50 research outputs found
Improvement of Monte Carlo estimates with covariance-optimized finite-size scaling at fixed phenomenological coupling
In the finite-size scaling analysis of Monte Carlo data, instead of computing
the observables at fixed Hamiltonian parameters, one may choose to keep a
renormalization-group invariant quantity, also called phenomenological
coupling, fixed at a given value. Within this scheme of finite-size scaling, we
exploit the statistical covariance between the observables in a Monte Carlo
simulation in order to reduce the statistical errors of the quantities involved
in the computation of the critical exponents. This method is general and does
not require additional computational time. This approach is demonstrated in the
Ising model in two and three dimensions, where large gain factors in CPU time
are obtained.Comment: 5 pages, 1 figure, 2 tables; v2: slightly changed title, improved
presentation, results unchange
The ordinary surface universality class of the 3D O() model
We study the critical behavior at the ordinary surface universality class of
the three-dimensional O() model, bounded by a two-dimensional surface. Using
high-precision Monte Carlo simulations of an improved lattice model, where the
leading bulk scaling correction is suppressed, and finite-size scaling analysis
of the fourth cumulant of the surface magnetization, we obtain precise
estimates of the scaling dimension of the surface field operator for .
We also determine the fixed-point values of two Renormalization-group invariant
observables, which characterize the finite-size scaling behavior at the
ordinary transition.Comment: 11 pages, 3 figure
Nonordinary edge criticaliy of two-dimensional quantum critical magnets
Based on large-scale quantum Monte Carlo simulations, we examine the
correlations along the edges of two-dimensional semi-infinite quantum critical
Heisenberg spin- systems. In particular, we consider coupled quantum
spin-dimer systems at their bulk quantum critical points, including the
columnar-dimer model and the plaquette-square lattice. The alignment of the
edge spins strongly affects these correlations and the corresponding scaling
exponents, with remarkably similar values obtained for various quantum
spin-dimer systems. We furthermore observe subtle effects on the scaling
behavior from perturbing the edge spins that exhibit the genuine quantum nature
of these edge states. Our observations furthermore challenge recent attempts
that relate the edge spin criticality to the presence of symmetry-protected
topological phases in such quantum spin systems.Comment: 9 pages, 11 figures, v2: as publishe
Line contribution to the critical Casimir force between a homogeneous and a chemically stepped surface
Recent experimental realizations of the critical Casimir effect have been
implemented by monitoring colloidal particles immersed in a binary liquid
mixture near demixing and exposed to a chemically structured substrate. In
particular, critical Casimir forces have been measured for surfaces consisting
of stripes with periodically alternating adsorption preferences, forming
chemical steps between them. Motivated by these experiments, we analyze the
contribution of such chemical steps to the critical Casimir force for the film
geometry and within the Ising universality class. By means of Monte Carlo
simulations, mean-field theory, and finite-size scaling analysis we determine
the universal scaling function associated with the contribution to the critical
Casimir force due to individual, isolated chemical steps facing a surface with
homogeneous adsorption preference or with Dirichlet boundary condition. In line
with previous findings, these results allow one to compute the critical Casimir
force for the film geometry and in the presence of arbitrarily shaped, but wide
stripes. In this latter limit the force decomposes into a sum of the
contributions due to the two homogeneous parts of the surface and due to the
chemical steps between the stripes. We assess this decomposition by comparing
the resulting sum with actual simulation data for the critical Casimir force in
the presence of a chemically striped substrate.Comment: 17 pages, 14 figures; v2: added references, 17 pages, 14 figures.
This is an author-created, un-copyedited version of an article published in
J. Phys.: Condens. Matter. IOP Publishing Ltd is not responsible for any
errors or omissions in this version of the manuscript or any version derived
from it. The Version of Record is available online at
http://dx.doi.org/10.1088/0953-8984/27/21/21401
Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations
In a recent article T. Grover [Phys. Rev. Lett. 111, 130402 (2013)]
introduced a simple method to compute Renyi entanglement entropies in the realm
of the auxiliary field quantum Monte Carlo algorithm. Here, we further develop
this approach and provide a stabilization scheme to compute higher order Renyi
entropies and an extension to access the entanglement spectrum. The method is
tested on systems of correlated topological insulators.Comment: 7+ pages, 5 figure