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arXiv:2302.03703 · Physical Review X

XY* Transition and Extraordinary Boundary Criticality from Fractional Exciton Condensation in Quantum Hall Bilayer

Ya-Hui Zhang, Zheng Zhu, Ashvin Vishwanath

Published Sep 5, 2023• 15 citations
arXivHTMLPDF

Abstract

XY* transitions represent one of the simplest examples of unconventional quantum criticality, in which fractionally charged excitations condense into a superfluid and display novel features that combine quantum criticality and fractionalization.Nevertheless, their experimental realization is challenging.Here we propose to study the XY* transition in quantum Hall bilayers at filling ðν 1 ; ν 2 Þ ¼ ð 1 3 ; 2 3 Þ where the exciton condensate (EC) phase plays the role of the superfluid.Supported by exact diagonalization calculation, we argue that there is a continuous transition between an EC phase at small bilayer separation to a pair of decoupled fractional quantum Hall states at large separation.The transition is driven by condensation of a fractional exciton, a bound state of a Laughlin quasiparticle and quasihole, and is in the XY* universality class.The fractionalization is manifested by unusual properties including a large anomalous exponent and fractional universal conductivity, which can be conveniently measured through interlayer tunneling and counterflow transport, respectively.We also show that the edge is likely to realize the newly predicted extraordinary log boundary criticality.Our work highlights the promise of quantum Hall bilayers as an ideal platform for exploring exotic bulk and boundary critical behaviors that are amenable to immediate experimental exploration in dual-gated bilayer systems.The XY* critical theory can be generalized to a bilayer system with an arbitrary Abelian state in one layer and its particle-hole partner in the other layer.Therefore, we anticipate many distinct XY* transitions corresponding to the different Laughlin states and Jain sequences in the single-layer case.

