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

Chinese Physics B

Phase transition in bilayer quantum Hall system with opposite magnetic field

Ke 珂 Yang 杨

Published Jul 11, 2023• 5 citations
Publisher

Abstract

We construct a mapped bilayer quantum Hall system to realize the proposal that two nearly flatbands have opposite Chern numbers. For the C = ±1 case, the two Landau levels of the bilayer experience opposite magnetic fields. We consider a mapped bilayer quantum Hall system at total filling ν t = 1 2 + 1 2 where the intralayer interaction is repulsive and the interlayer interaction is attractive. We take exact diagonalization (ED) calculations on a torus to study the phase transition when the separation distance d/lB is driven. The critical point at d c/lB = 0.68 is characterized by a collapse of degeneracy and a crossing of energy levels. In the region d/lB < d c/lB , the states of each level are highly degenerate. The pair-correlation function indicates electrons with opposite pseudo-spins are strong correlated at r = 0. We find an exciton stripe phase composed of bound pairs. The ferromagnetic ground state is destroyed by the strong effective attractive potential. An electron composite-Fermion (eCF) and a hole composite Fermion (hCF) are tightly bound. In the region d/lB > d c/lB , a crossover from the d → d c limit to the large d limit is observed. The electron and hole composite Fermion liquids (CFL) are realized by composite Fermions (CF) which attach opposite fluxes, respectively.

DOI
10.1088/1674-1056/ace61d

Related papers

Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances

Zheng Zhu, Liang Fu, D. N. Sheng

We study the phase diagram of quantum Hall bilayer systems with total filing ν_{T}=1/2+1/2 of the lowest Landau level as a function of layer distances d. Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small d, a composite Fermi liquid at large d, and an intermediate phase for 1.1<d/l_{B}<1.8 (l_{B} is the magnetic length). The transition from the exciton superfluid to the intermediate phase is identified by (i) a dramatic change in the Berry curvature of the ground state under twisted boundary conditions on the two layers and (ii) an energy level crossing of the first excited state. The transition from the intermediate phase to the composite Fermi liquid is identified by the vanishing of the exciton superfluid stiffness. Furthermore, from our finite-size study, the energy cost of transferring one electron between the layers shows an even-odd effect and possibly extrapolates to a finite value in the thermodynamic limit, indicating the enhanced intralayer correlation. Our identification of an intermediate phase and its distinctive features shed new light on the theoretical understanding of the quantum Hall bilayer system at total filling ν_{T}=1.

arXiv:1703.08463•Physical Review Letters•Oct 23, 2017•23 citations

DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene

Paul Myles Eugenio, Ceren B. Dağ

Strong interactions between electrons occupying bands of opposite (or like) topological quantum numbers (Chern =\pm1 = ± 1 ), and with flat dispersion, are studied by using lowest Landau level (LLL) wavefunctions. More precisely, we determine the ground states for two scenarios at half-filling: (i) LLL’s with opposite sign of magnetic field, and therefore opposite Chern number; and (ii) LLL’s with the same magnetic field. In the first scenario – which we argue to be a toy model inspired by the chirally symmetric continuum model for twisted bilayer graphene – the opposite Chern LLL’s are Kramer pairs, and thus there exists time-reversal symmetry ( \mathbb{Z}_2 ℤ 2 ). Turning on repulsive interactions drives the system to spontaneously break time-reversal symmetry – a quantum anomalous Hall state described by one particle per LLL orbital, either all positive Chern |{++\cdots+}\rangle | + + ⋯ + ⟩ or all negative |{--\cdots-}\rangle | − − ⋯ − ⟩ . If instead, interactions are taken between electrons of like-Chern number, the ground state is an SU(2) S U ( 2 ) ferromagnet, with total spin pointing along an arbitrary direction, as with the \nu=1 ν = 1 spin- \frac{1}{2} 1 2 quantum Hall ferromagnet. The ground states and some of their excitations for both of these scenarios are argued analytically, and further complimented by density matrix renormalization group (DMRG) and exact diagonalization.

