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:2405.18269 · Physical Review Letters

Continuous Transition between Bosonic Fractional Chern Insulator and Superfluid

Hongyu Lu, Han-Qing Wu, Binbin Chen, Zi Yang Meng

Published Feb 18, 2025• 4 citations
arXivHTMLPDF

Abstract

The properties of fractional Chern insulator (FCI) phases and the phase transitions between FCIs and Mott insulators in bosonic systems are well studied. The continuous transitions between FCI and superfluids (SFs), however, despite the inspiring field theoretical predictions [M. Barkeshli and J. McGreevy, Phys. Rev. B 89, 235116 (2014)PRBMDO1098-012110.1103/PhysRevB.89.235116; M. Barkeshli and J. McGreevy, Phys. Rev. B 86, 075136 (2012)PRBMDO1098-012110.1103/PhysRevB.86.075136; M. Barkeshli et al., Phys. Rev. Lett. 115, 026802 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.026802; X.-Y. Song et al., Phys. Rev. B 109, 085143 (2024)PRBMDO2469-995010.1103/PhysRevB.109.085143; and X.-Y. Song and Y.-H. Zhang, SciPost Phys. 15, 215 (2023)2542-465310.21468/SciPostPhys.15.5.215], have not been directly verified. The existing numerical results of the FCI-SF transition are either indirect or clearly first order. Here, by simply tuning the bandwidth of the Haldane honeycomb lattice model, we find direct transitions from a bosonic FCI at ν=1/2 filling of a flat Chern band to two SF states with bosons condensed at momenta M or Γ, respectively. While the FCI-SF(M) transition is first order, the FCI-SF(Γ) transition is found to be continuous, and the bipartite entanglement entropy at the critical point with the area-law scaling is consistent with the critical theories. Through finite-size criticality analysis, the obtained critical exponents β≈0.35(5) and ν≈0.62(12) are both compatible with those of the 3D XY universality class within numerical uncertainty and possibly more exotic beyond-Landau ones. This Letter thence presents a direct numerical demonstration of a continuous FCI-SF transition between a topologically ordered phase and a spontaneous continuous symmetry-breaking phase, and further indicates the zero-field bosonic FCI might be realized from a SF state by gradually flattening the dispersion of the Chern band, through the (quasi)adiabatic preparation in ultracold atom systems.

DOI
10.1103/physrevlett.134.076601

Related papers

Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold-atom model

Johannes Motruk, Frank Pollmann

We investigate the fate of hardcore bosons in a Harper-Hofstadter model which was experimentally realized by Aidelsburger et al. [Nat. Phys. 11, 162 (2015)] at half-filling of the lowest band. We discuss the stability of an emergent fractional Chern insulator (FCI) state in a finite region of the phase diagram that is separated from a superfluid state by a first-order transition when tuning the band topology following the protocol used in the experiment. Since crossing a first-order transition is unfavorable for adiabatically preparing the FCI state, we extend the model to stabilize a featureless insulating state. The transition between this phase and the topological state proves to be continuous, providing a path in parameter space along which an FCI state could be adiabatically prepared. To further corroborate this statement, we perform time-dependent DMRG calculations which demonstrate that the FCI state may indeed be reached by adiabatically tuning a simple product state.

arXiv:1707.01100•Physical review. B./Physical review. B•Oct 5, 2017•57 citations

Paired Parton Trial States for the Superfluid-Fractional Chern Insulator Transition

Tevž Lotrič, Steven H. Simon

We consider a model of hard-core bosons on a lattice half-filling a Chern band such that the system has a continuous transition between a fractional Chern insulator (FCI) and a superfluid state (SF) depending on the bandwidth to bandspacing ratio. We construct a parton-inspired trial wave function Ansatz for the ground states that has remarkably high overlap with exact diagonalization in both phases and throughout the phase transition. Our Ansatz is stable to adding some bosonic interactions beyond the on-site hard-core constraint. We confirm that the transition is well described by a projective translation symmetry-protected multiple parton bandgap closure, as has been previously predicted. However, unlike prior work, we find that our wave functions require anomalous (BCS-like) parton correlations to describe the phase transition and SF phase accurately.

