206 research outputs found
A Variational Approach to Monte Carlo Renormalization Group
We present a Monte Carlo method for computing the renormalized coupling
constants and the critical exponents within renormalization theory. The scheme,
which derives from a variational principle, overcomes critical slowing down, by
means of a bias potential that renders the coarse grained variables
uncorrelated. The 2D Ising model is used to illustrate the method.Comment: 4 pages, 3 figures, 1 tabl
A Variational Approach to Monte Carlo Renormalization Group
We present a Monte Carlo method for computing the renormalized coupling
constants and the critical exponents within renormalization theory. The scheme,
which derives from a variational principle, overcomes critical slowing down, by
means of a bias potential that renders the coarse grained variables
uncorrelated. The 2D Ising model is used to illustrate the method.Comment: 4 pages, 3 figures, 1 tabl
Monte Carlo Renormalization Group for Systems with Quenched Disorder
We extend to quenched disordered systems the variational scheme for real
space renormalization group calculations that we recently introduced for
homogeneous spin Hamiltonians. When disorder is present our approach gives
access to the flow of the renormalized Hamiltonian distribution, from which one
can compute the critical exponents if the correlations of the renormalized
couplings retain finite range. Key to the variational approach is the bias
potential found by minimizing a convex functional in statistical mechanics.
This potential reduces dramatically the Monte Carlo relaxation time in large
disordered systems. We demonstrate the method with applications to the
two-dimensional dilute Ising model, the random transverse field quantum Ising
chain, and the random field Ising in two and three dimensional lattices
Continuous-time Monte Carlo Renormalization Group
We implement Monte Carlo Renormalization Group (MCRG) in the continuous-time
Monte Carlo simulation of a quantum system. We demonstrate numerically the
emergent isotropy between space and time at large distances for the systems
that exhibit Lorentz invariance at quantum criticality. This allows us to
estimate accurately the sound velocity for these quantum systems. -state
Potts models in one and two space dimensions are used to illustrate the method
Quantum Momentum Distribution and Quantum Entanglement in the Deep Tunneling Regime
In this paper, we consider the momentum operator of a quantum particle
directed along the displacement of two of its neighbors. A modified open-path
path integral molecular dynamics is presented to sample the distribution of
this directional momentum distribution, where we derive and use a new estimator
for this distribution. Variationally enhanced sampling is used to obtain this
distribution for an example molecule, Malonaldehyde, in the very low
temperature regime where deep tunneling happens. We find no secondary feature
in the directional momentum distribution, and that its absence is due to
quantum entanglement through a further study of the reduced density matrix
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