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.     

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.     

Exotic gapless mott insulators of bosons on multileg ladders

We present evidence for an exotic gapless insulating phase of hard-core bosons on multileg ladders with a density commensurate with the number of legs. In particular, we study in detail a model of bosons moving with direct hopping and frustrating ring exchange on a 3-leg ladder at ν=1/3 filling. For sufficiently large ring exchange, the system is insulating along the ladder but has two gapless modes and power law transverse density correlations at incommensurate wave vectors. We propose a determinantal wave function for this phase and find excellent comparison between variational Monte Carlo and density matrix renormalization group calculations on the model Hamiltonian, thus providing strong evidence for the existence of this exotic phase. Finally, we discuss extensions of our results to other N-leg systems and to N-layer two-dimensional structures.     

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   

Hard-core bosons on the kagome lattice: valence-bond solids and their quantum melting

Using large scale quantum Monte Carlo simulations and dual vortex theory, we analyze the ground state phase diagram of hard-core bosons on the kagome lattice with nearest-neighbor repulsion. In contrast with the case of a triangular lattice, no supersolid emerges for strong interactions. While a uniform superfluid prevails at half filling, two novel solid phases emerge at densities rho=1/3 and rho=2/3. These solids exhibit an only partial ordering of the bosonic density, allowing for local resonances on a subset of hexagons of the kagome lattice. We provide evidence for a weakly first-order phase transition at the quantum melting point between these solid phases and the superfluid.     

SU(2)-invariant continuum theory for an unconventional phase transition in a three-dimensional classical dimer model

We derive a continuum theory for the phase transition in a classical dimer model on the cubic lattice, observed in recent Monte Carlo simulations. Our derivation relies on the mapping from a three-dimensional classical problem to a two-dimensional quantum problem, by which the dimer model is related to a model of hard-core bosons on the kagome lattice. The dimer-ordering transition becomes a superfluid-Mott insulator quantum phase transition at fractional filling, described by an SU(2)-invariant continuum theory.     

Hard-Core Bosons on a Two-Dimensional Square Optical Superlattice

In this work,we theoretically study hard-core bosons on a two-dimensional square optical superlattice at T = 0.First of all,we present the mean field phase diagram of this model in terms of the chemical potential μ and the alternating potential strength △.Besides a superfluid(SF) phase at △ = 0 and a charge density wave(CDW)phase in the large △ at half filling,we demonstrate that a supersolid(SS) phase emerges in the moderate △.Then,we focus on the μ = 0,e.g.,half filling case,using large-S semi-classical spin-wave approximation to study the SS to CDW quantum phase transition.In particular,we calculate the ground-state energy and the superfluid density at the level of1/S correction.We then compare the spin-wave results with the large scale quantum Monte Carlo(QMC) simulations using the cluster stochastic series expansion(CSSE) algorithm,and find that while the spin wave method is intuitive with clear physical pictures,the quantum critical point is quite different from that of numerical results which is believed to be accurate.We suggest that as simple as it is,this model still exhibits strong quantum fluctuations near the quantum critical point beyond the power of semiclassical spin-wave approach.     

Ultracold atoms in one-dimensional optical lattices approaching the Tonks-Girardeau regime

Recent experiments on ultracold atomic alkali gases in a one-dimensional optical lattice have demonstrated the transition from a gas of soft-core bosons to a Tonks-Girardeau gas in the hard-core limit, where one-dimensional bosons behave like fermions in many respects. We have studied the underlying many-body physics through numerical simulations which accommodate both the soft-core and hard-core limits in one single framework. We find that the Tonks-Girardeau gas is reached only at the strongest optical lattice potentials. Results for slightly higher densities, where the gas develops a Mott-like phase already at weaker optical lattice potentials, show that these Mott-like short-range correlations do not enhance the convergence to the hard-core limit.     

Supersolid Phase in One-Dimensional Hard-Core Boson Hubbard Model with a Superlattice Potential

The ground state of the one-dimensional hard-core boson Hubbard model with a superlattice potential is studied by quantum Monte Carlo methods. We demonstrate that besides the CDW phase and the Mott insulator phase, the supersolid phase emerges due to the presence of the superlattice potential, which reflects the competition with the hopping term. We also study the densities of sublattices and have a clear idea about the distribution of the bosons on the lattice.     

Bose-Einstein condensation of S = 1 nickel spin degrees of freedom in NiCl2-4SC(NH2)2

It has recently been suggested that the organic compound NiCl2-4SC(NH2)2 (DTN) undergoes field-induced Bose-Einstein condensation (BEC) of the Ni spin degrees of freedom. The Ni S = 1 spins exhibit three-dimensional XY antiferromagnetism above a critical field H(c1) approximately 2 T. The spin fluid can be described as a gas of hard-core bosons where the field-induced antiferromagnetic transition corresponds to Bose-Einstein condensation. We have determined the spin Hamiltonian of DTN using inelastic neutron diffraction measurements, and we have studied the high-field phase diagram by means of specific heat and magnetocaloric effect measurements. Our results show that the field-temperature phase boundary approaches a power-law H - H(c1) proportional variant T(alpha)(c) near the quantum critical point, with an exponent that is consistent with the 3D BEC universal value of alpha = 1.5.     