arXiv:2504.20139•Physical Review Letters•Feb 12, 2026•2 citations

Continuous transition between fractional quantum Hall and superfluid states

Maissam Barkeshli, John McGreevy

We develop a theory of a direct, continuous quantum phase transition between a bosonic Laughlin fractional quantum Hall state and a superfluid, generalizing the Mott insulator to superfluid phase diagram of bosons to allow for the breaking of time-reversal symmetry. The direct transition can be protected by a spatial symmetry, and the critical theory is a pair of Dirac fermion fields coupled to an emergent Chern-Simons gauge field. The transition may be achieved in optical traps of ultracold atoms by starting with a $\ensuremath{\nu}=1/2$ bosonic Laughlin state and tuning an appropriate periodic potential to change the topology of the composite fermion band structure.

arXiv:1201.4393•Physical Review B•Jun 13, 2014•87 citations

Emergent QED$_3$ at the bosonic Laughlin state to superfluid transition

Taige Wang, Xue-Yang Song, Michael P. Zaletel +1 more

Quantum phase transitions between topologically ordered and symmetry-broken phases lie beyond Landau theory. A prime example is the conjectured continuous transition from the bosonic $ν= 1/2$ Laughlin state to a superfluid, proposed to be governed by a QED$_3$--Chern--Simons (CS) critical point whose stability remains uncertain. We study half-filled bosons in the lowest Landau level subject to a lattice potential. Infinite-cylinder DMRG reveals a single continuous Laughlin--to--superfluid transition. Adiabatic flux insertion collapses the many-body gap and exposes massless Dirac quasiparticles, while momentum-resolved correlation lengths show that three lattice-related density modes share the same critical exponent, evidencing an emergent $SO(3)$ symmetry. The joint appearance of Dirac dispersion and symmetry enlargement provides microscopic support for a stable QED$_3$--CS fixed point. Our numerical strategy also offers a blueprint for exploring Landau-forbidden transitions in fractional Chern insulators and composite Fermi liquids realised in moire and cold-atom systems.

arXiv:2507.07611•Jul 10, 2025•0 citations

Boson localization and the superfluid-insulator transition

Matthew P. A. Fisher, Peter B. Weichman, G. Grinstein +1 more

The phase diagrams and phase transitions of bosons with short-ranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluid-insulator transition induced by varying a parameter such as the density. Bosons in periodic potentials (e.g., on a lattice) at T=0 exhibit two types of phases: a superfluid phase and Mott insulating phases characterized by integer (or commensurate) boson densities, by the existence of a gap for particle-hole excitations, and by zero compressibility. Generically, the superfluid onset transition in d dimensions from a Mott insulator to superfluidity is ``ideal,'' or mean field in character, but at special multicritical points with particle-hole symmetry it is in the universality class of the (d+1)-dimensional XY model. In the presence of disorder, a third, ``Bose glass'' phase exists. This phase is insulating because of the localization effects of the randomness and analogous to the Fermi glass phase of interacting fermions in a strongly disordered potential.The Bose glass phase is characterized by a finite compressibility, no gap, but an infinite superfluid susceptibility. In the presence of disorder the transition to superfluidity is argued to occur only from the Bose glass phase, and never directly from the Mott insulator. This zero-temperature superfluid-insulator transition is studied via generalizations of the Josephson scaling relation for the superfluid density at the ordinary \ensuremath{\lambda} transition, highlighting the crucial role of quantum fluctuations. The transition is found to have a dynamic critical exponent z exactly equal to d and correlation length and order-parameter correlation exponents \ensuremath{\nu} and \ensuremath{\eta} which satisfy the bounds \ensuremath{\nu}\ensuremath{\ge}2/d and \ensuremath{\eta}\ensuremath{\le}2-d, respectively. It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension ${d}_{c}$ which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed. Many of these conclusions are verified by explicit calculations on a model of one-dimensional bosons in the presence of both random and periodic potentials. The general results are applied to experiments on $^{4}\mathrm{He}$ absorbed in porous media such as Vycor. Some measurable properties of the superfluid onset are predicted exactly [e.g., the exponent x relating the \ensuremath{\lambda} transition temperature to the zero-temperature superfluid density is found to be d/2(d-1)], while stringent bounds are placed on others. Analysis of preliminary data is consistent with these predictions.

