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We study level statistics of a critical random matrix ensemble of a power-law banded complex Hermitean matrices. We compute numerically the level compressibility via the level number variance and compare it with the analytical formula for the exactly solvable model of Moshe, Neuberger and Shapiro.
We numerically study the level statistics of the Gaussian $beta$ ensemble. These statistics generalize Wigner-Dyson level statistics from the discrete set of Dyson indices $beta = 1,2,4$ to the continuous range $0 < beta < infty$. The Gaussian $beta$
Building upon techniques employed in the construction of the Sachdev-Ye-Kitaev (SYK) model, which is a solvable $0+1$ dimensional model of a non-Fermi liquid, we develop a solvable, infinite-ranged random-hopping model of fermions coupled to fluctuat
We study level statistics in ensembles of integrable $Ntimes N$ matrices linear in a real parameter $x$. The matrix $H(x)$ is considered integrable if it has a prescribed number $n>1$ of linearly independent commuting partners $H^i(x)$ (integrals of
An important yet largely unsolved problem in the statistical mechanics of disordered quantum systems is to understand how quenched disorder affects quantum phase transitions in systems of itinerant fermions. In the clean limit, continuous quantum pha
We demonstrate a method to solve a general class of random matrix ensembles numerically. The method is suitable for solving log-gas models with biorthogonal type two-body interactions and arbitrary potentials. We reproduce standard results for a vari