Supersolid hard-core bosons on the triangular lattice

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相似文献   

Supersolid phase of hard-core bosons on a triangular lattice

We study properties of the supersolid phase observed for hard-core bosons on the triangular lattice near half-integer filling factor, and the phase diagram of the system at finite temperature. We find that the solid order is always of the (2m, -m, -m) with m changing discontinuously from positive to negative values at half filling, in contrast with phases observed for Ising spins in a transverse magnetic field. At finite temperature we find two intersecting second-order transition lines: one in the 3-state Potts universality class and the other of the Kosterlitz-Thouless type.     

Persistent supersolid phase of hard-core bosons on the triangular lattice

We study hard-core bosons with unfrustrated hopping (t) and nearest neighbor repulsion (U) (spin S=1/2 XXZ model) on the triangular lattice. At half filling, the system undergoes a zero temperature (T) quantum phase transition from a superfluid phase at small U to a supersolid at Uc approximately 4.45 in units of 2t. This supersolid phase breaks the lattice translation symmetry in a characteristic sqrt[3] x square root of 3 pattern, and is remarkably stable--indeed, a smooth extrapolation of our results indicates that the supersolid phase persists for arbitrarily large U/t.     

Supersolid order from disorder: hard-core bosons on the triangular lattice

We study the interplay of Mott localization, geometric frustration, and superfluidity for hard-core bosons with nearest-neighbor repulsion on the triangular lattice. For this model at half filling, we demonstrate that superfluidity survives for arbitrarily large repulsion, and that diagonal solid order emerges in the strongly correlated regime from an order-by-disorder mechanism. This is thus an unusual example of a stable supersolid phase of hard-core lattice bosons at a commensurate filling.     

Critical behaviour of the hard-core lattice gas on the honeycomb lattice

The hard triangle lattice-gas model (lattice-gas on the honeycomb lattice with first neighbour exclusion) is studied by the phenomenological renormalization method. The critical activity is found to be z = 7.85 and the critical exponents suggest that this model belongs to the 2-D Ising universality class.     

Emergence of quasicondensates of hard-core bosons at finite momentum

An exact treatment of the nonequilibrium dynamics of hard-core bosons on one-dimensional lattices shows that, starting from a pure Fock-state, quasi-long-range correlations develop dynamically, and lead to the formation of quasicondensates at finite momenta. Scaling relations characterizing the quasicondensate and the dynamics of its formation are obtained. The relevance of our findings for atom lasers with full control of the wavelength by means of a lattice is discussed.     

Quantum phase transitions of hard-core bosons in background potentials

We study the zero temperature phase diagram of hard-core bosons in two dimensions subjected to three types of background potentials: staggered, uniform, and random. In all three cases there is a quantum phase transition from a superfluid (at small potential) to a normal phase (at large potential), but with different universality classes. As expected, the staggered case belongs to the XY universality, while the uniform potential induces a mean field transition. The disorder driven transition is clearly different from both; in particular, we find z approximately 1.4, nu approximately 1, and beta approximately 0.6.     

Finite-temperature phase diagram of hard-core bosons in two dimensions

We determine the finite-temperature phase diagram of the square lattice hard-core boson Hubbard model with nearest neighbor repulsion using quantum Monte Carlo simulations. This model is equivalent to an anisotropic spin-1/2 XXZ model in a magnetic field. We present the rich phase diagram with a first order transition between a solid and superfluid phase, instead of a previously conjectured supersolid and a tricritical end point to phase separation. Unusual reentrant behavior with ordering upon increasing the temperature is found, similar to the Pomeranchuk effect in 3He.     

Supercurrent survival under a Rosen-Zener quench of hard-core bosons

We study the survival of supercurrents in a system of impenetrable bosons on a lattice, subject to a quantum quench from its critical superfluid phase to an insulating phase. We show that the evolution of the current when the quench follows a Rosen-Zener profile is exactly solvable. This allows us to analyze a quench of arbitrary rate, from a sudden destruction of the superfluid to a slow opening of a gap. The decay and oscillations of the current are analytically derived and studied numerically along with the momentum distribution after the quench. In the case of small supercurrent boosts nu, we find that the current surviving at long times is proportional to nu3.     

