4,540 research outputs found
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
Quantum oscillations in from an incommensurate -density wave order
We consider quantum oscillation experiments in
from the perspective of an incommensurate
Fermi surface reconstruction using an exact transfer matrix method and the
Pichard-Landauer formula for the conductivity. The specific density wave order
considered is a period-8 -density wave in which the current density is
unidirectionally modulated. The current modulation is also naturally
accompanied by a period-4 site charge modulation in the same direction, which
is consistent with recent magnetic resonance measurements. In principle Landau
theory also allows for a period-4 bond charge modulation, which is not
discussed, but should be simple to incorporate in the future. This scenario
leads to a natural, but not a unique, explanation of why only oscillations from
a single electron pocket is observed, and a hole pocket of roughly twice the
frequency as dictated by two-fold commensurate order, and the corresponding
Luttinger sum rule, is not observed. However, it is possible that even higher
magnetic fields will reveal a hole pocket of half the frequency of the electron
pocket or smaller. This may be at the borderline of achievable high field
measurements because at least a few complete oscillations have to be clearly
resolved.Comment: 8 pages, 7 figure
Short-coherence length superconductivity in the Attractive Hubbard Model in three dimensions
We study the normal state and the superconducting transition in the
Attractive Hubbard Model in three dimensions, using self-consistent
diagrammatics. Our results for the self-consistent -matrix approximation are
consistent with 3D-XY power-law critical scaling and finite-size scaling. This
is in contrast to the exponential 2D-XY scaling the method was able to capture
in our previous 2D calculation. We find the 3D transition temperature at
quarter-filling and to be . The 3D critical regime is much
narrower than in 2D and the ratio of the mean-field transition to is
about 5 times smaller than in 2D. We also find that, for the parameters we
consider, the pseudogap regime in 3D (as in 2D) coincides with the critical
scaling regime.Comment: 4 pages, 5 figure
The effects of magnetic field on the d-density wave order in the cuprates
We consider the effects of a perpendicular magnetic field on the d-density
wave order and conclude that if the pseudogap phase in the cuprates is due to
this order, then it is highly insensitive to the magnetic field in the
underdoped regime, while its sensitivity increases as the gap vanishes in the
overdoped regime. This appears to be consistent with the available experiments
and can be tested further in neutron scattering experiments. We also
investigate the nature of the de Haas- van Alphen effect in the ordered state
and discuss the possibility of observing it.Comment: 5 pages, 4 eps figures, RevTex4. Corrected a silly but important typo
in the abstrac
From Spin Ladders to the 2-d O(3) Model at Non-Zero Density
The numerical simulation of various field theories at non-zero chemical
potential suffers from severe complex action problems. In particular, QCD at
non-zero quark density can presently not be simulated for that reason. A
similar complex action problem arises in the 2-d O(3) model -- a toy model for
QCD. Here we construct the 2-d O(3) model at non-zero density via dimensional
reduction of an antiferromagnetic quantum spin ladder in a magnetic field. The
complex action problem of the 2-d O(3) model manifests itself as a sign problem
of the ladder system. This sign problem is solved completely with a
meron-cluster algorithm.Comment: Based on a talk by U.-J. Wiese, 6 pages, 12 figures, to be published
in computer physics communication
On Soliton Content of Self Dual Yang-Mills Equations
Exploiting the formulation of the Self Dual Yang-Mills equations as a
Riemann-Hilbert factorization problem, we present a theory of pulling back
soliton hierarchies to the Self Dual Yang-Mills equations. We show that for
each map \C^4 \to \C^{\infty } satisfying a simple system of linear
equations formulated below one can pull back the (generalized) Drinfeld-Sokolov
hierarchies to the Self Dual Yang-Mills equations. This indicates that there is
a class of solutions to the Self Dual Yang-Mills equations which can be
constructed using the soliton techniques like the function method. In
particular this class contains the solutions obtained via the symmetry
reductions of the Self Dual Yang-Mills equations. It also contains genuine 4
dimensional solutions . The method can be used to study the symmetry reductions
and as an example of that we get an equation exibiting breaking solitons,
formulated by O. Bogoyavlenskii, as one of the dimensional reductions
of the Self Dual Yang-Mills equations.Comment: 11 pages, plain Te
Excess entropy, Diffusivity and Structural Order in liquids with water-like anomalies
The excess entropy, Se, defined as the difference between the entropies of
the liquid and the ideal gas under identical density and temperature
conditions, is shown to be the critical quantity connecting the structural,
diffusional and density anomalies in water-like liquids. Based on simulations
of silica and the two-scale ramp liquids, water-like density and diffusional
anomalies can be seen as consequences of a characteristic non-monotonic density
dependence of Se. The relationship between excess entropy, the order metrics
and the structural anomaly can be understood using a pair correlation
approximation to Se.Comment: 9 pages, 5 figues in ps forma
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