Physical review. B, Condensed matter•Jul 1, 1989•3,511 citations

Continuous Preparation of a Fractional Chern Insulator

Maissam Barkeshli, Norman Y. Yao, Chris R. Laumann

We present evidence of a direct, continuous quantum phase transition between a Bose superfluid and the ν=1/2 fractional Chern insulator in a microscopic lattice model. In the process, we develop a detailed field theoretic description of this transition in terms of the low energy vortex dynamics. The theory explicitly accounts for the structure of lattice symmetries and predicts a Landau forbidden transition that is protected by inversion. That the transition is continuous enables the quasiadiabatic preparation of the fractional Chern insulator in nonequilibrium, quantum optical systems.

arXiv:1407.7034•Physical Review Letters•Jul 7, 2015•45 citations
The properties of fractional Chern insulator (FCI) phases and the phase transitions between FCIs and Mott insulators in bosonic systems are well studied. The continuous transitions between FCI and superfluids (SFs), however, despite the inspiring field theoretical predictions [M. Barkeshli and J. McGreevy, Phys. Rev. B 89, 235116 (2014)PRBMDO1098-012110.1103/PhysRevB.89.235116; M. Barkeshli and J. McGreevy, Phys. Rev. B 86, 075136 (2012)PRBMDO1098-012110.1103/PhysRevB.86.075136; M. Barkeshli et al., Phys. Rev. Lett. 115, 026802 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.026802; X.-Y. Song et al., Phys. Rev. B 109, 085143 (2024)PRBMDO2469-995010.1103/PhysRevB.109.085143; and X.-Y. Song and Y.-H. Zhang, SciPost Phys. 15, 215 (2023)2542-465310.21468/SciPostPhys.15.5.215], have not been directly verified. The existing numerical results of the FCI-SF transition are either indirect or clearly first order. Here, by simply tuning the bandwidth of the Haldane honeycomb lattice model, we find direct transitions from a bosonic FCI at ν=1/2 filling of a flat Chern band to two SF states with bosons condensed at momenta M or Γ, respectively. While the FCI-SF(M) transition is first order, the FCI-SF(Γ) transition is found to be continuous, and the bipartite entanglement entropy at the critical point with the area-law scaling is consistent with the critical theories. Through finite-size criticality analysis, the obtained critical exponents β≈0.35(5) and ν≈0.62(12) are both compatible with those of the 3D XY universality class within numerical uncertainty and possibly more exotic beyond-Landau ones. This Letter thence presents a direct numerical demonstration of a continuous FCI-SF transition between a topologically ordered phase and a spontaneous continuous symmetry-breaking phase, and further indicates the zero-field bosonic FCI might be realized from a SF state by gradually flattening the dispersion of the Chern band, through the (quasi)adiabatic preparation in ultracold atom systems.
We investigate the fate of hardcore bosons in a Harper-Hofstadter model which was experimentally realized by Aidelsburger et al. [Nat. Phys. 11, 162 (2015)] at half-filling of the lowest band. We discuss the stability of an emergent fractional Chern insulator (FCI) state in a finite region of the phase diagram that is separated from a superfluid state by a first-order transition when tuning the band topology following the protocol used in the experiment. Since crossing a first-order transition is unfavorable for adiabatically preparing the FCI state, we extend the model to stabilize a featureless insulating state. The transition between this phase and the topological state proves to be continuous, providing a path in parameter space along which an FCI state could be adiabatically prepared. To further corroborate this statement, we perform time-dependent DMRG calculations which demonstrate that the FCI state may indeed be reached by adiabatically tuning a simple product state.
We consider a model of hard-core bosons on a lattice half-filling a Chern band such that the system has a continuous transition between a fractional Chern insulator (FCI) and a superfluid state (SF) depending on the bandwidth to bandspacing ratio. We construct a parton-inspired trial wave function Ansatz for the ground states that has remarkably high overlap with exact diagonalization in both phases and throughout the phase transition. Our Ansatz is stable to adding some bosonic interactions beyond the on-site hard-core constraint. We confirm that the transition is well described by a projective translation symmetry-protected multiple parton bandgap closure, as has been previously predicted. However, unlike prior work, we find that our wave functions require anomalous (BCS-like) parton correlations to describe the phase transition and SF phase accurately.
