Multifractal dimensions for orthogonal-to-unitary crossover ensemble
- URL: http://arxiv.org/abs/2310.03526v1
- Date: Thu, 5 Oct 2023 13:22:43 GMT
- Title: Multifractal dimensions for orthogonal-to-unitary crossover ensemble
- Authors: Ayana Sarkar, Ashutosh Dheer and Santosh Kumar
- Abstract summary: We show that finite-size versions of multifractal dimensions converge to unity logarithmically slowly with increase in the system size $N$.
We apply our results to analyze the multifractal dimensions in a quantum kicked rotor, a Sinai billiard system, and a correlated spin chain model in a random field.
- Score: 1.0793830805346494
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Multifractal analysis is a powerful approach for characterizing ergodic or
localized nature of eigenstates in complex quantum systems. In this context,
the eigenvectors of random matrices belonging to invariant ensembles naturally
serve as models for ergodic states. However, it has been found that the
finite-size versions of multifractal dimensions for these eigenvectors converge
to unity logarithmically slowly with increase in the system size $N$. In fact,
this strong finite-size effect is capable of distinguishing the ergodicity
behavior of orthogonal and unitary invariant classes. Motivated by this
observation, in this work, we provide semi-analytical expressions for the
ensemble-averaged multifractal dimensions associated with eigenvectors in the
orthogonal-to-unitary crossover ensemble. Additionally, we explore shifted and
scaled variants of multifractal dimensions, which, in contrast to the
multifractal dimensions themselves, yield distinct values in the orthogonal and
unitary limits as $N\to\infty$ and therefore may serve as a convenient measure
for studying the crossover. We substantiate our results using Monte Carlo
simulations of the underlying crossover random matrix model. We then apply our
results to analyze the multifractal dimensions in a quantum kicked rotor, a
Sinai billiard system, and a correlated spin chain model in a random field. The
orthogonal-to-unitary crossover in these systems is realized by tuning relevant
system parameters, and we find that in the crossover regime, the observed
finite-dimension multifractal dimensions can be captured very well with our
results.
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