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:cond-mat/0005014 · Physical review. B, Condensed matter

Transition between compressible and incompressible states in infinite-layer fractional quantum Hall systems

Sei Suzuki, Yoshio Kuramoto

Published Jul 15, 2000• 5 citations
arXivHTMLPDF

Abstract

Possible phase transitions between incompressible quantum Hall states and compressible three-dimensional states are discussed for infinite-layer electron systems in strong magnetic field. By variational Monte Carlo calculation, relative stability of some trial states is studied. If the interlayer distance is large enough, the Laughlin state is stabilized for the Landau level filling $\ensuremath{\nu}=1/3$ of each layer. When the interlayer distance is comparable to the magnetic length, the Laughlin state becomes unstable against a different fractional quantum Hall state with interlayer correlation, and/or against a three-dimensional compressible state. It is discussed how the quantum phase transition between them can be controlled in actual systems.

DOI
10.1103/physrevb.62.1921

Related papers

Third-order quantum phase transitions of bosonic non-Abelian fractional quantum Hall states

Kai‐Wen Huang, Xinggang Hou, Ying-Hai Wu

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 $ν=1/2$ or $1$ 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 $ν=1/2$ Laughlin states to the Moore-Read state in bilayer systems; (2) from one $ν=1/2$ Laughlin state plus one $ν=1$ Moore-Read state to the Read-Rezayi $\mathbb{Z}_{3}$ state in bilayer systems; (3) from three decoupled $ν=1/2$ Laughlin states to the Read-Rezayi $\mathbb{Z}_{3}$ 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.

arXiv:2509.17113•Sep 21, 2025•0 citations

Non-Abelian interlayer coherent fractional quantum Hall states

Xinggang Hou, Lei Wang, Ying-Hai Wu

We study non-Abelian fractional quantum Hall state in double layer systems at total filling factor $1/2$. Recent progresses in two-dimensional van der Waals materials made it possible to explore the regime with very small interlayer distance. Numerical calculations suggests interlayer phase coherence can develop between the layers such that the electrons may redistribute between them without changing the Hall response. It corresponds to spontaneous breaking of the U(1) symmetry associated with the particle number difference in the layers. This state manifests itself as superfluid in counterflow measurement and has characteristic Hall response when current is passed through one layer and voltages in both layers are measured. As the interlayer distance increases, a phase transition to the Halperin 331 state occurs. We also discuss similar physics for bosonic systems with specially designed interactions.

arXiv:2501.06041•Jan 10, 2025•0 citations

Quantized Hall effect and quantum phase transitions in coupled two-layer electron systems

Song He, S. Das Sarma, X. C. Xie

We study the nature of the many-body electron states (and quantum phase transitions between them) in a double-quantum-well structure under a strong external magnetic field as a function of the materials parameters that define the two-layer system, namely, the thickness of individual layers, the separation between them, the individual well potentials confining the electrons, and the potential barrier between them. Motivated by two recent experiments, we consider two different situations, one with (almost) no quantum tunneling between the wells, and the other with substantial interwell quantum tunneling. We use the spherical system finite-size exact diagonalization technique for our calculations. By calculating the overlap of our exact small-system numerical wave functions with various (postulated) analytic wave functions, we comment on the nature of the incompressibility for various Landau-level filling factors (\ensuremath{\nu}). We investigate, in particular details, the possibility of \ensuremath{\nu}=1/2 (i.e., 1/4 average occupancy in each well), and, 1 (i.e., 1/2 occupancy in each well) incompressible states where \ensuremath{\nu} is the total filling factor for the system. We also provide results for the \ensuremath{\nu}=2/3 situation. Our conclusion, based on our use of realistic system parameters in our calculations, is that in both the recent experimental realizations of the \ensuremath{\nu}=1/2 fractional quantum Hall effect, the relevant ground state is the so-called ``331'' state which is stabilized by the competition between intrawell and interwell electron-electron correlations.We calculate for various double-quantum-well structural parameters and magnetic fields the \ensuremath{\nu}=1/2 excitation spectra and the energy gaps, and compare it with the recent experimental data, obtaining excellent quantitative agreement. We provide a detailed quantum phase diagram for the \ensuremath{\nu}=1 state as a function of the interwell Coulomb interaction and the symmetric-antisymmetric single-particle gap, and find that the \ensuremath{\nu}=1 quantum Hall effect observed in the two recent experiments, in contrast to the \ensuremath{\nu}=1/2 effect, belongs in some sense to two different universality classes. We also predict the existence of a reentrant \ensuremath{\nu}=1 quantum Hall effect in double-quantum-well systems.

