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arXiv:2208.06893 · Journal of Statistical Mechanics Theory and Experiment

Finite temperature phases and excitations of bosons on a square lattice: a cluster mean field study

Manali Malakar, Sudip Sinha, Subhasis Sinha

Published Apr 1, 2023• 1 citation
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Abstract

Abstract We study the finite temperature phases and collective excitations of hardcore as well as softcore bosons on a square lattice with nearest and next nearest neighbor interactions, focusing on the formation of various types of supersolid (SS) phases and their stability under thermal fluctuations. The interplay between the on-site, nearest, and next nearest neighbor interactions leads to various density ordering and structural transitions, which we have plotted out. Thermodynamic properties and phase diagrams are obtained by cluster mean field theory at finite temperatures, which includes quantum effects systematically, and they are compared with the single-site mean field (MF) results. We investigate the melting process of the SS phase to normal fluid (NF), which can occur in at least two steps due to the presence of two competing orders in the SS. A tetra-critical point exists at finite temperature and exhibits intriguing behavior, which is analyzed for different regimes of interactions. The phase diagrams reveal the different pathways of the thermal transition of SSs to the NF phase, for different interaction regimes, which can be accessible by thermal quench protocols used in recent experiments. We show how the phases and the transitions between them can be identified from the characteristic features of the excitation spectrum. We analyze the appearance of a low-energy gapped mode apart from the gapless sound mode in the SS phase, which is analogous to the gapped mode recently studied for dipolar SS phases. Finally, we discuss the relevance of the results of the present work in the context of ongoing experiments on ultracold atomic gases and newly observed SS phases.

