104 research outputs found
Static properties of the dissipative random quantum Ising ferromagnetic chain
We study the zero temperature static properties of dissipative ensembles of
quantum Ising spins arranged on periodic one dimensional finite clusters and on
an infinite chain. The spins interact ferro-magnetically with nearest-neighbour
pure and random couplings. They are subject to a transverse field and coupled
to an Ohmic bath of quantum harmonic oscillators. We analyze the coupled system
using Monte Carlo simulations of the classical two-dimensional counterpart
model. The coupling to the bath enhances the extent of the ordered phase, as
found in mean-field spin-glasses. In the case of finite clusters we show that a
generalization of the Caldeira-Leggett localization transition exists. In the
case of the infinite random chain we study the effect of dissipation on the
transition and the Griffiths phase.Comment: 21 pages, 10 figure
Finite-size scaling properties of random transverse-field Ising chains : Comparison between canonical and microcanonical ensembles for the disorder
The Random Transverse Field Ising Chain is the simplest disordered model
presenting a quantum phase transition at T=0. We compare analytically its
finite-size scaling properties in two different ensembles for the disorder (i)
the canonical ensemble, where the disorder variables are independent (ii) the
microcanonical ensemble, where there exists a global constraint on the disorder
variables. The observables under study are the surface magnetization, the
correlation of the two surface magnetizations, the gap and the end-to-end
spin-spin correlation for a chain of length . At criticality, each
observable decays typically as in both ensembles, but the
probability distributions of the rescaled variable are different in the two
ensembles, in particular in their asymptotic behaviors. As a consequence, the
dependence in of averaged observables differ in the two ensembles. For
instance, the correlation decays algebraically as 1/L in the canonical
ensemble, but sub-exponentially as in the microcanonical
ensemble. Off criticality, probability distributions of rescaled variables are
governed by the critical exponent in both ensembles, but the following
observables are governed by the exponent in the microcanonical
ensemble, instead of the exponent in the canonical ensemble (a) in the
disordered phase : the averaged surface magnetization, the averaged correlation
of the two surface magnetizations and the averaged end-to-end spin-spin
correlation (b) in the ordered phase : the averaged gap. In conclusion, the
measure of the rare events that dominate various averaged observables can be
very sensitive to the microcanonical constraint.Comment: 24 page
A Crash Course on Aging
In these lecture notes I describe some of the main theoretical ideas emerged
to explain the aging dynamics. This is meant to be a very short introduction to
aging dynamics and no previous knowledge is assumed. I will go through simple
examples that allow one to grasp the main results and predictions.Comment: Lecture Notes (22 pages) given at "Unifying Concepts in Glass Physics
III", Bangalore (2004); to be published in JSTA
Universal and nonuniversal contributions to block-block entanglement in many-fermion systems
We calculate the entanglement entropy of blocks of size x embedded in a
larger system of size L, by means of a combination of analytical and numerical
techniques. The complete entanglement entropy in this case is a sum of three
terms. One is a universal x and L-dependent term, first predicted by Calabrese
and Cardy, the second is a nonuniversal term arising from the thermodynamic
limit, and the third is a finite size correction. We give an explicit
expression for the second, nonuniversal, term for the one-dimensional Hubbard
model, and numerically assess the importance of all three contributions by
comparing to the entropy obtained from fully numerical diagonalization of the
many-body Hamiltonian. We find that finite-size corrections are very small. The
universal Calabrese-Cardy term is equally small for small blocks, but becomes
larger for x>1. In all investigated situations, however, the by far dominating
contribution is the nonuniversal term steming from the thermodynamic limit.Comment: 6 pages, 3 figure
Retarding Sub- and Accelerating Super-Diffusion Governed by Distributed Order Fractional Diffusion Equations
We propose diffusion-like equations with time and space fractional
derivatives of the distributed order for the kinetic description of anomalous
diffusion and relaxation phenomena, whose diffusion exponent varies with time
and which, correspondingly, can not be viewed as self-affine random processes
possessing a unique Hurst exponent. We prove the positivity of the solutions of
the proposed equations and establish the relation to the Continuous Time Random
Walk theory. We show that the distributed order time fractional diffusion
