Direct mapping of the finite temperature phase diagram of strongly correlated quantum models

Optical lattice experiments, with the unique potential of tuning interactions and density, have emerged as emulators of nontrivial theoretical models that are directly relevant for strongly correlated materials. However, so far the finite temperature phase diagram has not been mapped out for any strongly correlated quantum model. We propose a remarkable method for obtaining such a phase diagram for the first time directly from experiments using only the density profile in the trap as the input. We illustrate the procedure explicitly for the Bose Hubbard model, a textbook example of a quantum phase transition from a superfluid to a Mott insulator. Using "exact" quantum Monte Carlo simulations in a trap with up to $10^6$ bosons, we show that kinks in the local compressibility, arising from critical fluctuations, demarcate the boundaries between superfluid and normal phases in the trap. The temperature of the bosons in the optical lattice is determined from the density profile at the edge. Our method can be applied to other phase transitions even when reliable numerical results are not available.Comment: 12 pages, 5 figure

Numerical study of the ordering of the +-J XY spin-glass ladder

The properties of the domain-wall energy and of the correlation length are studied numerically for the one-dimensional +-J XY spin glass on the two-leg ladder lattice, focusing on both the spin and the chirality degrees of freedom. Analytic results obtained by Ney-Niftle et al for the same model were confirmed for asymptotically large lattices, while the approach to the asymptotic limit is slow and sometimes even non-monotonic. Attention is called to the occurrence of the SO(2)-Z_2 decoupling and its masking in spin correlations, the latter reflecting the inequality between the SO(2) and Z_2 exponents. Discussion is given concerning the behaviors of the higher-dimensional models.Comment: 14 pages, 10 figure

Generalization of the Fortuin-Kasteleyn transformation and its application to quantum spin simulations,

We generalize the Fortuin-Kasteleyn (FK) cluster representation of the partition function of the Ising model to represent the partition function of quantum spin models with an arbitrary spin magnitude in arbitrary dimensions. This generalized representation enables us to develop a new cluster algorithm for the simulation of quantum spin systems by the worldline Monte Carlo method. Because the Swendsen-Wang algorithm is based on the FK representation, the new cluster algorithm naturally includes it as a special case. As well as the general description of the new representation, we present an illustration of our new algorithm for some special interesting cases: the Ising model, the antiferromagnetic Heisenberg model with $S=1$, and a general Heisenberg model. The new algorithm is applicable to models with any range of the exchange interaction, any lattice geometry, and any dimensions.Comment: 46 pages, 10 figures, to appear in J.Stat.Phy

Quantum simulations of the superfluid-insulator transition for two-dimensional, disordered, hard-core bosons

We introduce two novel quantum Monte Carlo methods and employ them to study the superfluid-insulator transition in a two-dimensional system of hard-core bosons. One of the methods is appropriate for zero temperature and is based upon Green's function Monte Carlo; the other is a finite-temperature world-line cluster algorithm. In each case we find that the dynamical exponent is consistent with the theoretical prediction of $z=2$ by Fisher and co-workers.Comment: Revtex, 10 pages, 3 figures (postscript files attached at end, separated by %%%%%% Fig # %%%%%, where # is 1-3). LA-UR-94-270

Crossovers in the Two Dimensional Ising Spin Glass with ferromagnetic next-nearest-neighbor interactions

By means of extensive computer simulations we analyze in detail the two dimensional $\pm J$ Ising spin glass with ferromagnetic next-nearest-neighbor interactions. We found a crossover from ferromagnetic to ``spin glass'' like order both from numerical simulations and analytical arguments. We also present evidences of a second crossover from the ``spin glass'' behavior to a paramagnetic phase for the largest volume studied.Comment: 19 pages with 9 postscript figures also available at http://chimera.roma1.infn.it/index_papers_complex.html. Some changes in captions of figures 1 and

Monte Carlo Simulation of the Three-dimensional Ising Spin Glass

We study the 3D Edwards-Anderson model with binary interactions by Monte Carlo simulations. Direct evidence of finite-size scaling is provided, and the universal finite-size scaling functions are determined. Using an iterative extrapolation procedure, Monte Carlo data are extrapolated to infinite volume up to correlation length \xi = 140. The infinite volume data are consistent with both a continuous phase transition at finite temperature and an essential singularity at finite temperature. An essential singularity at zero temperature is excluded.Comment: 5 pages, 6 figures. Proceedings of the Workshop "Computer Simulation Studies in Condensed Matter Physics XII", Eds. D.P. Landau, S.P. Lewis, and H.B. Schuettler, (Springer Verlag, Heidelberg, Berlin, 1999

Scalings of domain wall energies in two dimensional Ising spin glasses

We study domain wall energies of two dimensional spin glasses. The scaling of these energies depends on the model's distribution of quenched random couplings, falling into three different classes. The first class is associated with the exponent theta =-0.28, the other two classes have theta = 0, as can be justified theoretically. In contrast to previous claims, we find that theta=0 does not indicate d=d_l but rather d <= d_l, where d_l is the lower critical dimension.Comment: Clarifications and extra reference