Physical review. B, Condensed matter•Feb 15, 1993•145 citations

Finite-Size Studies of the Incompressible State of the Fractionally Quantized Hall Effect and its Excitations

F. D. M. Haldane, Edward H. Rezayi

The incompressible states of interacting two-dimensional electrons in a high magnetic field has been studied by finite-size calculations in the spherical geometry. The excitation spectrum at $\frac{1}{3}$ Landau-level filling is described, and the Laughlin-Jastrow character of the Coulomb-interaction ground state is unambiguously confirmed. As the interaction is varied, a transition to a gapless compressible state is observed.

Physical Review Letters•Jan 21, 1985•448 citations

Three-dimensional Foliated Fractional Quantum Hall Phases

Sahana Das, Navketan Batra, Andrea Kouta Dagnino +4 more

Foliated topological orders in three dimensions are layered systems in which anyons are free to move within a layer but cannot hop between them. A simple model with such a phase is a stack of decoupled two-dimensional electron gases in a strong magnetic field, each in the same fractional quantum Hall state. By focusing on the case of filling $ν=1/3$ of the lowest Landau level in each layer, we show that (i) the limit of decoupled Laughlin states is stable upon introducing interlayer interactions and (ii) the system can enter a spontaneously layer-trimerized foliated non-Abelian Fibonacci phase. We support our claims by numerical exact diagonalization of up to 10 layers as well as perturbative analytical calculations. Specifically, we show that the foliated Fibonacci phase exists in the 9-layer system with pseudopotential interactions within and between neighboring layers. We identify the phase via quasihole counting and by calculating the overlap with a model wave function which we derive from the associated conformal field theory. Our numerical results suggest the possibility of realizing these phases in layered van der Waals crystals in strong magnetic fields, as well as in multilayer heterostructures.

arXiv:2606.19426•Jun 17, 2026•0 citations

Strong Correlation to Weak Correlation Phase Transition in Bilayer Quantum Hall Systems

John Schliemann, S. M. Girvin, Allan H. MacDonald

At small layer separations, the ground state of a nu = 1 bilayer quantum Hall system exhibits spontaneous interlayer phase coherence. The evolution of this state with increasing layer separation d has been a matter of controversy. We report on small system exact diagonalization calculations which suggest that a single-phase transition, likely of first order, separates incompressible states with strong interlayer correlations from compressible states with weak interlayer correlations. We find a dependence of the phase boundary on d and interlayer tunneling amplitude that is in very good agreement with recent experiments.

