-to-one correspondence to the sets of condensates, each being able to completely break the phase, and we substantiate this by examples. The GSD resulting from a particular boundary condition coincides with the number of confined topological sectors due to the corresponding condensation. These lead to a generalization of the Laughlin-Tao-Wu (LTW) charge-pumping argument for Abelian fractional quantum Hall states (FQHS) to encompass non-Abelian topological phases, in the sense that an anyon loop of a confined anyon winding a non-trivial cycle can pump a condensed anyon from one boundary to another. Such generalized pumping may find applications in quantum control of anyons, eventually realizing topological quantum computation.

show abstract

Section: Introductionmentioning

confidence: 99%

Ground-State Degeneracy of Topological Phases on Open Surfaces

Hung

Wan

2015

Phys. Rev. Lett.

View full text Add to dashboard Cite

show abstract

“…The reason for this was discussed in Ref. 5. Consider the fusion of a Φ 2 2 quasiparticle, which we will label as γ, and its conjugate: γ ×γ = 0+3+13.…”

mentioning

confidence: 99%

“…As we increase the repulsion between the electrons in the two layers, the energy gap of the f-exciton will be reduced; when it is reduced to zero, the f-exciton will condense and drive a phase transition. When the anyon number has only a mod n conservation, this can even lead to a non-Abelian FQH state [2], yet little is known about "anyon condensation" [5][6][7][8]. A better understanding of these phase transitions may aid the quest for experimental detection of non-Abelian FQH states, because one side of the transition -in our case the (330) state at ν = 2/3 -can be accessed experimentally [9,10].…”

mentioning

confidence: 99%

Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States

Barkeshli

Wen

2010

Phys. Rev. Lett.

View full text Add to dashboard Cite

We find a series of possible continuous quantum phase transitions between fractional quantum Hall (FQH) states at the same filling fraction in two-component quantum Hall systems. These can be driven by tuning the interlayer tunneling and/or interlayer repulsion. One side of the transition is the Halperin (p, p, p − 3) Abelian two-component state while the other side is the non-Abelian Z4 parafermion (Read-Rezayi) state. We predict that the transition is a continuous transition in the 3D Ising class. The critical point is described by a Z2 gauged Ginzburg-Landau theory. These results have implications for experiments on two-component systems at ν = 2/3 and single-component systems at ν = 8/3.One of the most challenging problems in the study of quantum many-body systems is to understand transitions between topologically ordered states [1]. Since topological states cannot be characterized by broken symmetry and local order parameters, we cannot use the conventional Ginzburg-Landau theory. When nonAbelian topological states are involved, the transitions that are currently understood are essentially all equivalent to the transition between weak and strong-paired BCS states [2,3]. Over the last ten years, while there has been much work on the subject, there has not been another quantum phase transition in a physically realizable system, involving a non-Abelian phase, for which we can answer the most basic questions of whether the transition can be continuous and what the critical theory is. Here we present an additional example in the context of fractional quantum Hall (FQH) systems.The quasiparticle excitations in FQH states carry fractional statistics and fractional charge [1]. In particular, in a (ppq) bilayer FQH state [1,4], there is a type of excitation, called a fractional exciton (f-exciton), which is a bound state of a quasiparticle in one layer and an oppositely charged quasihole in the other layer. It carries fractional statistics. As we increase the repulsion between the electrons in the two layers, the energy gap of the f-exciton will be reduced; when it is reduced to zero, the f-exciton will condense and drive a phase transition. When the anyon number has only a mod n conservation, this can even lead to a non-Abelian FQH state [2], yet little is known about "anyon condensation" [5][6][7][8]. A better understanding of these phase transitions may aid the quest for experimental detection of non-Abelian FQH states, because one side of the transition -in our case the (330) state at ν = 2/3 -can be accessed experimentally [9,10]. The results of this paper suggest a new way of experimentally tuning to a non-Abelian state in bilayer FQH states, similar to the transition from the (331) state to the Moore-Read Pfaffian at ν = 1/2 [2, 3, 11].In the (ppq) state, when the energy gap of the f-exciton at k = 0 is reduced to zero, the f-exciton will condense [2]. The transition can be described by the φ = 0 → φ = 0 transition in a Ginzburg-Landau theory with a Chern-where θ is the statistical angle of the f-exciton. Suc...

show abstract

“…Based on general considerations, 12 we expect the following regarding the topological quantum numbers of such phases. Upon condensation of j, quasiparticles that differed from each other by fusion with j become topologically equivalent.…”

Section: Slave Ising Descriptionmentioning

confidence: 99%

“…This class of phase transitions are induced by boson condensation described by the standard AndersonHiggs mechanism of "gauge symmetry" breaking. 11,12 But there exist more general classes of topological phases described by pattern of zeros, [13][14][15][16] Z n vertex algera, [17][18][19] and/or string-net condensates. 20 The above picture of topological phase transitions is clearly incomplete.…”

mentioning

confidence: 99%

Phase transitions inZNgauge theory and twistedZNtopological phases

Barkeshli

Wen

2012

Phys. Rev. B

View full text Add to dashboard Cite

We find a series of non-Abelian topological phases that are separated from the deconfined phase of ZN gauge theory by a continuous quantum phase transition. These non-Abelian states, which we refer to as the "twisted" ZN states, are described by a recently studied U (1) × U (1) ⋊ Z2 ChernSimons (CS) field theory. The U (1) × U (1) ⋊ Z2 CS theory provides a way of gauging the global Z2 electric-magnetic symmetry of the Abelian ZN phases, yielding the twisted ZN states. We introduce a parton construction to describe the Abelian ZN phases in terms of integer quantum Hall states, which then allows us to obtain the non-Abelian states from a theory of Z2 fractionalization. The non-Abelian twisted ZN states do not have topologically protected gapless edge modes and, for N > 2, break time-reversal symmetry.

show abstract

Condensate-induced transitions between topologically ordered phases

Cited by 283 publications

References 113 publications

Ground-State Degeneracy of Topological Phases on Open Surfaces

Ground-State Degeneracy of Topological Phases on Open Surfaces

Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States

Phase transitions inZNgauge theory and twistedZNtopological phases

Contact Info

Product

Resources

About