Meron-Cluster Solution of Fermion and Other Sign Problems

Numerical simulations of numerous quantum systems suffer from the notorious sign problem. Important examples include QCD and other field theories at non-zero chemical potential, at non-zero vacuum angle, or with an odd number of flavors, as well as the Hubbard model for high-temperature superconductivity and quantum antiferromagnets in an external magnetic field. In all these cases standard simulation algorithms require an exponentially large statistics in large space-time volumes and are thus impossible to use in practice. Meron-cluster algorithms realize a general strategy to solve severe sign problems but must be constructed for each individual case. They lead to a complete solution of the sign problem in several of the above cases.Comment: 15 pages,LATTICE9

A many-fermion generalization of the Caldeira-Leggett model

We analyze a model system of fermions in a harmonic oscillator potential under the influence of a dissipative environment: The fermions are subject to a fluctuating force deriving from a bath of harmonic oscillators. This represents an extension of the well-known Caldeira-Leggett model to the case of many fermions. Using the method of bosonization, we calculate one- and two-particle Green's functions of the fermions. We discuss the relaxation of a single extra particle added above the Fermi sea, considering also dephasing of a particle added in a coherent superposition of states. The consequences of the separation of center-of-mass and relative motion, the Pauli principle, and the bath-induced effective interaction are discussed. Finally, we extend our analysis to a more generic coupling between system and bath, that results in complete thermalization of the system.Comment: v3: fixed pdf problem; v2: added exact formula (Eq. 42) for Green's function and discussion of equilibrium density matrix (new Fig. 2); 10 figures, 21 pages, see quant-ph/0305098 for brief version of some of these result

Correlation Lengths in Quantum Spin Ladders

Analytic expressions for the correlation length temperature dependences are given for antiferromagnetic spin-1/2 Heisenberg ladders using a finite-size non-linear sigma-model approach. These calculations rely on identifying three successive crossover regimes as a function of temperature. In each of these regimes, precise and controlled approximations are formulated. The analytical results are found to be in excellent agreement with Monte Carlo simulations for the Heisenberg Hamiltonian.Comment: 5 pages LaTeX using RevTeX, 3 encapsulated postscript figure

Dynamical simulation of current fluctuations in a dissipative two-state system

Current fluctuations in a dissipative two-state system have been studied using a novel quantum dynamics simulation method. After a transformation of the path integrals, the tunneling dynamics is computed by deterministic integration over the real-time paths under the influence of colored noise. The nature of the transition from coherent to incoherent dynamics at low temperatures is re-examined.Comment: 4 pages, 4 figures; to appear in Phys. Rev. Letter

The Square-Lattice Heisenberg Antiferromagnet at Very Large Correlation Lengths

The correlation length of the square-lattice spin-1/2 Heisenberg antiferromagnet is studied in the low-temperature (asymptotic-scaling) regime. Our novel approach combines a very efficient loop cluster algorithm -- operating directly in the Euclidean time continuum -- with finite-size scaling. This enables us to probe correlation lengths up to $\xi \approx 350,000$ lattice spacings -- more than three orders of magnitude larger than any previous study. We resolve a conundrum concerning the applicability of asymptotic-scaling formulae to experimentally- and numerically-determined correlation lengths, and arrive at a very precise determination of the low-energy observables. Our results have direct implications for the zero-temperature behavior of spin-1/2 ladders.Comment: 12 pages, RevTeX, plus two Postscript figures. Some minor modifications for final submission to Physical Review Letters. (accepted by PRL

Pseudo-gap behavior in dynamical properties of high-Tc cuprates

Dynamical properties of 2D antiferromagnets with hole doping are investigated to see the effects of short range local magnetic order on the temperature dependence of the dynamical magnetic susceptibility. We show the pseudo-gap like behavior of the temperature dependence of the NMR relaxation rate. We also discuss implications of the results in relations to the observed spin gap like behavior of low-doped copper oxide high-$T_c$ superconductors.Comment: 3 pages, Revtex, with 2 eps figures, to appear in J.Phys.Soc.Jpn. Vol.67 No.

Nontrivial behavior of the Fermi arc in the staggered-flux ordered phase

The doping and temperature dependences of the Fermi arc in the staggered-flux, or the d-density wave, ordered phase of the t-J model are analyzed by the U(1) slave boson theory. Nontrivial behavior is revealed by the self-consistent calculation. At low doped and finite-temperature region, both the length of the Fermi arc and the width of the Fermi pocket are proportional to $\delta$ and the area of the Fermi pocket is proportional to $\delta^2$. This behavior is completely different from that at the zero temperature, where the area of the Fermi pocket becomes $\pi^2 \delta$. This behavior should be observed by detailed experiments of angle-resolved photoemission spectroscopy in the pseudogap phase of high-T_c cuprates if the pseudogap phase is the staggered-flux ordered phase.Comment: 4 pages, 4 figure

Critical exponents of the quantum phase transition in a planar antiferromagnet

We have performed a large scale quantum Monte Carlo study of the quantum phase transition in a planar spin-1/2 Heisenberg antiferromagnet with CaV4O9 structure. We obtain a dynamical exponent z=1.018+/-0.02. The critical exponents beta, nu and eta agree within our errors with the classical 3D O(3) exponents, expected from a mapping to the nonlinear sigma model. This confirms the conjecture of Chubukov, Sachdev and Ye [Phys. Rev. B 49, 11919 (1994)] that the Berry phase terms in the planar Heisenberg antiferromagnet are dangerously irrelevant.Comment: 5 pages including 4 figures; revised version: some minor changes and added reference

Fermionic Mach-Zehnder interferometer subject to a quantum bath

We study fermions in a Mach-Zehnder interferometer, subject to a quantum-mechanical environment leading to inelastic scattering, decoherence, renormalization effects, and time-dependent conductance fluctuations. Both the loss of interference contrast as well as the shot noise are calculated, using equations of motion and leading order perturbation theory. The full dependence of the shot-noise correction on setup parameters, voltage, temperature and the bath spectrum is presented. We find an interesting contribution due to correlations between the fluctuating renormalized phase shift and the output current, discuss the limiting behaviours at low and high voltages, and compare with simpler models of dephasing.Comment: 5 pages, 3 figure

Phase diagram of depleted Heisenberg model for CaV4O9

We have numerically investigated the 1/5-depleted Heisenberg square lattice representing CaV4O9 using the Quantum Monte Carlo loop algorithm. We have determined the phase diagram of the model as a function of the ratio of the two different couplings: bonds within a plaquette and dimer bonds between plaquettes. By calculating both the spin gap and the staggered magnetization we determine the range of stability of the long range ordered (LRO) phase. At isotropic coupling LRO survives the depletion. But the close vicinity of the isotropic point to the spin gap phase leads us to the conclusion that already a small frustrating next nearest neighbor interaction can drive the system into the quantum disordered phase and thus explain the spin gap behavior of CaV4O9