arXiv:cond-mat/0006309•Physical Review Letters•Feb 26, 2001•96 citations
Possible phase transitions between incompressible quantum Hall states and compressible three-dimensional states are discussed for infinite-layer electron systems in strong magnetic field. By variational Monte Carlo calculation, relative stability of some trial states is studied. If the interlayer distance is large enough, the Laughlin state is stabilized for the Landau level filling \ensuremathν=1/3\ensuremath{\nu}=1/3\ensuremathν=1/3 of each layer. When the interlayer distance is comparable to the magnetic length, the Laughlin state becomes unstable against a different fractional quantum Hall state with interlayer correlation, and/or against a three-dimensional compressible state. It is discussed how the quantum phase transition between them can be controlled in actual systems.
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.
We study non-Abelian fractional quantum Hall state in double layer systems at total filling factor 1/21/21/2. Recent progresses in two-dimensional van der Waals materials made it possible to explore the regime with very small interlayer distance. Numerical calculations suggests interlayer phase coherence can develop between the layers such that the electrons may redistribute between them without changing the Hall response. It corresponds to spontaneous breaking of the U(1) symmetry associated with the particle number difference in the layers. This state manifests itself as superfluid in counterflow measurement and has characteristic Hall response when current is passed through one layer and voltages in both layers are measured. As the interlayer distance increases, a phase transition to the Halperin 331 state occurs. We also discuss similar physics for bosonic systems with specially designed interactions.
We study the nature of the many-body electron states (and quantum phase transitions between them) in a double-quantum-well structure under a strong external magnetic field as a function of the materials parameters that define the two-layer system, namely, the thickness of individual layers, the separation between them, the individual well potentials confining the electrons, and the potential barrier between them. Motivated by two recent experiments, we consider two different situations, one with (almost) no quantum tunneling between the wells, and the other with substantial interwell quantum tunneling. We use the spherical system finite-size exact diagonalization technique for our calculations. By calculating the overlap of our exact small-system numerical wave functions with various (postulated) analytic wave functions, we comment on the nature of the incompressibility for various Landau-level filling factors (\ensuremath{\nu}). We investigate, in particular details, the possibility of \ensuremath{\nu}=1/2 (i.e., 1/4 average occupancy in each well), and, 1 (i.e., 1/2 occupancy in each well) incompressible states where \ensuremath{\nu} is the total filling factor for the system. We also provide results for the \ensuremath{\nu}=2/3 situation. Our conclusion, based on our use of realistic system parameters in our calculations, is that in both the recent experimental realizations of the \ensuremath{\nu}=1/2 fractional quantum Hall effect, the relevant ground state is the so-called ``331'' state which is stabilized by the competition between intrawell and interwell electron-electron correlations.We calculate for various double-quantum-well structural parameters and magnetic fields the \ensuremath{\nu}=1/2 excitation spectra and the energy gaps, and compare it with the recent experimental data, obtaining excellent quantitative agreement. We provide a detailed quantum phase diagram for the \ensuremath{\nu}=1 state as a function of the interwell Coulomb interaction and the symmetric-antisymmetric single-particle gap, and find that the \ensuremath{\nu}=1 quantum Hall effect observed in the two recent experiments, in contrast to the \ensuremath{\nu}=1/2 effect, belongs in some sense to two different universality classes. We also predict the existence of a reentrant \ensuremath{\nu}=1 quantum Hall effect in double-quantum-well systems.
The incompressible states of interacting two-dimensional electrons in a high magnetic field has been studied by finite-size calculations in the spherical geometry. The excitation spectrum at 13\frac{1}{3}31​ Landau-level filling is described, and the Laughlin-Jastrow character of the Coulomb-interaction ground state is unambiguously confirmed. As the interaction is varied, a transition to a gapless compressible state is observed.
Foliated topological orders in three dimensions are layered systems in which anyons are free to move within a layer but cannot hop between them. A simple model with such a phase is a stack of decoupled two-dimensional electron gases in a strong magnetic field, each in the same fractional quantum Hall state. By focusing on the case of filling ν=1/3ν=1/3ν=1/3 of the lowest Landau level in each layer, we show that (i) the limit of decoupled Laughlin states is stable upon introducing interlayer interactions and (ii) the system can enter a spontaneously layer-trimerized foliated non-Abelian Fibonacci phase. We support our claims by numerical exact diagonalization of up to 10 layers as well as perturbative analytical calculations. Specifically, we show that the foliated Fibonacci phase exists in the 9-layer system with pseudopotential interactions within and between neighboring layers. We identify the phase via quasihole counting and by calculating the overlap with a model wave function which we derive from the associated conformal field theory. Our numerical results suggest the possibility of realizing these phases in layered van der Waals crystals in strong magnetic fields, as well as in multilayer heterostructures.
At small layer separations, the ground state of a nu = 1 bilayer quantum Hall system exhibits spontaneous interlayer phase coherence. The evolution of this state with increasing layer separation d has been a matter of controversy. We report on small system exact diagonalization calculations which suggest that a single-phase transition, likely of first order, separates incompressible states with strong interlayer correlations from compressible states with weak interlayer correlations. We find a dependence of the phase boundary on d and interlayer tunneling amplitude that is in very good agreement with recent experiments.