We develop a theory of a direct, continuous quantum phase transition between a bosonic Laughlin fractional quantum Hall state and a superfluid, generalizing the Mott insulator to superfluid phase diagram of bosons to allow for the breaking of time-reversal symmetry. The direct transition can be protected by a spatial symmetry, and the critical theory is a pair of Dirac fermion fields coupled to an emergent Chern-Simons gauge field. The transition may be achieved in optical traps of ultracold atoms by starting with a $\ensuremath{\nu}=1/2$ bosonic Laughlin state and tuning an appropriate periodic potential to change the topology of the composite fermion band structure.
Emergent QED3_33​ at the bosonic Laughlin state to superfluid transition
Quantum phase transitions between topologically ordered and symmetry-broken phases lie beyond Landau theory. A prime example is the conjectured continuous transition from the bosonic ν=1/2ν= 1/2ν=1/2 Laughlin state to a superfluid, proposed to be governed by a QED3_33​--Chern--Simons (CS) critical point whose stability remains uncertain. We study half-filled bosons in the lowest Landau level subject to a lattice potential. Infinite-cylinder DMRG reveals a single continuous Laughlin--to--superfluid transition. Adiabatic flux insertion collapses the many-body gap and exposes massless Dirac quasiparticles, while momentum-resolved correlation lengths show that three lattice-related density modes share the same critical exponent, evidencing an emergent SO(3)SO(3)SO(3) symmetry. The joint appearance of Dirac dispersion and symmetry enlargement provides microscopic support for a stable QED3_33​--CS fixed point. Our numerical strategy also offers a blueprint for exploring Landau-forbidden transitions in fractional Chern insulators and composite Fermi liquids realised in moire and cold-atom systems.
The phase diagrams and phase transitions of bosons with short-ranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluid-insulator transition induced by varying a parameter such as the density. Bosons in periodic potentials (e.g., on a lattice) at T=0 exhibit two types of phases: a superfluid phase and Mott insulating phases characterized by integer (or commensurate) boson densities, by the existence of a gap for particle-hole excitations, and by zero compressibility. Generically, the superfluid onset transition in d dimensions from a Mott insulator to superfluidity is ``ideal,'' or mean field in character, but at special multicritical points with particle-hole symmetry it is in the universality class of the (d+1)-dimensional XY model. In the presence of disorder, a third, ``Bose glass'' phase exists. This phase is insulating because of the localization effects of the randomness and analogous to the Fermi glass phase of interacting fermions in a strongly disordered potential.The Bose glass phase is characterized by a finite compressibility, no gap, but an infinite superfluid susceptibility. In the presence of disorder the transition to superfluidity is argued to occur only from the Bose glass phase, and never directly from the Mott insulator. This zero-temperature superfluid-insulator transition is studied via generalizations of the Josephson scaling relation for the superfluid density at the ordinary \ensuremath{\lambda} transition, highlighting the crucial role of quantum fluctuations. The transition is found to have a dynamic critical exponent z exactly equal to d and correlation length and order-parameter correlation exponents \ensuremath{\nu} and \ensuremath{\eta} which satisfy the bounds \ensuremath{\nu}\ensuremath{\ge}2/d and \ensuremath{\eta}\ensuremath{\le}2-d, respectively. It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension dc{d}_{c}dc​ which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed. Many of these conclusions are verified by explicit calculations on a model of one-dimensional bosons in the presence of both random and periodic potentials. The general results are applied to experiments on 4He^{4}\mathrm{He}4He absorbed in porous media such as Vycor. Some measurable properties of the superfluid onset are predicted exactly [e.g., the exponent x relating the \ensuremath{\lambda} transition temperature to the zero-temperature superfluid density is found to be d/2(d-1)], while stringent bounds are placed on others. Analysis of preliminary data is consistent with these predictions.
We present evidence of a direct, continuous quantum phase transition between a Bose superfluid and the ν=1/2 fractional Chern insulator in a microscopic lattice model. In the process, we develop a detailed field theoretic description of this transition in terms of the low energy vortex dynamics. The theory explicitly accounts for the structure of lattice symmetries and predicts a Landau forbidden transition that is protected by inversion. That the transition is continuous enables the quasiadiabatic preparation of the fractional Chern insulator in nonequilibrium, quantum optical systems.