15,655 research outputs found
Exact Monte Carlo time dynamics in many-body lattice quantum systems
On the base of a Feynman-Kac--type formula involving Poisson stochastic
processes, recently a Monte Carlo algorithm has been introduced, which
describes exactly the real- or imaginary-time evolution of many-body lattice
quantum systems. We extend this algorithm to the exact simulation of
time-dependent correlation functions. The techniques generally employed in
Monte Carlo simulations to control fluctuations, namely reconfigurations and
importance sampling, are adapted to the present algorithm and their validity is
rigorously proved. We complete the analysis by several examples for the
hard-core boson Hubbard model and for the Heisenberg model
A matrix product algorithm for stochastic dynamics on networks, applied to non-equilibrium Glauber dynamics
We introduce and apply a novel efficient method for the precise simulation of
stochastic dynamical processes on locally tree-like graphs. Networks with
cycles are treated in the framework of the cavity method. Such models
correspond, for example, to spin-glass systems, Boolean networks, neural
networks, or other technological, biological, and social networks. Building
upon ideas from quantum many-body theory, the new approach is based on a matrix
product approximation of the so-called edge messages -- conditional
probabilities of vertex variable trajectories. Computation costs and accuracy
can be tuned by controlling the matrix dimensions of the matrix product edge
messages (MPEM) in truncations. In contrast to Monte Carlo simulations, the
algorithm has a better error scaling and works for both, single instances as
well as the thermodynamic limit. We employ it to examine prototypical
non-equilibrium Glauber dynamics in the kinetic Ising model. Because of the
absence of cancellation effects, observables with small expectation values can
be evaluated accurately, allowing for the study of decay processes and temporal
correlations.Comment: 5 pages, 3 figures; minor improvements, published versio
Quantum trajectories and open many-body quantum systems
The study of open quantum systems has become increasingly important in the
past years, as the ability to control quantum coherence on a single particle
level has been developed in a wide variety of physical systems. In quantum
optics, the study of open systems goes well beyond understanding the breakdown
of quantum coherence. There, the coupling to the environment is sufficiently
well understood that it can be manipulated to drive the system into desired
quantum states, or to project the system onto known states via feedback in
quantum measurements. Many mathematical frameworks have been developed to
describe such systems, which for atomic, molecular, and optical (AMO) systems
generally provide a very accurate description of the open quantum system on a
microscopic level. In recent years, AMO systems including cold atomic and
molecular gases and trapped ions have been applied heavily to the study of
many-body physics, and it has become important to extend previous understanding
of open system dynamics in single- and few-body systems to this many-body
context. A key formalism that has already proven very useful in this context is
the quantum trajectories technique. This was developed as a numerical tool for
studying dynamics in open quantum systems, and falls within a broader framework
of continuous measurement theory as a way to understand the dynamics of large
classes of open quantum systems. We review the progress that has been made in
studying open many-body systems in the AMO context, focussing on the
application of ideas from quantum optics, and on the implementation and
applications of quantum trajectories methods. Control over dissipative
processes promises many further tools to prepare interesting and important
states in strongly interacting systems, including the realisation of parameter
regimes in quantum simulators that are inaccessible via current techniques.Comment: 66 pages, 29 figures, review article submitted to Advances in Physics
- comments and suggestions are welcom
Quantum Annealing and Analog Quantum Computation
We review here the recent success in quantum annealing, i.e., optimization of
the cost or energy functions of complex systems utilizing quantum fluctuations.
The concept is introduced in successive steps through the studies of mapping of
such computationally hard problems to the classical spin glass problems. The
quantum spin glass problems arise with the introduction of quantum
fluctuations, and the annealing behavior of the systems as these fluctuations
are reduced slowly to zero. This provides a general framework for realizing
analog quantum computation.Comment: 22 pages, 7 figs (color online); new References Added. Reviews of
Modern Physics (in press
The Coupled Electron-Ion Monte Carlo Method
In these Lecture Notes we review the principles of the Coupled Electron-Ion
Monte Carlo methods and discuss some recent results on metallic hydrogen.Comment: 38 pages, 6 figures, Lecture notes for the International School of
Solid State Physics, 34th course: "Computer Simulation in Condensed Matter:
from Materials to Chemical Biology", 20 July-1 August 2005 Erice (Italy). To
appear in Lecture Notes in Physics (2006
Stochastic Differential Equations for Quantum Dynamics of Spin-Boson Networks
The quantum dynamics of open many-body systems poses a challenge for
computational approaches. Here we develop a stochastic scheme based on the
positive P phase-space representation to study the nonequilibrium dynamics of
coupled spin-boson networks that are driven and dissipative. Such problems are
at the forefront of experimental research in cavity and solid state
realizations of quantum optics, as well as cold atom physics, trapped ions and
superconducting circuits. We demonstrate and test our method on a driven,
dissipative two-site system, each site involving a spin coupled to a photonic
mode, with photons hopping between the sites, where we find good agreement with
Monte Carlo Wavefunction simulations. In addition to numerically reproducing
features recently observed in an experiment [Phys. Rev. X 4, 031043 (2014)], we
also predict a novel steady state quantum dynamical phase transition for an
asymmetric configuration of drive and dissipation.Comment: 15 pages, 8 figure
Metropolis Methods for Quantum Monte Carlo Simulations
Since its first description fifty years ago, the Metropolis Monte Carlo
method has been used in a variety of different ways for the simulation of
continuum quantum many-body systems. This paper will consider some of the
generalizations of the Metropolis algorithm employed in quantum Monte Carlo:
Variational Monte Carlo, dynamical methods for projector monte carlo ({\it
i.e.} diffusion Monte Carlo with rejection), multilevel sampling in path
integral Monte Carlo, the sampling of permutations, cluster methods for lattice
models, the penalty method for coupled electron-ionic systems and the Bayesian
analysis of imaginary time correlation functions.Comment: Proceedings of "Monte Carlo Methods in the Physical Sciences"
Celebrating the 50th Anniversary of the Metropolis Algorith
Quantum gases in optical lattices
The experimental realization of correlated quantum phases with ultracold
gases in optical lattices and their theoretical understanding has witnessed
remarkable progress during the last decade. In this review we introduce basic
concepts and tools to describe the many-body physics of quantum gases in
optical lattices. This includes the derivation of effective lattice
Hamiltonians from first principles and an overview of the emerging quantum
phases. Additionally, state-of-the-art numerical tools to quantitatively treat
bosons or fermions on different lattices are introduced.Comment: 29 pages, 3 figures. This article will be published as Chapter 2 in
"Quantum gas experiments - exploring many-body states", edited by P. Torma
and K. Sengstock, Imperial College Press, London, to be published 201
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