equation describes the sub-diffusion random process which is subordinated to
the Wiener process and whose diffusion exponent diminishes in time (retarding
sub-diffusion) leading to superslow diffusion, for which the square
displacement grows logarithmically in time. We also demonstrate that the
distributed order space fractional diffusion equation describes super-diffusion
phenomena when the diffusion exponent grows in time (accelerating
super-diffusion).Comment: 11 pages, LaTe
Universal corrections to scaling for block entanglement in spin-1/2 XX chains
We consider the R\'enyi entropies in the one dimensional spin-1/2
Heisenberg XX chain in a magnetic field. The case n=1 corresponds to the von
Neumann ``entanglement'' entropy. Using a combination of methods based on the
generalized Fisher-Hartwig conjecture and a recurrence relation connected to
the Painlev\'e VI differential equation we obtain the asymptotic behaviour,
accurate to order , of the R\'enyi entropies
for large block lengths . For n=1,2,3,10 this constitutes the 3,6,10,48
leading terms respectively. The o(1) contributions are found to exhibit a rich
structure of oscillatory behaviour, which we analyze in some detail both for
finite and in the limit .Comment: 25 pages, 5 figure
Real-time non-equilibrium dynamics of quantum glassy systems
We develop a systematic analytic approach to aging effects in quantum
disordered systems in contact with an environment. Within the closed-time
path-integral formalism we include dissipation by coupling the system to a set
of independent harmonic oscillators that mimic a quantum thermal bath. After
integrating over the bath variables and averaging over disorder we obtain an
effective action that determines the real-time dynamics of the system. The
classical limit yields the Martin-Siggia-Rose generating functional associated
to a colored noise. We apply this general formalism to a prototype model
related to the spin-glass. We show that the model has a dynamic phase
transition separating the paramagnetic from the spin-glass phase and that
quantum fluctuations depress the transition temperature until a quantum
critical point is reached. We show that the dynamics in the paramagnetic phase
is stationary but presents an interesting crossover from a region controlled by
the classical critical point to another one controlled by the quantum critical
point. The most characteristic property of the dynamics in a glassy phase,
namely aging, survives the quantum fluctuations. In the sub-critical region the
quantum fluctuation-dissipation theorem is modified in a way that is consistent
with the notion of effective temperatures introduced for the classical case. We
discuss these results in connection with recent experiments in dipolar quantum
spin-glasses and the relevance of the effective temperatures with respect to
the understanding of the low temperature dynamics.Comment: 56 pages, Revtex, 17 figures include
Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
We consider the Renyi entanglement entropies in the one-dimensional XX
spin-chains with open boundary conditions in the presence of a magnetic field.
In the case of a semi-infinite system and a block starting from the boundary,
we derive rigorously the asymptotic behavior for large block sizes on the basis
of a recent mathematical theorem for the determinant of Toeplitz plus Hankel
matrices. We conjecture a generalized Fisher-Hartwig form for the corrections
to the asymptotic behavior of this determinant that allows the exact
characterization of the corrections to the scaling at order o(1/l) for any n.
By combining these results with conformal field theory arguments, we derive
exact expressions also in finite chains with open boundary conditions and in
the case when the block is detached from the boundary.Comment: 24 pages, 9 figure
Entanglement entropy of two disjoint intervals in c=1 theories
We study the scaling of the Renyi entanglement entropy of two disjoint blocks
of critical lattice models described by conformal field theories with central
charge c=1. We provide the analytic conformal field theory result for the
second order Renyi entropy for a free boson compactified on an orbifold
describing the scaling limit of the Ashkin-Teller (AT) model on the self-dual
line. We have checked this prediction in cluster Monte Carlo simulations of the
classical two dimensional AT model. We have also performed extensive numerical
simulations of the anisotropic Heisenberg quantum spin-chain with tree-tensor
network techniques that allowed to obtain the reduced density matrices of
disjoint blocks of the spin-chain and to check the correctness of the
predictions for Renyi and entanglement entropies from conformal field theory.
In order to match these predictions, we have extrapolated the numerical results
by properly taking into account the corrections induced by the finite length of
the blocks to the leading scaling behavior.Comment: 37 pages, 23 figure
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