Anderson transition in three-dimensional systems with non-Hermitian disorder

Abstract

We study the Anderson transition for three-dimensional (3D) $N\times N\times N$ tightly bound cubic lattices where both real and imaginary parts of onsite energies are independent random variables distributed uniformly between $-W/2$ and $W/2$. Such a non-Hermitian analog of the Anderson model is used to describe random-laser medium with local loss and amplification. We employ eigenvalue statistics to search for the Anderson transition. For 25\% smallest-modulus complex eigenvalues we find the average ratio $r$ of distances to the first and the second nearest neighbor as a function of $W$. For a given $N$ the function $r(W)$ crosses from $0.72$ to 2/3 with a growing $W$ demonstrating a transition from delocalized to localized states. When plotted at different $N$ all $r(W)$ cross at $W_c=6.0\pm 0.1$ (in units of nearest neighbor overlap integral) clearly demonstrating the 3D Anderson transition. We find that in the non-Hermitian 2D Anderson model, the transition is replaced by a crossover.

3 pages, 3 figures

References in corpus (2)

• Localization of interacting fermions at high temperature
• Light Localization induced by Random Imaginary Permittivities

Cited by in corpus (7)

• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Spectral deformations in non-Hermitian lattices with disorder and skin effect: a solvable model
• Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{P}\mathcal{T}$ symmetry
• Spectral rigidity of non-Hermitian symmetric random matrices near Anderson transition
• Universality classes of the Anderson transitions driven by quasiperiodic potential in the three-dimensional Wigner-Dyson symmetry classes
• Phase transitions in non-Hermitian superlattices
• Dissipative quantum dynamics, phase transitions and non-Hermitian random matrices