arXiv:2004.10363•SciPost Physics Core•Dec 9, 2020•28 citations

Meron deconfinement in the quantum Hall bilayer at intermediate distances

Milica V. Milovanović, Edib Dobardžić, Zlatko Papić

Quantum Hall bilayer phase diagram with respect to interlayer distance bears a remarkable similarity with phase diagrams of strongly correlated systems as a function of doping, with magnetic ordering on the one end and Fermi-liquid-like behavior on the other. Moreover, it has been suggested [Phys. Rev. Lett. 101, 176803 (2008)] that a BCS correlated state of composite fermions with $p$-wave pairing may exist in the intermediate region. In the same region, an exact diagonalization study in the torus geometry [Phys. Rev. B 69, 045319 (2004)] pointed out the existence of state(s) with pseudospin spiraling order. Here we reconcile these two descriptions of the intermediate state by considering the underlying bosonic representation of the composite fermion paired state in the long-distance limit, and by performing extensive exact diagonalizations on the torus. We argue that the spiraling states belong to the manifold of degenerate ground state(s), and are a consequence of Bose condensation of the quasiparticles (with critical algebraic correlations) at nonzero momenta in the two pseudospin states. The spiraling states, generated in this way as spin textures, can be identified with meron-antimeron constructions. Thus, merons---the fractionally charged vortex excitations of the $\mathit{XY}$ magnetically ordered state---constitute some of the topological sectors. It follows that merons are deconfined in the intermediate state, and allow for a smooth transition between the magnetically ordered and Fermi-liquid-like phases, in which they are bound in pairs.

arXiv:1509.01921•Physical Review B•Nov 30, 2015•18 citations

Evolution between quantum Hall and conducting phases: Simple models and some results

Zhihuan Dong, T. Senthil

Quantum many-particle systems in which the kinetic energy, strong correlations, and band topology are all-important pose an interesting and topical challenge. Here we introduce and study particularly simple models where all of these elements are present. We consider interacting quantum particles in two dimensions in a strong magnetic field such that the Hilbert space is restricted to the lowest Landau level (LLL). This is the familiar quantum Hall regime with rich physics determined by particle filling and statistics. A periodic potential with a unit cell enclosing one flux quantum broadens the LLL into a Chern band with a finite bandwidth. The states obtained in the quantum Hall regime evolve into conducting states in the limit of large bandwidth. We study this evolution in detail for the specific case of bosons at filling factor $\ensuremath{\nu}=1$. In the quantum Hall regime, the ground state at this filling is a gapped quantum hall state (the ``bosonic Pfaffian''), which may be viewed as descending from a (bosonic) composite Fermi liquid. At large bandwidth, the ground state is a bosonic superfluid. We show how both phases and their evolution can be described within a single theoretical framework based on a LLL composite fermion construction. Building on our previous work on the bosonic composite Fermi liquid, we show that the evolution into the superfluid can be usefully described by a noncommutative quantum field theory in a periodic potential.

arXiv:2107.06911•Physical review. B./Physical review. B•Feb 1, 2022•6 citations

Numeric and Analytic Investigation on Phase Diagrams and Phasetransitions of the ν = 2/3 Bilayer Fractional Quantum Hall Systems

Yangdong Zheng, T. Sorita

The phase diagrams and phase transitions of a typical bilayer fractional quantum Hall (QH) system with filling factor ν = 2/3 at the layer balanced point are investigated theoretically by finite size exact-diagonalization calculations and an exactly solvable model. We find some basic features essentially different from the bilayer integer QH systems at ν = 2, reflecting the special characteristics of the fractional QH systems. The degeneracy of the ground states occurs depending on the difference between intralayer and interlayer Coulomb energies, when interlayer tunneling energy (ΔSAS) gets close to zero. The continuous transitions of the finite size systems between the spin-polarized and spin-unpolarized phases are determined by the competition between the Zeeman energy (ΔZ) and the electron Coulomb energy, and are almost not affected by ΔSAS.