Hard-core bosonization of the one-dimensional t-J model

The one-dimensional t-J model Hamiltonian is realized by using hard-core boson operators. A simple algorithm written in Mathematica based on a differential realization of the hard-core bosons for finding exact solutions of the model is proposed. As a simple example, some low-lying excitation energies, the inverse compressibility, and the superconducting structure factors, as well as the particle and spin entanglement of a system with 8 sites are calculated. The results not only confirm the validity of the hard-core boson picture, but also indicate that a quantum phase transition near phase-separation at zero temperature can also be recognized by the particle and spin entanglement.     

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.     

Topological phase separation in 2D hard-core Bose-Hubbard system away from half-filling

We suppose that the doping of the 2D hard-core boson system away from half-filling may result in the formation of a multicenter topological defect such as charge order (CO) bubble domain(s) with Bose superfluid (BS) and extra bosons both localized in domain wall(s), or a topological CO + BS phase separation, rather than a uniform mixed CO + BS supersolid phase. Starting from the classical model, we predict the properties of the respective quantum system. The long-wavelength behavior of the system is believed to resemble that of granular superconductors, CDW materials, Wigner crystals, and multiskyrmion system akin in a quantum Hall ferromagnetic state of a 2D electron gas.     

Long-Range Orders in Models of Itinerant Electrons Interacting with Heavy Quantum Fields

The Falicov–Kimball model consists of itinerant lattice fermions interacting with Ising spins by an on-site potential of strength U. Kennedy and Lieb proved that at half filling there is a low temperature phase with chessboard long range order on ^d , d2, for all non-zero values of U. Here we investigate the stability of this phase when small quantum fluctuations of the Ising spins are introduced in two different ways. The first one corresponds to replace the classical spins by quantum two level systems attached to each site of the lattice. In the second one we interpret the spins as occupation numbers of localized f-electrons or heavy ions which have a small kinetic energy. This leads to the so-called asymmetric Hubbard model. For both models we prove that for all non-zero values of U the long range order of the original Falicov–Kimball model remains stable if the additional quantum fluctuations are small enough. This result is proved by non-perturbative methods based on a chessboard estimate and the principle of exponential localisation. In order to derive the chessboard estimate the phase factors in the kinetic energy of fermions must have a flux equal to . We also investigate the models where the fermions are replaced by hard-core bosons and prove the same result for large U. For hard core bosons the kinetic term is the conventional one with zero phase factors. For small U and hard-core bosons we find that there is an off-diagonal long range order for low enough temperature and any strength of the additional quantum fluctuations. Open problems are 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.     

Quantum Monte Carlo study of hard-core bosons in Creutz ladder with zero flux

The quantum phase of hard-core bosons in Creutz ladder with zero flux is studied.For a specific regime of the parameters(t_x=t_p,t_y0),the exact ground-state is found analytically,which is a dimerized insulator with one electron bound in each rung of the ladder.For the case t_x,t_y,t_p0,the system is exactly studied using quantum Monte Carlo(QMC)method without a sign problem.It is found that the system is a Mott insulator for small t_p and a quantum phase transition to a superfluid phase is driven by increasing t_p.The critical t~c _pis determined precisely by a scaling analysis.Since it is possible that the Creutz ladder is realized experimentally,the theoretical results are interesting to the cold-atom experiments.     

Non-abelian quantum Hall effect in topological flat bands

Inspired by the recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-abelian quantum Hall effect in lattice models with topological flat bands. Through extensive numerical studies on the Haldane model with three-body hard-core bosons loaded into a topological flat band, we find convincing numerical evidence of a stable ν=1 bosonic non-abelian quantum Hall effect, with the characteristic threefold quasidegeneracy of ground states on a torus, a quantized Chern number, and a robust spectrum gap. Moreover, the spectrum for two-quasihole states also shows a finite energy gap, with the number of states in the lower-energy sector satisfying the same counting rule as the Moore-Read pfaffian state.     

Solids and supersolids of three-body interacting polar molecules on an optical lattice

We study the physics of cold polar molecules loaded into an optical lattice in the regime of strong three-body interactions, as put forward recently by Büchler et al. [Nature Phys. 3, 726 (2007)]. To this end, quantum Monte Carlo simulations, exact diagonalization, and a semiclassical approach are used to explore hard-core bosons on the 2D square lattice which interact solely by long-ranged three-body terms. The resulting phase diagram shows a sequence of solid and supersolid phases. Our findings are directly relevant for future experimental implementations and open a new route towards the discovery of a lattice supersolid phase in experiment.     

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.