DOI
10.1103/physrevx.13.031023

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XY* transitions represent one of the simplest examples of unconventional quantum criticality, in which fractionally charged excitations condense into a superfluid and display novel features that combine quantum criticality and fractionalization.Nevertheless, their experimental realization is challenging.Here we propose to study the XY* transition in quantum Hall bilayers at filling ðν 1 ; ν 2 Þ ¼ ð 1 3 ; 2 3 Þ where the exciton condensate (EC) phase plays the role of the superfluid.Supported by exact diagonalization calculation, we argue that there is a continuous transition between an EC phase at small bilayer separation to a pair of decoupled fractional quantum Hall states at large separation.The transition is driven by condensation of a fractional exciton, a bound state of a Laughlin quasiparticle and quasihole, and is in the XY* universality class.The fractionalization is manifested by unusual properties including a large anomalous exponent and fractional universal conductivity, which can be conveniently measured through interlayer tunneling and counterflow transport, respectively.We also show that the edge is likely to realize the newly predicted extraordinary log boundary criticality.Our work highlights the promise of quantum Hall bilayers as an ideal platform for exploring exotic bulk and boundary critical behaviors that are amenable to immediate experimental exploration in dual-gated bilayer systems.The XY* critical theory can be generalized to a bilayer system with an arbitrary Abelian state in one layer and its particle-hole partner in the other layer.Therefore, we anticipate many distinct XY* transitions corresponding to the different Laughlin states and Jain sequences in the single-layer case.
We study continuous quantum phase transitions that can occur in bilayer fractional quantum Hall (FQH) systems as the interlayer tunneling and interlayer repulsion are tuned. We introduce a slave-particle gauge theory description of a series of continuous transitions from the (ppq)(ppq)(ppq) Abelian bilayer states to a set of non-Abelian FQH states, which we dub orbifold FQH states, of which the Z4{Z}_{4}Z4​ parafermion (Read-Rezayi) state is a special case. This provides an example in which Z2{Z}_{2}Z2​ electron fractionalization leads to non-Abelian topological phases. The naive ``ideal'' wave functions and ideal Hamiltonians associated with these orbifold states do not in general correspond to incompressible phases but, instead, lie at a nearby critical point. We discuss this unusual situation from the perspective of the pattern-of-zeros/vertex algebra frameworks and discuss implications for the conceptual foundations of these approaches. Due to the proximity in the phase diagram of these non-Abelian states to the (ppq)(ppq)(ppq) bilayer states, they may be experimentally relevant, both as candidates for describing the plateaus in single-layer systems at filling fractions 8/38/38/3 and 12/512/512/5 and as a way to tune to non-Abelian states in double-layer or wide quantum wells.
Quantum Hall bilayers have proven to be an inexhaustible platform for emerging exotic states and novel phase transitions in the strongly correlated arena. Here, the authors study coupled quantum Hall bilayers at half-filled first excited Landau levels by varying the layer distance. The authors find a continuous transition between the exciton superfluid phase and two copies of the Moore-Read state. This transition breaks symmetry and changes topology simultaneously, providing an exotic example of a quantum phase transition beyond the Landau paradigm.
We study phase transitions in bilayer and trilayer bosonic quantum Hall systems. In the absence of interlayer tunneling and interaction, each layer is chosen to have filling factor ν=1/2ν=1/2ν=1/2 or 111 to realize the Laughlin state or the Moore-Read state. By tuning interlayer tunneling and/or interaction, multiple phases can be generated. In the absence of interlayer interaction, three phase transitions appear when interlayer tunneling becomes sufficiently strong: (1) from two decoupled ν=1/2ν=1/2ν=1/2 Laughlin states to the Moore-Read state in bilayer systems; (2) from one ν=1/2ν=1/2ν=1/2 Laughlin state plus one ν=1ν=1ν=1 Moore-Read state to the Read-Rezayi Z3\mathbb{Z}_{3}Z3​ state in bilayer systems; (3) from three decoupled ν=1/2ν=1/2ν=1/2 Laughlin states to the Read-Rezayi Z3\mathbb{Z}_{3}Z3​ state in trilayer systems. Numerical calculations suggest that these transitions are third-order ones. We propose non-Abelian Chern-Simons-Higgs theory to describe them. If both interlayer tunneling and interaction are present, one-component or multi-component composite fermion liquids and Jain states can be realized. This leads to intricate phase diagrams that host multiple phase transitions and possibly exotic critical points.
Deconfined quantum critical points (DQCPs) represent an unconventional class of quantum criticality beyond the Landau-Ginzburg-Wilson-Fisher paradigm. Nevertheless, both their theoretical identification and experimental realization remain challenging. Here we report compelling evidence of a DQCP in quantum Hall bilayers with half-filled n=2n=2n=2 Landau levels in each layer, based on large-scale variational uniform matrix product state (VUMPS) simulations and exact diagonalization (ED). By systematically analyzing the ground-state fidelity, low-lying energy spectra, exciton superfluid and stripe order parameters, and ground-state energy derivatives, we identify a direct and continuous quantum phase transition between two distinct symmetry-breaking phases by tuning the layer separation: an exciton superfluid phase with spontaneous U(1)U(1)U(1) symmetry breaking at small separation, and a unidirectional charge density wave with broken translational symmetry at large separation. Our results highlight quantum Hall bilayers as an ideal platform for realizing and experimentally probing DQCPs under precisely tunable interactions.
Motivated by the structure of the quasiparticle wavefunction in the composite fermion (CF) theory for fractional quantum Hall filling factor [Formula: see text] (m odd), I consider a suitable quasiparticle operator in differential form, as a modified form of Laughlin's quasiparticle operator, that reproduces quasiparticle wave function as predicted in the CF theory, without a priori assumption of the presence of CFs. I further consider the conjugate of this operator as quasihole operator for obtaining a novel quasihole wave function for 1/m state. Each of these wave functions is interpreted as expelling an electron into a different Hilbert subspace from the original Hilbert space of the Laughlin condensate while still maintaining its correlation (although changed) with the electrons in the condensate such that the expelled electron behaves as a CF with respect to the electrons in the condensate. With this interpretation, I show that the ground state wavefunctions for general states at filling fractions [Formula: see text], respectively, can be constructed as coherent superposition of n coupled Laughlin condensates and their 'conjugates', formed at different Hilbert subspaces. The corresponding wave functions, specially surprising for [Formula: see text] sequence of states, are identical with those proposed in the theory of noninteracting CFs. The states which were considered as fractional quantum Hall effect of interacting CFs, can also be treated in the same footing as for the prominent sequences of states describing as the coupled condensates among which one is a non-Laughlin condensate in a different Hilbert subspace. Further, I predict that the half filling of the lowest Landau level is a quantum critical point for phase transition between two topologically distinct phases each corresponding to a family of states: one consists of large number of coupled Laughlin condensates of filling factor 1/3 and the other corresponds to large number of coupled conjugate Laughlin condensates of filling factor 1, which may be distinguished, respectively, by the absence and presence of upstream edge modes.
We find a series of possible continuous quantum phase transitions between fractional quantum Hall 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.