Journal of Applied Mathematics and Physics•Jan 1, 2018•0 citations

Existence of strong-pairing quantum Hall phase in bilayer cold-atom systems with dipolar interactions

Yuhui Zhang, Edward H. Rezayi, Kun Yang

We study bilayer fermionic cold-atom systems with dipolar interactions, as well as a two-component tunable pseudopotential (TCTP) model which keeps only the zeroth- and first-order Haldane pseudopotentials, at a total Landau-level filling factor of 1/2. Our numerical results on the TCTP model indicate that a Haldane-Rezayi state describes the critical point between strong and weak $d$-wave pairing quantum Hall phases. Upon further increasing the attractive zeroth-order pseudopotentials, the system transits from the strong-pairing phase to a stripe phase and then to a cluster phase (or phase separation). The dipolar interaction can be mapped onto the TCTP model in the strong-pairing phase if high-order pseudopotentials are ignored. Our numerical results show that this is indeed the case, so the strong-pairing phase exists in the cold-atom system.

arXiv:1407.7935•Physical Review B•Oct 2, 2014•12 citations
We construct a mapped bilayer quantum Hall system to realize the proposal that two nearly flatbands have opposite Chern numbers. For the C = ±1 case, the two Landau levels of the bilayer experience opposite magnetic fields. We consider a mapped bilayer quantum Hall system at total filling ν t = 1 2 + 1 2 where the intralayer interaction is repulsive and the interlayer interaction is attractive. We take exact diagonalization (ED) calculations on a torus to study the phase transition when the separation distance d/lB is driven. The critical point at d c/lB = 0.68 is characterized by a collapse of degeneracy and a crossing of energy levels. In the region d/lB < d c/lB , the states of each level are highly degenerate. The pair-correlation function indicates electrons with opposite pseudo-spins are strong correlated at r = 0. We find an exciton stripe phase composed of bound pairs. The ferromagnetic ground state is destroyed by the strong effective attractive potential. An electron composite-Fermion (eCF) and a hole composite Fermion (hCF) are tightly bound. In the region d/lB > d c/lB , a crossover from the d → d c limit to the large d limit is observed. The electron and hole composite Fermion liquids (CFL) are realized by composite Fermions (CF) which attach opposite fluxes, respectively.
We study the phase diagram of quantum Hall bilayer systems with total filing ν_{T}=1/2+1/2 of the lowest Landau level as a function of layer distances d. Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small d, a composite Fermi liquid at large d, and an intermediate phase for 1.1<d/l_{B}<1.8 (l_{B} is the magnetic length). The transition from the exciton superfluid to the intermediate phase is identified by (i) a dramatic change in the Berry curvature of the ground state under twisted boundary conditions on the two layers and (ii) an energy level crossing of the first excited state. The transition from the intermediate phase to the composite Fermi liquid is identified by the vanishing of the exciton superfluid stiffness. Furthermore, from our finite-size study, the energy cost of transferring one electron between the layers shows an even-odd effect and possibly extrapolates to a finite value in the thermodynamic limit, indicating the enhanced intralayer correlation. Our identification of an intermediate phase and its distinctive features shed new light on the theoretical understanding of the quantum Hall bilayer system at total filling ν_{T}=1.
DMRG study of strongly interacting Z2\mathbb{Z}_2Z2​ flatbands: a toy model inspired by twisted bilayer graphene
Strong interactions between electrons occupying bands of opposite (or like) topological quantum numbers (Chern =\pm1 = ± 1 ), and with flat dispersion, are studied by using lowest Landau level (LLL) wavefunctions. More precisely, we determine the ground states for two scenarios at half-filling: (i) LLL’s with opposite sign of magnetic field, and therefore opposite Chern number; and (ii) LLL’s with the same magnetic field. In the first scenario – which we argue to be a toy model inspired by the chirally symmetric continuum model for twisted bilayer graphene – the opposite Chern LLL’s are Kramer pairs, and thus there exists time-reversal symmetry ( \mathbb{Z}_2 ℤ 2 ). Turning on repulsive interactions drives the system to spontaneously break time-reversal symmetry – a quantum anomalous Hall state described by one particle per LLL orbital, either all positive Chern |{++\cdots+}\rangle | + + ⋯ + ⟩ or all negative |{--\cdots-}\rangle | − − ⋯ − ⟩ . If instead, interactions are taken between electrons of like-Chern number, the ground state is an SU(2) S U ( 2 ) ferromagnet, with total spin pointing along an arbitrary direction, as with the \nu=1 ν = 1 spin- \frac{1}{2} 1 2 quantum Hall ferromagnet. The ground states and some of their excitations for both of these scenarios are argued analytically, and further complimented by density matrix renormalization group (DMRG) and exact diagonalization.
