We report results from a systematic analytic strong-coupling expansion of the Bose-Hubbard model in one and two spatial dimensions. We obtain numerically exact results for the dispersion of single particle and single hole excitations in the Mott insulator. The boundary of the Mott phase can be determined with previously unattainable accuracy in one and two dimensions. In one dimension we observe the occurrence of reentrant behavior from the compressible to the insulating phase in a region close to the critical point which was conjectured in earlier work. Our calculation can be used as a benchmark for the development of new numerical techniques for strongly correlated systems.PACS numbers: 05.30. Jp, 05.70.Jk, 67.40.Db Quantum phase transitions in strongly correlated systems have attracted a lot of interest in recent years. In fermionic systems the Mott transition is complicated by the fact that in unfrustrated systems the antiferromagnetic transition and localization transition occur at the same point (see e.g. [1]). For interacting Bose systems with spin zero the situation is much simpler and one can focus on the physics of the Mott transition. Strongly interacting bosonic systems are not only of academic interest. Physical realizations include Josephson junction arrays, granular and short-correlation-length superconductors, flux-lattices in type-II superconductors and possibly in the future ultracold atoms in a periodic potential [2,3,4].To be specific we investigate the generic model for the Mott transition, the Hubbard model, for bosons (BH model):where the b † i and b i are bosonic creation and annihilation operators,n i = b † i b i is the number of particles on site i, t the hopping matrix element, U > 0 the on-site repulsion and µ the chemical potential. With short range interactions only the model has two phases at zero temperature: a superfluid phase and a Mott phase. Much of the physics of the model was already understood qualitatively in an early paper by Fisher et al. [5] and subsequent papers (see e.g. [6,7,8 ]).It is however interesting to obtain a quantitative understanding of the model -for example to compare with experiments. To this end the BH model has been studied numerically by Quantum Monte Carlo simulations [9,10,11,12,13,14,15] in one and two spatial dimensions. Recently the one-dimensional case was also investigated using the density-matrix renormalisation group (DMRG) [16]. This study found indications for an unexpected reentrant behavior from the superfluid to the Mottinsulator as a function of the hopping amplitude t for certain values of the chemical potential.In this Letter we report for the first time a systematic analytic strong coupling series to high order for the Bose-Hubbard model. Previous attempts which were restricted to rather low order [17] showed promising results but were not sufficient to investigate the asymptotic behavior of the series. Recently M. Gelfand [18] proposed a method for a linked cluster expansion with degenerate states. We have implemented the series ...

We have studied the spin-;| Heisenberg antiferromagnet on the triangular lattice by high temperature series expansions. Prom an analysis of the antiferromagnetic structure factor and correlation length, we deduce that the ground state has small but nonzero long range antiferromagnetic order. We also determine the temperature dependence of the uniform susceptibility and the specific heat.PACS numbers: 75.10.JmThe behavior of frustrated quantum-spin systems in two dimensions is of considerable interest, particular attention being given to whether quantum fluctuations destroy the long range magnetic order (LRMO) which is generally present in the classical ground state. The simplest frustrated quantum-spin system is probably the spin-\ Heisenberg antiferromagnet (HAF) on the triangular lattice, which was the original model for Anderson's proposed resonant valence bond state [1]. More recently Kalmeyer and Laughlin (KL) [2] proposed a different ground state for this model, also without long range magnetic order but with chiral symmetry breaking. However, Huse and Elser [3] found variational states with a large antiferromagnetic order parameter, which had significantly lower energy than the KL states, which suggests that the ground state may have LRMO. This possibility is also consistent with spin-wave theory, for which the lowest order approximation [4] predicts the staggered magnetization to be about 48% of the classical value and the next order correction actually increases this a little [5]. Exact diagonalization of small clusters [6, 7] suggested no LRMO, while two recent calculations, which included the cluster with N = 36 sites [8,9], have come to opposite conclusions about the existence of LRMO. Another useful approach is series expansions. One of us (R.R.P.S.) and D. Huse [10] investigated the HAF on the triangular and kagome lattices by introducing an Isingtype anisotropy into the Hamiltonian. Ground state properties were determined by expanding away from the ground state in the Ising limit. Extrapolation of the results to the Heisenberg model indicated that the ground state is close to the critical point for antiferromagnetism, so if there is long range order, it is very small compared with the classical value.In this paper we investigate the spin-| HAF on the triangular lattice by high temperature series expansions. It seems a particularly useful approach for the HAF on the triangular lattice, since other methods have been rather inconclusive and quantum Monte Carlo simulations have sign problems [11]. Furthermore, there is at least one corresponding experimental system, NaTi02 [12]. Ex-periments are done at finite temperatures, so it is important to have accurate results for the temperature dependence of measurable quantities. By contrast, most of the earlier calculations just investigated ground state properties. Although there is no long range magnetic order at finite temperature for two-dimensional systems with continuous symmetry, the temperature dependence of certain quantities, discussed below, indic...

For the spin-1 2 Heisenberg antiferromagnet on the Kagomé lattice we calculate the high temperature series for the specific heat and the structure factor. A comparison of the series with exact diagonalisation studies shows that the specific heat has further structure at lower temperature in addition to a high temperature peak at T ≈ 2/3. At T = 0.25 the structure factor agrees quite well with results for the ground state of a finite cluster with 36 sites.At this temperature the structure factor is less than two times its T = ∞ value and depends only weakly on the wavevector q, indicating the absence of magnetic order and a correlation length of less than one lattice spacing. The uniform susceptibility has a maximum at T ≈ 1/6 and vanishes exponentially for lower temperatures.

We present a series expansion study of spin-S square-lattice Heisenberg antiferromagnets. The numerical data are in excellent agreement with recent neutron scattering measurements. Our key result is that the correlation length ξ for S > 1/2 strongly deviates from the exact T → 0 (renormalized classical, or RC) scaling prediction for all experimentally and numerically accessible temperatures. We note basic trends with S of the experimental and series expansion correlation length data and propose a scaling crossover scenario to explain them.