Supersolid phase transitions for hard-core bosons on a triangular lattice

Abstract

Hard-core bosons on a triangular lattice with nearest neighbor repulsion are a prototypical example of a system with supersolid behavior on a lattice. We show that in this model the physical origin of the supersolid phase can be understood quantitatively and analytically by constructing quasiparticle excitations of defects that are moving on an ordered background. The location of the solid to supersolid phase transition line is predicted from the effective model for both positive and negative (frustrated) hopping parameters. For positive hopping parameters the calculations agree very accurately with numerical quantum Monte Carlo simulations. The numerical results indicate that the supersolid to superfluid transition is first order.

Tuning the quantum phase transition of bosons in optical lattices via periodic modulation of thes-wave scattering length

“…This agreement order by order in the hopping expansion is insofar surprising as the strong-coupling method yields reliable results for low dimensions, whereas EPLT has shown to be most accurate for high dimensions [37]. In addition we have obtained high-precision QMC results from developing an algorithm on the basis of a stochastic series expansion [52][53][54][55][56]. In order to get the high accuracy quantum phase diagram in the thermodynamic limit from QMC, we performed a finite-size scaling with the lattice sizes N = 8 × 8, 10 × 10, and 12 × 12 at the temperature T = U/(20N ).…”

Supersolid States in a Hard-Core Bose–Hubbard Model on a Layered Triangular Lattice

“…The supersolid state is the coexistence between the solid state with a certain particle distribution and the superfluid state. Therefore, the stability of the supersolid state with n > 1/3 is roughly discussed in terms of the effective model, which is composed of localized particles and itinerant "defect" particles [16]. In this case, the defect particles can hop on layered honeycomb lattices, as shown in Fig.…”

Quantum Domain Walls Induce Incommensurate Supersolid Phase on the Anisotropic Triangular Lattice

“…On the triangular lattice [49,50] they have been predicted to show supersolid behavior [12][13][14][15][16][17][18][19][20][21], which is characterized by two independent spontaneously broken symmetries -U(1) and translation -with corresponding superfluid and density order. For an anisotropic triangular lattice the commensurate supersolid phase is found to be unstable [26,27], and the solid order turns out to be incommensurate [41].Supersolid phases with two independently broken order parameters were first discussed for solid He [51,52] and were more recently shown to exist theoretically [12][13][14][15][16][17][18][19][20][21] and experimentally [53,54] in optical lattices for ultracold gases. Although high-temperature superconductors [55][56][57] are not often mentioned in this context, the coexistence of superconductivity and anti-ferromagnetic density order, so-called superstripes, are the defining characteristics of an incommensurate supersolid.…”

“…In this case, nearest neighbor interacting bosons are realizable, for instance, with magnetic erbium atoms [48]. On the triangular lattice [49,50] they have been predicted to show supersolid behavior [12][13][14][15][16][17][18][19][20][21], which is characterized by two independent spontaneously broken symmetries -U(1) and translation -with corresponding superfluid and density order. For an anisotropic triangular lattice the commensurate supersolid phase is found to be unstable [26,27], and the solid order turns out to be incommensurate [41].…”

“…Supersolid phases with two independently broken order parameters were first discussed for solid He [51,52] and were more recently shown to exist theoretically [12][13][14][15][16][17][18][19][20][21] and experimentally [53,54] in optical lattices for ultracold gases. Although high-temperature superconductors [55][56][57] are not often mentioned in this context, the coexistence of superconductivity and anti-ferromagnetic density order, so-called superstripes, are the defining characteristics of an incommensurate supersolid.…”