10 research outputs found
The directed-loop algorithm
The directed-loop scheme is a framework for generalized loop-type updates in
quantum Monte Carlo, applicable both to world-line and stochastic series
expansion methods. Here, the directed-loop equations, the solution of which
gives the probabilities of the various loop-building steps, are discussed in
the context of the anisotropic Heisenberg model in a uniform magnetic
field. This example shows how the directed-loop concept emerges as a natural
generalization of the conventional loop algorithm, where the loops are
selfavoiding, to cases where selfintersection must be allowed in order to
satisfy detailed balance.Comment: 10 pages, for the proceedings of "The Monte Carlo Method in the
Physical Sciences: Celebrating the 50th Anniversary of the Metropolis
Algorithm", Los Alamos, June 9-11, 200
Quantum Monte Carlo with Directed Loops
We introduce the concept of directed loops in stochastic series expansion and
path integral quantum Monte Carlo methods. Using the detailed balance rules for
directed loops, we show that it is possible to smoothly connect generally
applicable simulation schemes (in which it is necessary to include
back-tracking processes in the loop construction) to more restricted loop
algorithms that can be constructed only for a limited range of Hamiltonians
(where back-tracking can be avoided). The "algorithmic discontinuities" between
general and special points (or regions) in parameter space can hence be
eliminated. As a specific example, we consider the anisotropic S=1/2 Heisenberg
antiferromagnet in an external magnetic field. We show that directed loop
simulations are very efficient for the full range of magnetic fields (zero to
the saturation point) and anisotropies. In particular for weak fields and
anisotropies, the autocorrelations are significantly reduced relative to those
of previous approaches. The back-tracking probability vanishes continuously as
the isotropic Heisenberg point is approached. For the XY-model, we show that
back-tracking can be avoided for all fields extending up to the saturation
field. The method is hence particularly efficient in this case. We use directed
loop simulations to study the magnetization process in the 2D Heisenberg model
at very low temperatures. For LxL lattices with L up to 64, we utilize the
step-structure in the magnetization curve to extract gaps between different
spin sectors. Finite-size scaling of the gaps gives an accurate estimate of the
transverse susceptibility in the thermodynamic limit: chi_perp = 0.0659 +-
0.0002.Comment: v2: Revised and expanded discussion of detailed balance, error in
algorithmic phase diagram corrected, to appear in Phys. Rev.
Directed Loop Updates for Quantum Lattice Models
This article outlines how the quantum Monte Carlo directed loop update
recently introduced can be applied to a wide class of quantum lattice models.
Several models are considered: Spin-S XXZ models with longitudinal and
transverse magnetic fields, boson models with two-body interactions, and 1D
spinful fermion models. Expressions are given for the parameter regimes were
very efficient "no-bounce" quantum Monte Carlo algorithms can be found.Comment: 18 pages, 19 figure
Pressure control of nonferroelastic ferroelectric domains in ErMnO3
Mechanical pressure controls the structural, electric, and magnetic order in solid-state systems, allowing tailoring of their physical properties. A well-established example is ferroelastic ferroelectrics, where the coupling between pressure and the primary symmetry-breaking order parameter enables hysteretic switching of the strain state and ferroelectric domain engineering. Here, we study the pressure-driven response in a nonferroelastic ferroelectric, ErMnO3, where the classical stress–strain coupling is absent and the domain formation is governed by creation–annihilation processes of topological defects. By annealing ErMnO3 polycrystals under variable pressures in the MPa regime, we transform nonferroelastic vortex-like domains into stripe-like domains. The width of the stripe-like domains is determined by the applied pressure as we confirm by three-dimensional phase field simulations, showing that pressure leads to oriented layer-like periodic domains. Our work demonstrates the possibility to utilize mechanical pressure for domain engineering in nonferroelastic ferroelectrics, providing a lever to control their dielectric and piezoelectric responses
Pressure Control of Nonferroelastic Ferroelectric Domains in ErMnO₃
Mechanical pressure controls the structural, electric, and magnetic order in solid-state systems, allowing tailoring of their physical properties. A well-established example is ferroelastic ferroelectrics, where the coupling between pressure and the primary symmetry-breaking order parameter enables hysteretic switching of the strain state and ferroelectric domain engineering. Here, we study the pressure-driven response in a nonferroelastic ferroelectric, ErMnO₃, where the classical stress–strain coupling is absent and the domain formation is governed by creation–annihilation processes of topological defects. By annealing ErMnO₃ polycrystals under variable pressures in the MPa regime, we transform nonferroelastic vortex-like domains into stripe-like domains. The width of the stripe-like domains is determined by the applied pressure as we confirm by three-dimensional phase field simulations, showing that pressure leads to oriented layer-like periodic domains. Our work demonstrates the possibility to utilize mechanical pressure for domain engineering in nonferroelastic ferroelectrics, providing a lever to control their dielectric and piezoelectric responses.ISSN:1530-6984ISSN:1530-699
Pressure Control of Nonferroelastic Ferroelectric Domains in ErMnO<sub>3</sub>
Mechanical pressure controls the structural, electric,
and magnetic
order in solid-state systems, allowing tailoring of their physical
properties. A well-established example is ferroelastic ferroelectrics,
where the coupling between pressure and the primary symmetry-breaking
order parameter enables hysteretic switching of the strain state and
ferroelectric domain engineering. Here, we study the pressure-driven
response in a nonferroelastic ferroelectric, ErMnO3, where
the classical stress–strain coupling is absent and the domain
formation is governed by creation–annihilation processes of
topological defects. By annealing ErMnO3 polycrystals under
variable pressures in the MPa regime, we transform nonferroelastic
vortex-like domains into stripe-like domains. The width of the stripe-like
domains is determined by the applied pressure as we confirm by three-dimensional
phase field simulations, showing that pressure leads to oriented layer-like
periodic domains. Our work demonstrates the possibility to utilize
mechanical pressure for domain engineering in nonferroelastic ferroelectrics,
providing a lever to control their dielectric and piezoelectric responses