DOI
10.1088/1742-5468/acc731

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Abstract We study the finite temperature phases and collective excitations of hardcore as well as softcore bosons on a square lattice with nearest and next nearest neighbor interactions, focusing on the formation of various types of supersolid (SS) phases and their stability under thermal fluctuations. The interplay between the on-site, nearest, and next nearest neighbor interactions leads to various density ordering and structural transitions, which we have plotted out. Thermodynamic properties and phase diagrams are obtained by cluster mean field theory at finite temperatures, which includes quantum effects systematically, and they are compared with the single-site mean field (MF) results. We investigate the melting process of the SS phase to normal fluid (NF), which can occur in at least two steps due to the presence of two competing orders in the SS. A tetra-critical point exists at finite temperature and exhibits intriguing behavior, which is analyzed for different regimes of interactions. The phase diagrams reveal the different pathways of the thermal transition of SSs to the NF phase, for different interaction regimes, which can be accessible by thermal quench protocols used in recent experiments. We show how the phases and the transitions between them can be identified from the characteristic features of the excitation spectrum. We analyze the appearance of a low-energy gapped mode apart from the gapless sound mode in the SS phase, which is analogous to the gapped mode recently studied for dipolar SS phases. Finally, we discuss the relevance of the results of the present work in the context of ongoing experiments on ultracold atomic gases and newly observed SS phases.
Motivated by the realization of Bose-Einstein condensates in noncubic lattices [J. Struck et al., Science 333, 996 (2011)], in this work we study the phases and collective excitation of bosons with nearest-neighbor interaction in a triangular lattice at finite temperature, using mean field (MF) and cluster mean field (CMF) theory. We compute the finite-temperature phase diagram both for hardcore and softcore bosons, as well analyze the effect of correlation arising due to geometric frustration of a triangular lattice and interaction systematically using the CMF method. A semianalytic estimate of the transition temperatures between different phases is derived within the framework of MF Landau theory, particularly for hardcore bosons. Apart from the usual phases such as density waves and superfluid, we also characterize different supersolids. These phases and their transitions at finite temperature are identified from the collective modes. The low-lying excitations, particularly Goldstone and Higgs modes of the supersolid, can be detected in the ongoing cold atom experiments.
We investigate the formation of paired states of bosons in an optical lattice, namely, pair superfluid (PSF) and pair supersolid (PSS) in the presence of pair hopping as well as the next-nearest-neighbor (NNN) interaction mimicking long-range forces. Both the zero- and finite-temperature phase diagrams are obtained using the cluster mean-field theory, which includes the effect of correlations systematically. We also compute the low-energy excitations, which capture the characteristic features of such paired states and their transitions. Apart from the gapless sound mode due to the PSF order, a gapped mode also appears in the PSF phase, similar to the Higgs mode of the usual atomic superfluid (ASF). The PSF to ASF transition exhibits an intriguing behavior due to the existence of a ``tricritical'' point, where the nature of transition changes. As a consequence of the continuous PSF-ASF transition, the gapped mode of both the phases becomes gapless at the critical point. For sufficiently strong NNN interaction strength, a PSS phase appears with coexisting pair superfluidity and stripe density order. The softening of the roton mode as a precursor of density ordering and the appearance of a low-energy gapped mode serve as robust features related to the formation of the PSS phase. We also investigate the melting of PSF and PSS phases to normal fluid at finite temperatures, particularly the melting pathway of PSS, which occurs in at least two steps due to the coexisting orders. Finally, we discuss the possibility of emulating such exotic phases in the ongoing cold atom experiments.
The effect of the next-nearest-neighbor (nnn) tunneling on the hard-core extended Bose–Hubbard model on square lattices is investigated. By means of the cluster mean-field theory, the ground-state phase diagrams are determined. When a modest nnn tunneling is introduced, depending on its sign, two distinct supersolid (SS) states with checkerboard crystal structures are found away from half-filing. The characters of various phase transitions out of these two SS states are discussed. In particular, for the case with kinetic frustration, the existence of a half SS phase possessing both solid and unconventional superfluid orders is established. Our work hence sheds light on the search of this interesting SS phase in real ultracold lattice gases with frustrated tunnelings.
We examine the zero- and finite-temperature phase diagrams of soft-core bosons of the extended Bose-Hubbard model on a square optical lattice. To study various quantum phases and their transitions we employ single-site and cluster Gutzwiller mean-field theory. We have observed that the Mott insulator phase vanishes above a critical value of nearest-neighbor interaction and the supersolid phase occupies a larger region in the phase diagram. We show that the presence of an artificial gauge field enlarges the domain of the supersolid phase. The finite temperature destroys the crystalline structure of the supersolid phase and thereby favors the normal fluid--to--superfluid phase transition. The presence of an envelope harmonic potential demonstrates the coexistence of different phases, and at $z{k}_{B}T\ensuremath{\geqslant}V$, thermal energy comparable to or higher than the long-range interaction energy, the supersolidity of the system is destroyed.
The supersolid phase of soft-core bosons in two dimensions is investigated using the self-consistent Hartree-Fock and quantum Monte Carlo methods. An approximate phase diagram at finite temperatures is initially constructed using the mean-field approach, which is subsequently validated through precise path-integral simulations, enabling a microscopic characterization of the various phases. Superfluid and melting/freezing transitions are analyzed through the superfluid density and the long-range behavior of correlation functions associated with positional and orientational order, in accordance with the general picture of Berezinskii-Kosterlitz-Thouless transitions. A broad region at low temperatures is identified where the supersolid phase exists, separating the uniform superfluid phase from the normal quasicrystal phase. Additionally, a potential intermediate hexatic phase with quasi-long-range orientational order is identified in a narrow region between the normal solid and fluid phases. These findings establish self-consistent Hartree-Fock theory beyond the local density approximation as an effective tool, complementary to computationally intensive quantum Monte Carlo simulations, for investigating the melting of the supersolid phase and the possible emergence of the hexatic superfluid phase in bosonic systems with various interaction potentials.
Motivated by the recent experiment on the Bose-Einstein condensation of 52^{52}52Cr atoms with long-range dipolar interactions (Werner J. et al., Phys. Rev. Lett., 94 (2005) 183201), we consider a system of bosons with repulsive nearest and next-nearest neighbor interactions in an optical lattice. The ground state phase diagram, calculated using the Gutzwiller ansatz, shows, apart from the superfluid (SF) and the Mott insulator (MI), two modulated phases, \textit{i.e.}, the charge density wave (CDW) and the supersolid (SS). Excitation spectra are also calculated which show a gap in the insulators, gapless, phonon mode in the superfluid and the supersolid, and a mode softening of superfluid excitations in the vicinity of the modulated phases. We discuss the possibility of observing these phases in cold dipolar atoms and propose experiments to detect them.