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arXiv:2305.15307 · Physical review. B./Physical review. B

Formation of paired phases of bosons and their excitations in a square lattice

Manali Malakar, Sudip Sinha, Subhasis Sinha

Published Aug 21, 2023• 2 citations
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Abstract

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.

DOI
10.1103/physrevb.108.054518

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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.
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 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.
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 obtain the phase diagram of a Bose-Fermi mixture of hardcore spinless bosons and spin-polarized fermions with nearest-neighbor intraspecies interaction and on-site interspecies repulsion in an optical lattice at half filling using a slave-boson mean-field theory. We show that such a system can have four possible phases which are (a) supersolid bosons coexisting with fermions in the Mott state, (b) Mott state of bosons coexisting with fermions in a metallic or charge-density wave state, (c) a metallic fermionic state coexisting with superfluid phase of bosons, and (d) Mott insulating state of fermions and bosons. We chart out the phase diagram of the system and provide analytical expressions for the phase boundaries within mean-field theory. We demonstrate that the transitions between these phases are generically first order with the exception of that between the supersolid and the Mott states which, within mean-field theory, is a continuous quantum phase transition. We also obtain the low-energy collective excitations of the system in these phases. Finally, we study the particle-hole excitations in the Mott insulating phase and use it to determine the dynamical critical exponent zzz for the supersolid-Mott insulator transition. We discuss experiments which can test our theory.
We systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in the presence of a three-body constraint on the triangular lattice. By means of large-scale quantum Monte Carlo simulations, the ground-state phase diagram is studied. We find a first-order transition between the atomic superfluid phase and the pair superfluid phase when the ratio of the atomic hopping and the atom-pair hopping is adapted. The first-order transition remains unchanged under various conditions. We then focus on the interplay among the atom-pair hopping, the on-site repulsion, and the nearest-neighbor repulsion. With on-site repulsion present, we observe first-order transitions between the Mott insulators and pair superfluid driven by the pair hopping. With the nearest-neighbor repulsion turning on, three typical solid phases with 2/32/32/3, 1, and 4/34/34/3 filling emerge at small atom-pair hopping region. A stable pair supersolid phase is found at small on-site repulsion. This is due to the three-body constraint and the pair hopping, which essentially make the model a quasihardcore boson system. Thus the pair supersolid state emerges basing on the order-by-disorder mechanism, by which hardcore bosons avoid classical frustration on the triangular lattice. Without on-site repulsion, the transitions between the pair supersolid and the atom superfluid or pair superfluid are first order, except for the particle-hole symmetric point. With weak on-site repulsion and atom hopping turning on, the transition between the pair supersolid and pair superfluid phase becomes continuous. The transition between solid and pair supersolid is three-dimensional XYXYXY university, with dynamical exponent z=1z=1z=1 and correlation exponent $\ensuremath{\nu}=0.671\phantom{\rule{0.16em}{0ex}}55$. The thermal melting of pair supersolid belongs to the two-dimensional Ising university. We check both energetic and mechanical balance of pair supersolid phase. Lowering the three-body constraint, no pair supersolid is found due to the absence of degeneracy of pair solids in classical limits. We describe the experimental realization of pair tunneling on state dependent lattice.
The competition between tunneling and interactions in bosonic lattice models generates a whole variety of different quantum phases. While, in the presence of a single species interacting via on site interaction, the phase diagram presents only superfluid or Mott insulating phases, for long-range interactions or multiple species, exotic phases such as supersolid or pair-superfluid appear. In this Letter, we show for the first time that the coexistence of effective multiple species and long-range interactions leads to the formation of a novel pair-supersolid phase, namely, a supersolid of composites. We propose a possible implementation with dipolar bosons in a bilayer two-dimensional optical lattice.