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arXiv:2106.05893 · Physical review. B./Physical review. B

Supersolid-superfluid phase separation in the extended Bose-Hubbard model

Korbinian Kottmann, Andreas Haller, Antonio Acín, G. E. Astrakharchik, Maciej Lewenstein

Published Nov 18, 2021• 21 citations
arXivHTMLPDF

Abstract

Recent studies have suggested a new phase in the extended Bose-Hubbard model in one dimension at integer filling. In this work, we show that this new phase is phase-separated into a supersolid and superfluid part, generated by mechanical instability. Numerical simulations are performed by means of the density matrix renormalization group algorithm in terms of matrix product states. In the phase-separated phase and the adjacent homogeneous superfluid and supersolid phases, we find peculiar spatial patterns in the entanglement spectrum and string-order correlation functions and show that they survive in the thermodynamic limit. In particular, we demonstrate that the elementary excitations of the homogeneous superfluid with enhanced periodic modulations are phonons, find the central charge to be $c=1$, and show that the velocity of sound, extracted from the intrinsic level splitting for finite systems, matches with the propagation velocity of local excitations in dynamical simulations. This suggests that the low-energy spectrum of the phase under investigation is effectively captured by a spinless Luttinger liquid, for which we find consistent results between the Luttinger parameter obtained from the linear dependence of the structure factor and the algebraic decay of the one-body density matrix.

DOI
10.1103/physrevb.104.174514

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Recent studies have suggested a new phase in the extended Bose-Hubbard model in one dimension at integer filling. In this work, we show that this new phase is phase-separated into a supersolid and superfluid part, generated by mechanical instability. Numerical simulations are performed by means of the density matrix renormalization group algorithm in terms of matrix product states. In the phase-separated phase and the adjacent homogeneous superfluid and supersolid phases, we find peculiar spatial patterns in the entanglement spectrum and string-order correlation functions and show that they survive in the thermodynamic limit. In particular, we demonstrate that the elementary excitations of the homogeneous superfluid with enhanced periodic modulations are phonons, find the central charge to be c=1c=1c=1, and show that the velocity of sound, extracted from the intrinsic level splitting for finite systems, matches with the propagation velocity of local excitations in dynamical simulations. This suggests that the low-energy spectrum of the phase under investigation is effectively captured by a spinless Luttinger liquid, for which we find consistent results between the Luttinger parameter obtained from the linear dependence of the structure factor and the algebraic decay of the one-body density matrix.
We study the one-dimensional extended Bose-Hubbard model in incommensurate densities using the density matrix renormalization group with the mean-filed (CMFT+DMRG)and density matrix renormalization group (DMRG) methods. We focus on the region of the phase diagram where onsite interaction (U) is smaller than the nearest-neighbor interaction (V). We determine the superfluid and the density wave order parameters to identify superfluid, phase-separated, supersolid, density wave phases, and obtain the phase diagram in the density-onsite interaction(ρ, U) plane for fixed nearest-neighbor interaction. The supersolid and phase-separation phases exist for a wide range of densities. The density ranges for which the phase-separation is seen shrinking with theincrease in the onsite interaction.
The search and characterization of supersolid phases remain a central topic in condensed matter physics. Inspired by the experimental discovery of local superfluid and insulating phases in two-dimensional moiré optical lattices [Meng et al., Nature 615, 231 (2023)], we systematically explore the emergence of a local supersolid (lllSS) phase in a one-dimensional Bose-Hubbard model subjected to a moiré potential, using the density-matrix renormalization group method. We impose a maximum site occupation nmax=2n_{\rm max}=2nmax​=2 to realize the soft-core boson constraint. In the absence of nearest-neighbor repulsion, we identify the conventional superfluid, local superfluid, Mott insulator, and moiré-induced insulator phases. When the nearest-neighbor repulsion is turned on, the lllSS phase emerges in the strong-moiré regime. This phase is uniquely characterized by three key signatures: (i) coexisting local staggered density order and local off-diagonal coherence within isolated moiré supercells; (ii) exponentially decaying global off-diagonal correlations; and (iii) a vanishing global structure factor in the thermodynamic limit, while the local structure factor remains finite. These features clearly distinguish the lllSS from the conventional global supersolid (SS) phase, which exhibits algebraic correlations and a finite global structure factor. Our results provide a complete microscopic picture of local quantum phases in moiré lattices and offer clear experimental observables for detecting lllSS states with ultracold atoms.
The one-dimensional extended bosonic Hubbard model has been shown to exhibit a variety of phases ranging from Mott insulator and superfluid to exotic supersolids and Haldane insulators depending on the filling and the relative value of the contact (UUU) and near neighbor (VVV) interaction strengths. In this paper we use the density matrix renormalization group and the time evolving block decimation numerical methods to study in detail the dynamics and excitation spectra of this model in its various phases. In particular, we study in detail the behavior of the charge and neutral gaps which characterize the Mott, charge density, and Haldane insulating phases. We also show that in addition to the gapless modes at k=0k=0k=0, the supersolid phase exhibits gapless modes at a finite kkk which depends on the filling.
We report our findings on the quantum phase transitions in cold bosonic atoms in a one-dimensional optical lattice using the finite-size density-matrix renormalization-group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest-neighbor interactions. At commensurate fillings, we obtain two different types of charge-density wave phases and a Mott insulator phase. However, departure from commensurate fillings yields the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain the signatures for the solitary waves and the superfluid phase.
We use strong-coupling perturbation theory, the variational cluster approach (VCA), and the dynamical density-matrix renormalization group (DDMRG) method to investigate static and dynamical properties of the one-dimensional Bose--Hubbard model in both the Mott-insulating and superfluid phases. From the von Neumann entanglement entropy we determine the central charge and the transition points for the first two Mott lobes. Our DMRG results for the ground-state energy, momentum distribution function, boson correlation function decay, Mott gap, and single-particle spectral function are reproduced very well by the strong-coupling expansion to fifth order, and by VCA with clusters up to 12 sites as long as the ratio between the hopping amplitude and onsite repulsion, t/Ut/Ut/U, is smaller than 0.15 and 0.25, respectively. In addition, in the superfluid phase VCA captures well the ground-state energy and the sound velocity of the linear phonon modes. This comparison provides an authoritative estimate for the range of applicability of these methods. In strong-coupling theory for the Mott phase, the dynamical structure factor is obtained from the solution of an effective single-particle problem with an attractive potential. The resulting resonances show up as double-peak structures close to the Brillouin zone boundary. These high-energy features also appear in the superfluid phase which is characterized by a pronounced phonon mode at small momenta and energies, as predicted by Bogoliubov and field theory. In one dimension, there are no traces of an amplitude mode in the dynamical single-particle and two-particle correlation functions.
Motivated by the recent progress in realizing and controlling extended Bose-Hubbard systems using excitonic or atomic devices, the present Letter theoretically investigates the case of a two-band Bose-Hubbard chain with nearest-neighbor interactions. Specifically, this study concentrates on the scenario where, due to the interactions, one band supports a density-wave phase, i.e., a correlated insulating phase with spontaneous breaking of translational symmetry in the lattice, while the other band supports superfluid behavior. Using the density matrix renormalization group method, we show that supersolid order can emerge from such a combination, that is, an elusive quantum state that combines crystalline order with long-range phase coherence. Depending on the filling of the bands and the interband interaction strength, the supersolid phase competes with phase-separation, superfluid order, or Mott insulating density-wave order. As a possible setup to observe supersolidity, we propose the combination of a lower band supporting density-wave order and a thermally excited band that supports superfluidity due to weaker lattice confinement.