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 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 3 He.A nearly universal feature of strongly correlated systems is a phase transition between a correlation-induced insulating phase with localized charge carriers, to an itinerant phase. High temperature superconductors [1], manganites [2] and the controversial two dimensional (2D) "metal-insulator-transition" [3] are just a few examples of this phenomenon. The 2D hard-core boson Hubbard model provides the simplest example of such a transition from a correlation-induced charge density wave insulator near half filling to a superfluid (SF). It is a prototypical model for preformed Cooper pairs [4], of spin flops in anisotropic quantum magnets [5,6], of SF Helium films [7] and of supersolids [8,9].In simulations on this model, which does not suffer from the negative sign problem of fermionic simulations, we can investigate some of the pertinent questions about such phase transitions: what is the order of the quantum phase transitions in the ground state and the finite temperature phase transitions? Are there special points with dynamically enhanced symmetry [10]? Can there be coexistence of two types of order (such as a supersolidcoexisting solid and superfluid order)? Answers to these questions provide insight also for the other problems alluded to above.The Hamiltonian of the hard-core boson Hubbard model we study iswhere a † i (a i ) is the creation (annihilation) operator for hard-core bosons, n i = a † i a i the number operator, V the nearest neighbor Coulomb repulsion and µ the chemical potential. This model is equivalent to an anisotropic spin-1/2 XXZ model with J z = V and |J xy | = 2t in a magnetic field h = 2V − µ. The zero field (and zero magnetization m z = 0) case of the spin model corresponds to the half filled bosonic model (density ρ = m z = 1/2) at µ = 2V . Throughout this Letter we will use the bosonic language, and refer to the corresponding quantities in the spin model where appropriate. Due to the absence of efficient Monte Carlo algorithms for classical magnets in a magnetic field there are still many open questions even in the classical version of this model, which was only studied by a local update method [11].In Fig. 1 we show the ground-state phase diagram [6,9,12]. For dominating chemical potential µ the system is in a band insulating state (ρ = 0 and ρ = 1 respectively), while it shows staggered checkerboard charge order (ρ = 1/2) for dominating repulsion V . These solid phases are separated from each other by a SF. Earlier in...

We use two Quantum Monte Carlo algorithms to map out the phase diagram of the twodimensional hardcore boson Hubbard model with near (V1) and next near (V2) neighbor repulsion. At half filling we find three phases: Superfluid (SF), checkerboard solid and striped solid depending on the relative values of V1, V2 and the kinetic energy. Doping away from half filling, the checkerboard solid undergoes phase separation: The superfluid and solid phases co-exist but not as a single thermodynamic phase. As a function of doping, the transition from the checkerboard solid is therefore first order. In contrast, doping the striped solid away from half filling instead produces a striped supersolid phase: Co-existence of density order with superfluidity as a single phase. One surprising result is that the entire line of transitions between the SF and checkerboard solid phases at half filling appears to exhibit dynamical O(3) symmetry restoration. The transitions appear to be in the same universality class as the special Heisenberg point even though this symmetry is explicitly broken by the V2 interaction.

We study various properties of bosons in two dimensions interacting only via onsite hardcore repulsion. In particular, we use the lattice spin-wave approximation to calculate the ground state energy, the density, the condensate density and the superfluid density in terms of the chemical potential. We also calculate the excitation spectrum, ω(k). In addition, we performed high precision numerical simulations using the stochastic series expansion algorithm. We find that the spin-wave results describe extremely well the numerical results over the whole density range 0 ≤ ρ ≤ 1. We also compare the lattice spin-wave results with continuum results obtained by summing the ladder diagrams at low density. We find that for ρ ≤ 0.1 there is good agreement, and that the difference between the two methods vanishes as ρ 2 for ρ → 0. This offers the possibility of obtaining precise continuum results by taking the continuum limit of the spin-wave results for all densities. Finaly, we studied numerically the finite temperature phase transition for the entire density range and compared with low density predictions.

The Stochastic Series Expansion method (SSE) is a Quantum Monte Carlo (QMC) technique working directly in the imaginary time continuum and thus avoiding "Trotter discretization" errors. Using a non-local "operator-loop update" it allows treating large quantum mechanical systems of many thousand sites. In this paper we first give a comprehensive review on SSE and present benchmark calculations of SSE's scaling behavior with system size and inverse temperature, and compare it to the loop algorithm, whose scaling is known to be one of the best of all QMC methods. Finally we introduce a new and efficient algorithm to measure Green's functions and thus dynamical properties within SSE.PACS numbers: 02.70.Ss, 05.10.Ln I. THE SSE TECHNIQUESince their first formulation in the early eightiesQuantum Monte Carlo (QMC) methods have become one of the most powerful numerical simulation techniques and tools in many-body physics. The first QMC algorithms were based on a discretization in imaginary time ("Trotter decomposition") and used purely local update steps to sample the system's statistically relevant states. These methods require a delicate extrapolation to zero discretization in order to reduce systematic errors. Furthermore, the purely local updates often proove incapable to traverse the accessible states in an efficient way: autocorrelation times grow rapidly with increasing system size.A more recent class of QMC algorithms, the so-called "loop algorithms" 5-12 , use non-local cluster or loop update schemes, thus reducing autocorrelation times by several orders of magnitude in some cases. Unfortunately, it is often highly non-trivial to construct a loop algorithm for a new Hamiltonian, and some important interactions cannot be incorporated into the loop scheme. These interactions have to be added as a posteriori acceptance probabilities after the construction of the loop, which can seriously decrease overall efficiency of the simulation. Some loop algorithms also suffer from "freezing" 5,13 when the probability is high that a certain type of cluster occupies almost the whole system. These insufficiencies can be overcome using the "stochastic series expansion" (SSE) approach together with a loop-type updating scheme (see Ref. 14 and earlier works referenced therein).• SSE is (almost) as efficient as loop algorithms on large systems.• It is a numerically exact method without any discretization error.• It is as easy to construct and general in applicability as world-line methods.Following Sandvik 14-16 we briefly outline the basic ideas of SSE now. The central quantity to be sampled in a QMC simulation is the partition functionwhereĤ is the system's Hamiltonian and β = 1/T the inverse temperature. Standard QMC techniques 17 split up the exponential into a product of many "imaginary time slices" e −∆τĤ and truncate the Taylor expansion of this expression after a certain order in ∆τ , thereby introducing a discretization error of order ∆τ n . In SSE, however, one chooses a convenient Hilbert base {| α } (for example the S z...

We present numerical studies of a quantum "projected" SO(5) model which aims at a unifying description of antiferromagnetism and superconductivity in the high- T(c) cuprates, while properly taking into account the Mott insulating gap. Our numerical results, obtained by the quantum Monte Carlo technique of stochastic series expansion, show that this model can give a realistic description of the global phase diagram of the high- T(c) superconductors and accounts for many of their physical properties. Moreover, we address the question of asymptotic restoring of the SO(5) symmetry at the critical point.