Ring exchange and phase separation in the two-dimensional boson Hubbard model

Abstract

We present Quantum Monte Carlo simulations of the soft-core bosonic Hubbard model with a ring exchange term K. For values of K which exceed roughly half the on-site repulsion U , the density is a non-monotonic function of the chemical potential, indicating that the system has a tendency to phase separate. This behavior is confirmed by an examination of the density-density structure factor at small momenta and real space images of the boson configurations. Adding a near-neighbor repulsion can compete with phase separation, but still does not give rise to a stable normal Bose liquid.

Bose metals and insulators on multileg ladders with ring exchange

“…The unfrustrated version of this model (K ≤ 0), with both hard-core and soft-core bosons at and away from half-filling, has a long history in the past decade as a proposed candidate for harboring a deconfined quantum critical point and/or an exotic quantum phase dubbed the "exciton Bose liquid" (EBL), 42 a relative of our DBL. However, for this particular model, both of these scenarios have been largely ruled out in a sequence of quantum Monte Carlo studies, [43][44][45][46][47] although recent work has shown that the EBL can be stabilized if one supplements a K-only model, Eq. (5), with ring exchange on 1 × 2 and 2 × 1 plaquettes.…”

Bose-Hubbard model on a kagome lattice with sextic ring-exchange terms

“…In particular, multiple particle exchange has been suggested as a possible candidate to induce a normal "Bose metal" or "Bose liquid" phase at zero temperature, in which there are no broken symmetries associated with superfluidity or charge density wave phases [8][9][10][11]. Studies on a square lattice with four-site ringexchange plaquettes suggest that ordered phases always dominate [4][5][6][7]. However, these results still leave the possibility that a Bose liquid or spin liquid phase may exist in certain frustrated lattices [3,12].…”

“…Interest in ring-exchange interactions in quantum many-body systems has a long history originating from the study of quantum solids, a typical example being solid Helium-3 [1,2]. Recently the study of ringexchange interactions has resurged with boson and spin models [3][4][5][6][7][8]. In particular, multiple particle exchange has been suggested as a possible candidate to induce a normal "Bose metal" or "Bose liquid" phase at zero temperature, in which there are no broken symmetries associated with superfluidity or charge density wave phases [8][9][10][11].…”

“…However, numerical studies on those models have proved to be rather difficult. There are some recent studies using the World-line and the Stochastic Series Expansion algorithms with loop update schemes on four-site ring-exchange models [4][5][6][7]. For these models, ring-exchange interactions are described by a term that performs a correlated hopping of two particles in opposite directions, with no contribution to the winding.…”

“…By construction, these loops can update only one or two sites at a time, and are therefore suitable only for one-site or two-site coupling terms. In brief, the treatment of fourth order ring-exchange terms in previous studies required some special developments [4,7] that are not easy to generalize to sixth or higher order.…”