4,396 research outputs found
Finite size scaling in crossover among different random matrix ensembles in microscopic lattice models
Using numerical diagonalization we study the crossover among different random
matrix ensembles [Poissonian, Gaussian Orthogonal Ensemble (GOE), Gaussian
Unitary Ensemble (GUE) and Gaussian Symplectic Ensemble (GSE)] realized in two
different microscopic models. The specific diagnostic tool used to study the
crossovers is the level spacing distribution. The first model is a one
dimensional lattice model of interacting hard core bosons (or equivalently spin
1/2 objects) and the other a higher dimensional model of non-interacting
particles with disorder and spin orbit coupling. We find that the perturbation
causing the crossover among the different ensembles scales to zero with system
size as a power law with an exponent that depends on the ensembles between
which the crossover takes place. This exponent is independent of microscopic
details of the perturbation. We also find that the crossover from the
Poissonian ensemble to the other three is dominated by the Poissonian to GOE
crossover which introduces level repulsion while the crossover from GOE to GUE
or GOE to GSE associated with symmetry breaking introduces a subdominant
contribution. We also conjecture that the exponent is dependent on whether the
system contains interactions among the elementary degrees of freedom or not and
is independent of the dimensionality of the system.Comment: 15 pages, 8 figure
Many body localization in the presence of a single particle mobility edge
In one dimension, noninteracting particles can undergo a
localization-delocalization transition in a quasiperiodic potential. Recent
studies have suggested that this transition transforms into a many-body
localization (MBL) transition upon the introduction of interactions. It has
also been shown that mobility edges can appear in the single particle spectrum
for certain types of quasiperiodic potentials. Here, we investigate the effect
of interactions in two models with such mobility edges. Employing the technique
of exact diagonalization for finite-sized systems, we calculate the level
spacing distribution, time evolution of entanglement entropy, optical
conductivity, and return probability to detect MBL. We find that MBL does
indeed occur in one of the two models we study, but the entanglement appears to
grow faster than logarithmically with time unlike in other MBL systems.Comment: 5 pages, 6 figure
Universal power law in crossover from integrability to quantum chaos
We study models of interacting fermions in one dimension to investigate the
crossover from integrability to non-integrability, i.e., quantum chaos, as a
function of system size. Using exact diagonalization of finite-sized systems,
we study this crossover by obtaining the energy level statistics and Drude
weight associated with transport. Our results reinforce the idea that for
system size non-integrability sets in for an arbitrarily small
integrability-breaking perturbation. The crossover value of the perturbation
scales as a power law when the integrable system is gapless and
the scaling appears to be robust to microscopic details and the precise form of
the perturbation. We conjecture that the exponent in the power law is
characteristic of the random matrix ensemble describing the non-integrable
system. For systems with a gap, the crossover scaling appears to be faster than
a power law.Comment: 5 pages, 7 figure
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