Comment on ``One-Dimensional Disordered Bosonic Hubbard Model: A Density-Matrix Renormalization Group Study"

We present the phase diagram of the system obtained by continuous-time worldline Monte Carlo simulations, and demonstrate that the actual phase diagram is in sharp contrast with that found in Phys. Rev. Lett., 76 (1996) 2937.Comment: 1 page, LaTex, 1 figur

Diagrammatic Quantum Monte Carlo for Two-Body Problem: Exciton

We present a novel method for precise numerical solution of the irreducible two-body problem and apply it to excitons in solids. The approach is based on the Monte Carlo simulation of the two-body Green function specified by Feynman's diagrammatic expansion. Our method does not rely on the specific form of the electron and hole dispersion laws and is valid for any attractive electron-hole potential. We establish limits of validity of the Wannier (large radius) and Frenkel (small radius) approximations, present accurate data for the intermediate radius excitons, and give evidence for the charge transfer nature of the monopolar exciton in mixed valence materials.Comment: 4 pages, 5 figure

Exact Critical Exponents for Pseudo-Particles in the Kondo Problem

Exact critical exponents of the Green functions for pseudo-fermions and slave bosons in the SU($N$) Anderson model with $U\rightarrow\infty$ are obtained by using the Bethe ansatz solution and boundary conformal field theory. They are evaluated exactly for mixed valence systems and Kondo systems with crystalline fields. The results agree with the prediction of Menge and M\"uller-Hartmann, which coincide with those of the X-ray problem. Some implication of our results in one-dimensional chiral systems is also discussed.Comment: 9 pages, no figure

Quantum Relaxation of Magnetisation in Magnetic Particles

At temperatures below the magnetic anisotropy energy, monodomain magnetic systems (small particles, nanomagnetic devices, etc.) must relax quantum mechanically. This quantum relaxation must be mediated by the coupling to both nuclear spins and phonons (and electrons if either particle or substrate is conducting. We analyze the effect of each of these couplings, and then combine them. Conducting systems can be modelled by a "giant Kondo" Hamiltonian, with nuclear spins added in as well. At low temperatures, even microscopic particles on a conducting substrate (containing only $10-50$ spins) will have their magnetisation frozen over millenia by a combination of electronic dissipation and the "degeneracy blocking" caused by nuclear spins. Raising the temperature leads to a sudden unblocking of the spin dynamics at a well defined temperature. Insulating systems are quite different. The relaxation is strongly enhanced by the coupling to nuclear spins. At short times the magnetisation of an ensemble of particles relaxes logarithmically in time, after an initial very fast decay; this relaxation proceeds entirely via the nuclear spins. At longer times phonons take over, but the decay rate is still governed by the temperature-dependent nuclear bias field acting on the particles - decay may be exponential or power-law depending on the temperature. The most surprising feature of the results is the pivotal role played by the nuclear spins. The results are relevant to any experiments on magnetic particles in which interparticle dipolar interactions are unimportant. They are also relevant to future magnetic device technology.Comment: 30 pages, RevTex, e:mail , Submitted to J.Low Temp.Phys. on 1 Nov. 199

Survival Probability of a Doorway State in regular and chaotic environments

We calculate survival probability of a special state which couples randomly to a regular or chaotic environment. The environment is modelled by a suitably chosen random matrix ensemble. The exact results exhibit non--perturbative features as revival of probability and non--ergodicity. The role of background complexity and of coupling complexity is discussed as well.Comment: 19 pages 5 Figure

Ultracold Dipolar Gases in Optical Lattices

This tutorial is a theoretical work, in which we study the physics of ultra-cold dipolar bosonic gases in optical lattices. Such gases consist of bosonic atoms or molecules that interact via dipolar forces, and that are cooled below the quantum degeneracy temperature, typically in the nK range. When such a degenerate quantum gas is loaded into an optical lattice produced by standing waves of laser light, new kinds of physical phenomena occur. These systems realize then extended Hubbard-type models, and can be brought to a strongly correlated regime. The physical properties of such gases, dominated by the long-range, anisotropic dipole-dipole interactions, are discussed using the mean-field approximations, and exact Quantum Monte Carlo techniques (the Worm algorithm).Comment: 56 pages, 26 figure

Magnetic qubits as hardware for quantum computers

We propose two potential realisations for quantum bits based on nanometre scale magnetic particles of large spin S and high anisotropy molecular clusters. In case (1) the bit-value basis states |0> and |1> are the ground and first excited spin states Sz = S and S-1, separated by an energy gap given by the ferromagnetic resonance (FMR) frequency. In case (2), when there is significant tunnelling through the anisotropy barrier, the qubit states correspond to the symmetric, |0>, and antisymmetric, |1>, combinations of the two-fold degenerate ground state Sz = +- S. In each case the temperature of operation must be low compared to the energy gap, \Delta, between the states |0> and |1>. The gap \Delta in case (2) can be controlled with an external magnetic field perpendicular to the easy axis of the molecular cluster. The states of different molecular clusters and magnetic particles may be entangled by connecting them by superconducting lines with Josephson switches, leading to the potential for quantum computing hardware.Comment: 17 pages, 3 figure

Bosons in optical lattices - from the Mott transition to the Tonks-Girardeau gas

We present results from quantum Monte Carlo simulations of trapped bosons in optical lattices, focusing on the crossover from a gas of softcore bosons to a Tonks-Girardeau gas in a one-dimensional optical lattice. We find that depending on the quantity being measured, the behavior found in the Tonks-Girardeau regime is observed already at relatively small values of the interaction strength. A finite critical value for entering the Tonks-Girardeau regime does not exist. Furthermore, we discuss the computational efficiency of two quantum Monte Carlo methods to simulate large scale trapped bosonic systems: directed loops in stochastic series expansions and the worm algorithm.Comment: 7 pages with 9 figures;v2: improved discussion on Tonks-Girardeau ga

Free energy of the Fr\"ohlich polaron in two and three dimensions

We present a novel Path Integral Monte Carlo scheme to solve the Fr\"ohlich polaron model. At intermediate and strong electron-phonon coupling, the polaron self-trapping is properly taken into account at the level of an effective action obtained by a preaveraging procedure with a retarded trial action. We compute the free energy at several couplings and temperatures in three and two dimensions. Our results show that the accuracy of the Feynman variational upper bound for the free energy is always better than 5% although the thermodynamics derived from it is not correct. Our estimates of the ground state energies demonstrate that the second cumulant correction to the variational upper bound predicts the self energy to better than 1% at intermediate and strong coupling.Comment: RevTeX 7 pages 3 figures, revised versio

Phase diagram of a Disordered Boson Hubbard Model in Two Dimensions

We study the zero-temperature phase transition of a two-dimensional disordered boson Hubbard model. The phase diagram of this model is constructed in terms of the disorder strength and the chemical potential. Via quantum Monte Carlo simulations, we find a multicritical line separating the weak-disorder regime, where a random potential is irrelevant, from the strong-disorder regime. In the weak-disorder regime, the Mott-insulator-to-superfluid transition occurs, while, in the strong-disorder regime, the Bose-glass-to-superfluid transition occurs. On the multicritical line, the insulator-to-superfluid transition has the dynamical critical exponent $z=1.35 \pm 0.05$ and the correlation length critical exponent $\nu=0.67 \pm 0.03$, that are different from the values for the transitions off the line. We suggest that the proliferation of the particle-hole pairs screens out the weak disorder effects.Comment: 4 pages, 4 figures, to be published in PR