Quantum Monte Carlo method for the Bose-Hubbard model with harmonic confining potential

Quadrupole Order in the Frustrated Pyrochlore Tb_{2+x}Ti_{2-x}O_{7+y}

A hidden order that emerges in the frustrated pyrochlore Tb_{2+x}Ti_{2-x}O_{7+y} with T_{c}=0.53  K is studied using specific heat, magnetization, and neutron scattering experiments on a high-quality single crystal. Semiquantitative analyses based on a pseudospin-1/2 Hamiltonian for ionic non-Kramers magnetic doublets demonstrate that it is an ordered state of electric quadrupole moments. The elusive spin liquid state of the nominal Tb_{2}Ti_{2}O_{7} is most likely a U(1) quantum spin-liquid state.

Quantum tricriticality at the superfluid-insulator transition of binary Bose mixtures

Quantum criticality near a tricritical point is studied in the two-component Bose-Hubbard model on square lattices. The existence of a quantum tricritical point on a boundary of a superfluid-insulator transition is confirmed by quantum Monte Carlo simulations. Moreover, we analytically derive the quantum tricritical behaviors on the basis of an effective field theory. We find two significant features of the quantum tricriticality that are its characteristic chemical potential dependence of the superfluid transition temperature and a strong density fluctuation. We suggest that these features are directly observable in existing experimental setups of Bose-Bose mixtures in optical lattices.

Multidiscontinuity algorithm for world-line Monte Carlo simulations

We introduce a multidiscontinuity algorithm for the efficient global update of world-line configurations in Monte Carlo simulations of interacting quantum systems. This algorithm is a generalization of the two-discontinuity algorithms introduced in Refs. [N. Prokof'ev, B. Svistunov, and I. Tupitsyn, Phys. Lett. A 238, 253 (1998)] and [O. F. Syljuåsen and A. W. Sandvik, Phys. Rev. E 66, 046701 (2002)]. This generalization is particularly effective for studying Bose-Einstein condensates (BECs) of composite particles. In particular, we demonstrate the utility of the generalized algorithm by simulating a Hamiltonian for an S=1 antiferromagnet with strong uniaxial single-ion anisotropy. The multidiscontinuity algorithm not only solves the freezing problem that arises in this limit, but also allows the efficient computing of the off-diagonal correlator that characterizes a BEC of composite particles.

Commensurate supersolid of three-dimensional lattice bosons

Using an unbiased quantum Monte Carlo method, we obtain convincing evidence of the existence of a checkerboard supersolid at a commensurate filling factor 1/2 (a commensurate supersolid) in the soft-core Bose-Hubbard model with nearest-neighbor repulsions on a cubic lattice. In conventional cases, supersolids are realized at incommensurate filling factors by a doped-defect-condensation mechanism, where particles (holes) doped into a perfect crystal act as interstitials (vacancies) and delocalize in the crystal order. However, in the model, a supersolid state is stabilized even at the commensurate filling factor 1/2 without doping. By performing grand canonical simulations, we obtain a ground-state phase diagram that suggests the existence of a supersolid at a commensurate filling. To obtain direct evidence of the commensurate supersolid, we next perform simulations in canonical ensembles at a particle density ρ=1/2 and exclude the possibility of phase separation. From the obtained snapshots, we discuss its microscopic structure and observe that interstitial-vacancy pairs are unbound in the crystal order.

Validity of projected Gross-Pitaevskii simulation: comparison with quantum Monte Carlo

We examine the validity of the projected Gross-Pitaevskii simulation by taking the two-dimensional homogeneous bosonic system as an example. The long-distance behaviors of the correlation function and equilibrium temperatures show good agreement with those of the quantum Monte Carlo calculations below temperatures near the Kosterlitz-Thouless transition. We find that in the projected Gross-Pitaevskii description, one needs to estimate the optimal wave-number cutoff in temperature. In the well-described region, the projected Gross-Pitaevskii equation presents reliable predictions for the long-wave bosonic components.

Finite-size scaling for quantum criticality above the upper critical dimension: Superfluid-Mott-insulator transition in three dimensions

The validity of modified finite-size scaling above the upper critical dimension is demonstrated for the quantum phase transition whose dynamical critical exponent is z=2. We consider the N -component Bose-Hubbard model, which is exactly solvable and exhibits mean-field type critical phenomena in the large- N limit. The modified finite-size scaling holds exactly in that limit. However, the usual procedure, taking the large system-size limit with fixed temperature, does not lead to the expected (and correct) mean-field critical behavior because of the limited range of applicability of the finite-size scaling form. By quantum Monte Carlo simulation, it is shown that the modified finite-size scaling holds in the case of N=1.

Phase transition in spin systems with various types of fluctuations

Various types ordering processes in systems with large fluctuation are overviewed. Generally, the so-called order-disorder phase transition takes place in competition between the interaction causing the system be ordered and the entropy causing a random disturbance. Nature of the phase transition strongly depends on the type of fluctuation which is determined by the structure of the order parameter of the system. As to the critical property of phase transitions, the concept "universality of the critical phenomena" is well established. However, we still find variety of features of ordering processes. In this article, we study effects of various mechanisms which bring large fluctuation in the system, e.g., continuous symmetry of the spin in low dimensions, contradictions among interactions (frustration), randomness of the lattice, quantum fluctuations, and a long range interaction in off-lattice systems.