Quantum Hall bilayer phase diagram with respect to interlayer distance bears a remarkable similarity with phase diagrams of strongly correlated systems as a function of doping, with magnetic ordering on the one end and Fermi-liquid-like behavior on the other. Moreover, it has been suggested [Phys. Rev. Lett. 101, 176803 (2008)] that a BCS correlated state of composite fermions with ppp-wave pairing may exist in the intermediate region. In the same region, an exact diagonalization study in the torus geometry [Phys. Rev. B 69, 045319 (2004)] pointed out the existence of state(s) with pseudospin spiraling order. Here we reconcile these two descriptions of the intermediate state by considering the underlying bosonic representation of the composite fermion paired state in the long-distance limit, and by performing extensive exact diagonalizations on the torus. We argue that the spiraling states belong to the manifold of degenerate ground state(s), and are a consequence of Bose condensation of the quasiparticles (with critical algebraic correlations) at nonzero momenta in the two pseudospin states. The spiraling states, generated in this way as spin textures, can be identified with meron-antimeron constructions. Thus, merons---the fractionally charged vortex excitations of the XY\mathit{XY}XY magnetically ordered state---constitute some of the topological sectors. It follows that merons are deconfined in the intermediate state, and allow for a smooth transition between the magnetically ordered and Fermi-liquid-like phases, in which they are bound in pairs.
Quantum many-particle systems in which the kinetic energy, strong correlations, and band topology are all-important pose an interesting and topical challenge. Here we introduce and study particularly simple models where all of these elements are present. We consider interacting quantum particles in two dimensions in a strong magnetic field such that the Hilbert space is restricted to the lowest Landau level (LLL). This is the familiar quantum Hall regime with rich physics determined by particle filling and statistics. A periodic potential with a unit cell enclosing one flux quantum broadens the LLL into a Chern band with a finite bandwidth. The states obtained in the quantum Hall regime evolve into conducting states in the limit of large bandwidth. We study this evolution in detail for the specific case of bosons at filling factor $\ensuremath{\nu}=1$. In the quantum Hall regime, the ground state at this filling is a gapped quantum hall state (the ``bosonic Pfaffian''), which may be viewed as descending from a (bosonic) composite Fermi liquid. At large bandwidth, the ground state is a bosonic superfluid. We show how both phases and their evolution can be described within a single theoretical framework based on a LLL composite fermion construction. Building on our previous work on the bosonic composite Fermi liquid, we show that the evolution into the superfluid can be usefully described by a noncommutative quantum field theory in a periodic potential.
The phase diagrams and phase transitions of a typical bilayer fractional quantum Hall (QH) system with filling factor ν = 2/3 at the layer balanced point are investigated theoretically by finite size exact-diagonalization calculations and an exactly solvable model. We find some basic features essentially different from the bilayer integer QH systems at ν = 2, reflecting the special characteristics of the fractional QH systems. The degeneracy of the ground states occurs depending on the difference between intralayer and interlayer Coulomb energies, when interlayer tunneling energy (ΔSAS) gets close to zero. The continuous transitions of the finite size systems between the spin-polarized and spin-unpolarized phases are determined by the competition between the Zeeman energy (ΔZ) and the electron Coulomb energy, and are almost not affected by ΔSAS.
We study bilayer fermionic cold-atom systems with dipolar interactions, as well as a two-component tunable pseudopotential (TCTP) model which keeps only the zeroth- and first-order Haldane pseudopotentials, at a total Landau-level filling factor of 1/2. Our numerical results on the TCTP model indicate that a Haldane-Rezayi state describes the critical point between strong and weak ddd-wave pairing quantum Hall phases. Upon further increasing the attractive zeroth-order pseudopotentials, the system transits from the strong-pairing phase to a stripe phase and then to a cluster phase (or phase separation). The dipolar interaction can be mapped onto the TCTP model in the strong-pairing phase if high-order pseudopotentials are ignored. Our numerical results show that this is indeed the case, so the strong-pairing phase exists in the cold-atom system.