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Communications in Theoretical Physics

Quantum coherence and ground-state phase transition in a four-chain Bose–Hubbard model

Ji-Guo Wang, Lin-Qi Guo, Ya-Fei Song

Published May 24, 2021• 0 citations
Publisher

Abstract

Abstract We study the quantum coherence and ground-state phase transition of a four-chain Bose–Hubbard model with the long-range interaction. In a special four-chain Bose–Hubbard model, i.e., each chain only has one optical potential, four types of the ground-state phases are discovered. The effects of the disorder, the on-site interaction and the long-range interaction on the quantum coherence are studied. For the system without the long-range interaction, the quantum coherence changes from one periodic oscillation to two periodic oscillations as the on-site interaction increases. By considering the long-range interaction, the quantum coherence goes back to one periodic oscillation again. The on-site interaction itself suppresses the quantum coherence, both the on-site interaction and long-range interaction together enhance the quantum coherence with the weak disorder. If the disorder strength is increased beyond a critical value, they start to suppress the quantum coherence. In a regular four-chain Bose–Hubbard model, i.e., each chain has many optical potentials, the ground-state phase transitions are obtained by using the cluster Gutzwiller mean-field method. Exotic ground-state phases are found, i.e., superfluid phase, integer Mott insulator phase, supersolid phase and loophole insulator phase. The combination of the loophole insulator phase and the supersolid phase expands the lobes with the half-integer filling per site for the small ratio β = t ∥ / t ⊥ .

DOI
10.1088/1572-9494/ac0427

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Abstract We study the quantum coherence and ground-state phase transition of a four-chain Bose–Hubbard model with the long-range interaction. In a special four-chain Bose–Hubbard model, i.e., each chain only has one optical potential, four types of the ground-state phases are discovered. The effects of the disorder, the on-site interaction and the long-range interaction on the quantum coherence are studied. For the system without the long-range interaction, the quantum coherence changes from one periodic oscillation to two periodic oscillations as the on-site interaction increases. By considering the long-range interaction, the quantum coherence goes back to one periodic oscillation again. The on-site interaction itself suppresses the quantum coherence, both the on-site interaction and long-range interaction together enhance the quantum coherence with the weak disorder. If the disorder strength is increased beyond a critical value, they start to suppress the quantum coherence. In a regular four-chain Bose–Hubbard model, i.e., each chain has many optical potentials, the ground-state phase transitions are obtained by using the cluster Gutzwiller mean-field method. Exotic ground-state phases are found, i.e., superfluid phase, integer Mott insulator phase, supersolid phase and loophole insulator phase. The combination of the loophole insulator phase and the supersolid phase expands the lobes with the half-integer filling per site for the small ratio β = t ∥ / t ⊥ .
The introduction of disorder in the extended Bose-Hubbard model gives rise to new glassy quantum phases, namely the Bose-glass and disordered solid phases. In this work, we present a rich phase diagram of interacting bosons in a disordered two-dimensional optical lattice, modeled by the disordered Bose-Hubbard model. We systematically probe the effect of long-range interaction truncated to the nearest neighbors and next-nearest neighbors on the phase diagram. We investigate the zero-temperature ground-state quantum phases using the single-site Gutzwiller mean-field theory. We also employ strong-coupling perturbative expansion to identify the nature of ground-state solid phases analytically. At sufficiently high disorder strength, we observe a quantum phase transition between the disordered solid and Bose-glass phases. We have investigated this transition in greater detail using cluster Gutzwiller mean-field theory to study the effect of intersite correlations which is absent in the single-site Gutzwiller mean-field theory. We have also studied this phase transition from the perspective of percolation theory.
The introduction of disorder in Bose-Hubbard model gives rise to new glassy quantum phases, namely the Bose-glass (BG) and disordered solid (DS) phases. In this work, we present the rich phase diagram of interacting bosons in disordered two-dimensional optical lattice, modelled by the disordered Bose-Hubbard model. We systematically probe the effect of long-range interaction truncated to the nearest neighbors and next-nearest neighbors on the phase diagram. We investigate the zero-temperature ground-state quantum phases using the single-site Gutzwiller mean field (SGMF) theory. We also employ strong-coupling perturbative expansion to identify the nature of ground-state solid phases analytically. At sufficiently high disorder strength, we observe a quantum phase transition between the DS and BG phases. We have investigated this transition in greater detail using cluster Gutzwiller mean field theory to study the effect of inter-site correlations which is absent in the SGMF method. We have also studied this phase transition from the perspective of percolation theory.
We present a cluster mean-field study for ground-state phase diagram and many-body dynamics of spin-1 bosons confined in a two-chain Bose–Hubbard ladder (BHL). For unbiased BHL, we find superfluid (SF) phase and integer filling Mott insulator (IntMI) phase. For biased BHL, in addition to the SF and IntMI phases, there appears half-integer filling Mott insulator (HIntMI) phase. The phase transition between the SF and IntMI phases can be first order at a part of phase boundaries, while the phase transition between the SF and HIntMI phases is always second order. By tuning the bias energy, we report on the change of the nature of SF–MI phase transitions. Furthermore, we study the effect of the spin-dependent interaction on the many-body population dynamics. The spin-dependent interaction can lead to rich dynamical behaviors, but does not influence the particle transfer efficiency. Our results indicate a way to tune the nature of the SF–MI phase transition and open a new avenue to study the many-body dynamics of spinor bosons in optical lattices.
We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose–Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling, the system features a phase transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background—instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with two particles per site is destroyed completely by particle–hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a two-dimensional (2D) slab, localized along one spatial direction that is chosen spontaneously.
Nonstandard Bose-Hubbard models can exhibit rich ground-state phase diagrams, even when considering the one-dimensional limit. Using a self-consistent Gutzwiller diagonalization approach, we study the mean-field ground-state properties of a long-range interacting atomic gas in a one-dimensional optical lattice. We first confirm that the inclusion of long-range two-body interactions to the standard Bose-Hubbard model introduces density-wave and supersolid phases. However, the introduction of pair and density-dependent tunneling can result in new phases with two-site periodic density, single-particle transport, and two-body transport order parameters. These staggered phases are potentially a mean-field signature of the known novel twisted superfluids found via a density-matrix renormalization group approach [Phys. Rev. A 94, 011603(R) (2016)]. We also observe other unconventional phases which are characterized by sign staggered order parameters between adjacent lattice sites.
Abstract Quantum coherence and phase transitions are studied in a finite one‐dimensional Bose–Hubbard model using exact diagonalization under thermal fluctuations, a Stark potential, and disorder. The condensate fraction, superfluid fraction, visibility, number fluctuations, and the ‐norm of coherence are computed to characterize the Mott insulator–superfluid transition. Although finite‐size effects prevent a sharp transition, ground‐state properties reveal signatures of quantum criticality. Thermal fluctuations can enhance coherence via tunneling, a Stark potential promotes localization, and disorder suppresses global superfluidity while preserving local coherence. These results highlight how disorder, tilt, and temperature reshape coherence and offer insights for quantum simulation and strongly correlated phases. For systems up to six sites with unit filling, a spectral analysis is also performed through the metric mean gap ratio (MGR). However, limited statistics due to the small system size and computational constraints prevent a complete characterization of quantum chaos, yielding only approximate signatures.