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Variational study of bosonic phases in two dimensions: fractional Chern insulator, Mott insulator and superfluid

Hassan Shapourian, Bryan K. Clark

Published Dec 17, 2014• 0 citations
OpenAlex

Abstract

We numerically study the model wave-functions for a system of hard core bosons at half filling on a square lattice. The candidate wave-functions are based on the projective construction approach [1] where a boson is decomposed into two (slave) fermions, each described by a Chern insulator model. Our results confirm that the wave-functions demonstrate the following phases: the superfluid, the Mott insulator and the fractional Chern insulator. In addition, we find that the wave-functions can be continuously tuned from one phase to another by varying the parameters of slave particles. We further propose a microscopic Hamiltonian with a rich phase diagram which variationally supports all the aforementioned phases in different regimes of parameters. The critical behavior across the phase boundaries is investigated and the critical exponents are computed.

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We numerically study the model wave-functions for a system of hard core bosons at half filling on a square lattice. The candidate wave-functions are based on the projective construction approach [1] where a boson is decomposed into two (slave) fermions, each described by a Chern insulator model. Our results confirm that the wave-functions demonstrate the following phases: the superfluid, the Mott insulator and the fractional Chern insulator. In addition, we find that the wave-functions can be continuously tuned from one phase to another by varying the parameters of slave particles. We further propose a microscopic Hamiltonian with a rich phase diagram which variationally supports all the aforementioned phases in different regimes of parameters. The critical behavior across the phase boundaries is investigated and the critical exponents are computed.
We study the extended Bose-Hubbard model on the square lattice at half-filling as a function of next-nearest neighbor hopping amplitude and interaction strength. To variationally map out the phase diagram of this model, we develop a two-parameter family of wave functions based on the parton construction which can describe both topological and broken symmetry phases on equal footing. In addition, our wave functions resolve long standing issues with more conventional short-range Jastrow wave functions. Using this variational ansatz, we show that a spontaneous time-reversal symmetry-breaking fractional Chern insulator is energetically favored over a critical region between two superfluid phases. In verifying the properties of these parton wave functions we exemplify a more robust way to identify topology through the Hall conductance.
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.
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 study, using quantum Monte Carlo simulations, the bosonic Kondo-Hubbard model in a two-dimensional square lattice. We explore the phase diagram and analyze the mobility of particles and magnetic properties. At unit filling, the transition from a paramagnetic Mott insulator to a ferromagnetic superfluid appears continuous, contrary to what was predicted with mean field. For double occupation per site, both the Mott insulating and superfluid phases are ferromagnetic and the transition is still continuous. Multiband tight-binding Hamiltonians can be realized in optical lattice experiments, which offer not only the possibility of tuning the different energy scales over wide ranges, but also the option of loading the system with either fermionic or bosonic atoms.
We study the Mott transition occurring for bosonic Hubbard models in one, two, and three spatial dimensions by means of a variational wave function benchmarked by Green's function Monte Carlo calculations. We show that a very accurate variational wave function, which is constructed by applying a long-range Jastrow factor to the noninteracting boson ground state, can describe the superfluid-insulator transition in any dimensionality. Moreover, by mapping the quantum averages over such a wave function into the partition function of a classical model, important insights into the insulating phase are uncovered. Finally, the evidence in favor of anomalous scenarios for the Mott transition in two dimensions is reported whenever additional long-range repulsive interactions are added to the Hamiltonian.