1,939 research outputs found
Quantum Griffiths Singularities in the Transverse-Field Ising Spin Glass
We report a Monte Carlo study of the effects of {\it fluctuations} in the
bond distribution of Ising spin glasses in a transverse magnetic field, in the
{\it paramagnetic phase} in the limit. Rare, strong fluctuations give
rise to Griffiths singularities, which can dominate the zero-temperature
behavior of these quantum systems, as originally demonstrated by McCoy for
one-dimensional () systems. Our simulations are done on a square lattice
in and a cubic lattice in , for a gaussian distribution of nearest
neighbor (only) bonds. In , where the {\it linear} susceptibility was
found to diverge at the critical transverse field strength for the
order-disorder phase transition at T=0, the average {\it nonlinear}
susceptibility diverges in the paramagnetic phase for well
above , as is also demonstrated in the accompanying paper by Rieger
and Young. In , the linear susceptibility remains finite at ,
and while Griffiths singularity effects are certainly observable in the
paramagnetic phase, the nonlinear susceptibility appears to diverge only rather
close to . These results show that Griffiths singularities remain
persistent in dimensions above one (where they are known to be strong), though
their magnitude decreases monotonically with increasing dimensionality (there
being no Griffiths singularities in the limit of infinite dimensionality).Comment: 20 pages, REVTEX, 6 eps figures included using the epsf macros; to
appear in Phys. Rev.
Probability distribution of the entanglement across a cut at an infinite-randomness fixed point
We calculate the probability distribution of entanglement entropy S across a
cut of a finite one dimensional spin chain of length L at an infinite
randomness fixed point using Fisher's strong randomness renormalization group
(RG). Using the random transverse-field Ising model as an example, the
distribution is shown to take the form , where , the large deviation function is found explicitly,
and is a nonuniversal microscopic length. We discuss the implications of
such a distribution on numerical techniques that rely on entanglement, such as
matrix product state (MPS) based techniques. Our results are verified with
numerical RG simulations, as well as the actual entanglement entropy
distribution for the random transverse-field Ising model which we calculate for
large L via a mapping to Majorana fermions.Comment: 6 pages, 4 figure
Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
We ask whether the Eigenstate Thermalization Hypothesis (ETH) is valid in a
strong sense: in the limit of an infinite system, {\it every} eigenstate is
thermal. We examine expectation values of few-body operators in highly-excited
many-body eigenstates and search for `outliers', the eigenstates that deviate
the most from ETH. We use exact diagonalization of two one-dimensional
nonintegrable models: a quantum Ising chain with transverse and longitudinal
fields, and hard-core bosons at half-filling with nearest- and
next-nearest-neighbor hopping and interaction. We show that even the most
extreme outliers appear to obey ETH as the system size increases, and thus
provide numerical evidences that support ETH in this strong sense. Finally,
periodically driving the Ising Hamiltonian, we show that the eigenstates of the
corresponding Floquet operator obey ETH even more closely. We attribute this
better thermalization to removing the constraint of conservation of the total
energy.Comment: 9 pages, 6 figures. Updated references and clarified some argument
Modulated phases in magnetic models frustrated by long-range interactions
We study an Ising model in one dimension with short range ferromagnetic and
long range (power law) antiferromagnetic interactions. We show that the zero
temperature phase diagram in a (longitudinal) field H involves a sequence of up
and down domains whose size varies continuously with H, between -H_c and H_c
which represent the edge of the ferromagnetic up and down phases. The
implications of long range interaction in many body systems are discussed.Comment: 5 pages, 3 figure
Finite Size Effects in Vortex Localization
The equilibrium properties of flux lines pinned by columnar disorder are
studied, using the analogy with the time evolution of a diffusing scalar
density in a randomly amplifying medium. Near H_{c1}, the physical features of
the vortices in the localized phase are shown to be determined by the density
of states near the band edge. As a result, H_{c1} is inversely proportional to
the logarithm of the sample size, and the screening length of the perpendicular
magnetic field decreases with temperature. For large tilt the extended ground
state turns out to wander in the plane perpendicular to the defects with
exponents corresponding to a directed polymer in a random medium, and the
energy difference between two competing metastable states in this case is
extensive. The divergence of the effective potential associated with strong
pinning centers as the tilt approaches its critical value is discussed as well.Comment: 10 pages, 2 figure
Zero Temperature Dynamics of the Weakly Disordered Ising Model
The Glauber dynamics of the pure and weakly disordered random-bond 2d Ising
model is studied at zero-temperature. A single characteristic length scale,
, is extracted from the equal time correlation function. In the pure
case, the persistence probability decreases algebraically with the coarsening
length scale. In the disordered case, three distinct regimes are identified: a
short time regime where the behaviour is pure-like; an intermediate regime
where the persistence probability decays non-algebraically with time; and a
long time regime where the domains freeze and there is a cessation of growth.
In the intermediate regime, we find that , where
. The value of is consistent with that
found for the pure 2d Ising model at zero-temperature. Our results in the
intermediate regime are consistent with a logarithmic decay of the persistence
probability with time, , where .Comment: references updated, very minor amendment to abstract and the
labelling of figures. To be published in Phys Rev E (Rapid Communications), 1
March 199
On the Use of Finite-Size Scaling to Measure Spin-Glass Exponents
Finite-size scaling (FSS) is a standard technique for measuring scaling
exponents in spin glasses. Here we present a critique of this approach,
emphasizing the need for all length scales to be large compared to microscopic
scales. In particular we show that the replacement, in FSS analyses, of the
correlation length by its asymptotic scaling form can lead to apparently good
scaling collapses with the wrong values of the scaling exponents.Comment: RevTeX, 5 page
Correct extrapolation of overlap distribution in spin glasses
We study in d=3 dimensions the short range Ising spin glass with Jij=+/-1
couplings at T=0. We show that the overlap distribution is non-trivial in the
limit of large system size.Comment: 6 pages, 3 figure
Interface Motion in Random Media at Finite Temperature
We have studied numerically the dynamics of a driven elastic interface in a
random medium, focusing on the thermal rounding of the depinning transition and
on the behavior in the pinned phase. Thermal effects are quantitatively
more important than expected from simple dimensional estimates. For sufficient
low temperature the creep velocity at a driving force equal to the
depinning force exhibits a power-law dependence on , in agreement with
earlier theoretical and numerical predictions for CDW's. We have also examined
the dynamics in the pinned phase resulting from slowly increasing the
driving force towards threshold. The distribution of avalanche sizes
decays as , with , in agreement with
recent theoretical predictions.Comment: harvmac.tex, 30 pages, including 9 figures, available upon request.
SU-rm-94073
Nonmagnetic Insulating States near the Mott Transitions on Lattices with Geometrical Frustration and Implications for -(ET)Cu
We study phase diagrams of the Hubbard model on anisotropic triangular
lattices, which also represents a model for -type BEDT-TTF compounds.
In contrast with mean-field predictions, path-integral renormalization group
calculations show a universal presence of nonmagnetic insulator sandwitched by
antiferromagnetic insulator and paramagnetic metals. The nonmagnetic phase does
not show a simple translational symmetry breakings such as flux phases,
implying a genuine Mott insulator. We discuss possible relevance on the
nonmagnetic insulating phase found in -(ET)Cu.Comment: 4pages including 7 figure
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