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arXiv:2007.06340 · Physical review. B./Physical review. B

Phases and collective modes of bosons in a triangular lattice at finite temperature: A cluster mean field study

Manali Malakar, Sayak Ray, Subhasis Sinha, D. Angom

Published Nov 24, 2020• 11 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.102.184515

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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.
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.
We investigate the zero-temperature quantum phases of a Bose-Bose mixture on a triangular lattice using the bosonic dynamical mean-field theory (BDMFT). We consider the case of total filling where geometric frustration arises for asymmetric hopping. We map out a rich ground-state phase diagram including xyxyxy-ferromagnetic, spin-density wave, superfluid, and supersolid phases. In particular, we identify a stripe spin-density wave phase for highly asymmetric hopping. On top of the spin-density wave, we find that the system generically shows weak charge (particle) density wave order.
We determine the phase diagram of hard-core bosons on a triangular lattice with nearest-neighbor repulsion, paying special attention to the stability of the supersolid phase. Similar to the same model on a square lattice we find that for densities rho<1/3 or rho>2/3 a supersolid phase is unstable and the transition between a commensurate solid and the superfluid is of first order. At intermediate fillings 1/3<rho<2/3 we find an extended supersolid phase even at half filling rho=1/2. The emergence of the supersolid on the triangular lattice reflects a novel and interesting way for a quantum system to avoid classical frustration, similar to an order-by-disorder mechanism. It also offers an exciting possibility of realizing such phenomena in ultracold atoms on optical lattices.
In this Brief Report, we study phase structure of a system of hard-core bosons with a nearest-neighbor (NN) repulsive interaction in a stacked triangular lattice. The Hamiltonian of the system contains two parameters, one of which is the hopping amplitude ttt between NN sites and the other is the NN repulsion VVV. We investigate the system by means of the Monte Carlo simulations and clarify the low- and high-temperature phase diagrams. Phase diagrams contain various phases, e.g., solid, superfluid, supersolid, and phase-separated states. The result is compared with the phase diagram of the two-dimensional system in a triangular lattice at vanishing temperature.
solitons, vortices, and topological excitations. PACS. 03.75.Nt – Other Bose-Einstein condensation phenomena. Abstract. – Motivated by the recent experiment on the Bose-Einstein condensation of 52 Cr 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, 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. The recent observation [2] of quantum phase transition of interacting bosons in an optical lattice has given a new impetus to the study of correlated bosons. The possibility of manipulating both the interactions among the constituents as well as disorder in the system
We analyze the hard-core Bose-Hubbard model with both three-body and nearest-neighbor repulsions on a triangular lattice. The phase diagram is achieved by means of the semiclassical approximation and a quantum Monte Carlo simulation. For a system with only three-body interactions, both the supersolid phase and the one-third solid disappear while the two-thirds solid is stable. As the thermal behavior of the bosons with nearest-neighbor repulsion, the solid and the superfluid undergo the three-state Potts- and Kosterlitz--Thouless-type phase transitions, respectively. In a system with both frustrated nearest-neighbor two-body and three-body interactions, the supersolid and one-third solid are revived. By tuning the strength of the three-body interactions, the phase diagram is distorted because the one-third solid and the supersolid are suppressed.