Two-step condensation of lattice bosons

We present a theoretical study of Bose-Einstein condensation in highly anisotropic harmonic traps. The bosons are considered to be moving in an optical lattice in an overall anisotropic harmonic confining potential. We find that two-step condensation occurs for lattice bosons at much reduced harmonic potential anisotropy when compared to the case of an ideal Bose gas in an anisotropic harmonic confinement. We also show that when the bosons are in an isotropic harmonic confinement but with highly anisotropic hopping in the optical lattice, two-step condensation does not occur. We interpret some of our results using single boson density of energy states corresponding to the potentials faced by the bosons.     

Non-Abelian braiding of lattice bosons

We report on a numerical experiment in which we use time-dependent potentials to braid non-Abelian quasiparticles. We consider lattice bosons in a uniform magnetic field within the fractional quantum Hall regime, where ν, the ratio of particles to flux quanta, is near 1/2, 1, or 3/2. We introduce time-dependent potentials which move quasiparticle excitations around one another, explicitly simulating a braiding operation which could implement part of a gate in a quantum computation. We find that different braids do not commute for ν near 1 and 3/2, with Berry matrices, respectively, consistent with Ising and Fibonacci anyons. Near ν=1/2, the braids commute.     

Analyticity of a hard-core multicomponent lattice gas

A multicomponent anti-Widom-Rowlinson lattice gas is introduced. An arbitrary numberM of particle types is permitted, all having the same activity. The only interactions are nearest-neighbor exclusions oflike particles (analogous to map-coloring problems). For any lattice it is shown that there is a finite numberM ₀ (depending only on the coordination number of the lattice) such that for allMM ₀ the infinite volume correlation functions exist and are analytic functions of the activity, for all positive values of the common activity.Research supported in part by NSF Grant No. GP-33535X, AFOSR Grant No. 73-2430B, and NSF Grant No. MPS75-20638.     

Commensurate two-component bosons in an optical lattice: ground state phase diagram

Two sorts of bosons in an optical lattice at commensurate filling factors can form five stable super-fluid and insulating ground states with rich and nontrivial phase diagram. The structure of the ground state diagram is established by mapping a d-dimensional quantum system onto a (d+1)-dimensional classical loop-current model and Monte Carlo (MC) simulations of the latter. Surprisingly, the quantum phase diagram features, besides second-order lines, first-order transitions and two multicritical points. We explain why first-order transitions are generic for models with pairing interactions using microscopic and mean-field (MF) arguments. In some cases, the MC results strongly deviate from the MF predictions.     

Upper bound on the condensate in the hard-core Bose lattice gas

Using methods developed by G. Roepstorf, we prove an upper bound for the amount of condensate in ahard-core Bose lattice gas.On leave from the Mathematical Institute of the Hungarian Academy of Sciences, Budapest, H-1053, Hungary.     

A remark on the condensation in the hard-core lattice Bose gas

We point out that Bose-Einstein condensation occurs at sufficiently low temperature in a hard-core ^d-lattice Bose gas for d3 and particle density 1/2, by exploiting its equivalence to a spin-1/2XY model.     

Applications of the Yang-Lee-Ruelle theory to hard-core lattice gases

The grand-partition-function-zero method is applied to lattice systems of rigid molecules, based on the algebraic technique of Ruelle. Consideration of small collections of lattice molecules, through this approach, provides rigorous delineation of regions of the complex activity plane which are free of zeros of the grand partition function, and hence free of thermodynamic singularities. Two conjectures, as yet unproved, are offered, which greatly reduce the computational effort required in using the technique. A simple proof is provided for the absence of physical phase transitions in monomerdimer systems, and bounds are obtained on the locations of the transitions of other lattice gases.Research supported in part by National Science Foundation Grant GP-17026.     

Fractional quantum Hall effect of hard-core bosons in topological flat bands

Recent proposals of topological flat band models have provided a new route to realize the fractional quantum Hall effect without Landau levels. We study hard-core bosons with short-range interactions in two representative topological flat band models, one of which is the well-known Haldane model (but with different parameters). We demonstrate that fractional quantum Hall states emerge with signatures of an even number of quasidegenerate ground states on a torus and a robust spectrum gap separating these states from the higher energy spectrum. We also establish quantum phase diagrams for the filling factor 1/2 and illustrate quantum phase transitions to other competing symmetry-breaking phases.