Vacancy supersolid of hard-core bosons on the square lattice

Abstract

The ground state of hard-core bosons on the square lattice with nearest and next-nearest neighbor repulsion is studied by Quantum Monte Carlo simulations. A supersolid phase with vacancy condensation and 'star' diagonal ordering is found for filling ρ < 0.25. At fillings ρ > 0.25 a supersolid phase exists between the star and the stripe crystal at ρ=0.5. No supersolid phase occurs for ρ > 0.25 if the ground state at half-filling is either a checkerboard crystal or a superfluid. No commensurate supersolid phase is observed.PACS numbers: 75.10. Jm, 05.30.Jp, 67.40.Kh, 74.25.Dw Experimental advances in the field of ultracold atoms in optical lattices [1] have given renewed impetus to the investigation of novel phases of matters, especially those displaying simultaneously different types of order. One such phase is the supersolid, featuring both diagonal and off-diagonal long range order, which has been the subject of much theoretical speculation [2]. Recent claims of observation of this phase in solid helium [3] have generated some controversy [4].Theoretical studies have yielded strong evidence of supersolid phases of lattice bosons, for various types of model interactions among atoms, as well as of lattice geometries [5,6,7,8]. In the presence of nearest-neighbor particle hopping and on-site hard core repulsion, the supersolid phase is only observed on the interstitial side of a commensurate solid phase (e.g., for 1/3 < ρ < 2/3 on the triangular lattice) [8]. In contrast, doping with vacancies results in the coexistence of an insulating crystal and a superfluid by the formation of a domain wall [9]. Phase separation of vacancies is also observed in ab initio simulations of helium crystals [10]. This seems remarkable, as Bose condensation of vacancies has long been regarded as the paradigm for supersolidity [2]. The purpose of this work is to gain understanding in the asymmetry between the behavior of vacancies and interstitials, and explore physical conditions that underlie a vacancy supersolid phase in lattice bosons.Our starting point is the well-known HamiltonianA square lattice with periodic boundary conditions of N = L × L sites is assumed. The boson density (filling) is ρ = N B /N , where the number of particles N B is determined by the chemical potential µ. The operatorb † i (b i ) creates (annihilates) a hard-core boson on site i, with a maximum occupation numbern i =b † ib i of one particle per site. The first term of (1) describes particle hopping to a nearest-neighboring site with amplitude t, which is our energy scale, t = 1. The second and third terms represent repulsive interactions between bosons on nearest and next-nearest neighboring sites, respectively.Previous studies of the ground state of (1) have yielded evidence of three possible phases at half-filling ( ρ=0.5): a superfluid, a checkerboard solid and a stripe solid. The latter two are commensurate and insulating phases. Doping the stripe crystal away from half filling yields a supersolid phase, whereas a first-order quantum phase transit...

The physics of dipolar bosonic quantum gases

“…Instead the striped supersolid, obtained for large next nearest-neighbor interaction, exists for all doping away from ρ = 1/2 both in the hard-core and soft-core cases [271,272,274]. Finally, at large next nearest-neighbor interaction, the star supersolid can always be obtained by doping a star solid at ρ = 1/4 with vacancies and by doping it with bosons in the case the ρ = 1/2 ground state is a striped crystal [274,275]. The most important conclusion on which most papers agree♯ is that no supersolid phase is found at commensurate density.…”

Ground-state phase diagram of the two-dimensional extended Bose-Hubbard model

“…Ultra-cold Bose gases trapped in optical lattice are ideal systems to realize the Bose-Hubbard models [15]. From the intensive theoretical and numerical studies, the existence of supersolid phases has been established in the extended Bose-Hubbard models [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Most of the supersolids in lattice systems are achieved by doping particles or holes into insulating solid states at commensurate filling factors.…”

Excitation spectra of hard-core bosons on square and triangular lattices in superfluid phase

“…[1][2][3][4][5][6][7] The hard-core bosons and related models have been actively investigated in a number of papers for the most part numerically. [8][9][10][11] The structure of a HCB phase diagram depends on the system parameters and commonly four main phases are identified at zero temperature.…”