arXiv subjects

Daniil Kochergin

Publications and source records attributed to Daniil Kochergin.

4 recordsLinked to original sources

arXiv2026

Localization Transition on Random Graphs with Chiral and Bogoliubov-de Gennes Symmetry Classes

We studied single-particle Anderson localization in ensembles of graphs that correspond to chiral and Bogoliubov-de Gennes (BdG) symmetry classes. For a random biregular bipartite graph with chiral symmetry, the density of states was found using the cavity approach. Calculating the fractal dimension shows the effects of disordered zero modes. For Bogoliubov-de Gennes ensembles with an underlying random regular graph (RRG), the density of states was calculated both numerically and analytically. The ensembles BdG-RRG with symmetry-conserving diagonal disorder in the delocalized phase have a smaller fractal dimension compared to the usual RRG.

cond-mat.dis-nn↗

arXiv2024

Robust extended states in Anderson model on partially disordered random regular graphs

In this work we analytically explain the origin of the mobility edge in the partially disordered random regular graphs of degree d, i.e., with a fraction $β$ of the sites being disordered, while the rest remain clean. It is shown that the mobility edge in the spectrum survives in {a certain range of parameters} $(d,β)$ at infinitely large uniformly distributed disorder. The critical curve separating extended and localized states is derived analytically and confirmed numerically. The duality in the localization properties between the sparse and extremely dense RRG has been found and understood.

cond-mat.dis-nn↗

arXiv2024

Localization transition in non-Hermitian systems depending on reciprocity and hopping asymmetry

We studied the single-particle Anderson localization problem for non-Hermitian systems on directed graphs. Random regular graph and various undirected standard random graph models were modified by controlling reciprocity and hopping asymmetry parameters. We found the emergence of left, biorthogonal and right localized states depending on both parameters and graph structure properties such as node degree $d$. For directed random graphs, the occurrence of biorthogonal localization near exceptional points is described analytically and numerically. The clustering of localized states near the center of the spectrum and the corresponding mobility edge for left and right states are shown numerically. Structural features responsible for localization, such as topologically invariant nodes or drains and sources, were also described. Considering the diagonal disorder, we observed the disappearance of localization dependence on reciprocity around $W \sim 20$ for a random regular graph $d=4$. With a small diagonal disorder, the average biorthogonal fractal dimension drastically reduces. Around $W \sim 5$ localization scars occur within the spectrum, alternating as vertical bands of clustering of left and right localized states.

cond-mat.dis-nn↗

arXiv2023

Anatomy of the fragmented Hilbert space: eigenvalue tunneling, quantum scars and localization in the perturbed random regular graph

We consider the properties of the random regular graph with node degree $d$ perturbed by chemical potentials $μ_k$ for a number of short $k$-cycles. We analyze both numerically and analytically the phase diagram of the model in the $(μ_k,d)$ plane. The critical curve separating the homogeneous and clusterized phases is found and it is demonstrated that the clusterized phase itself generically is separated as the function of $d$ into the phase with ideal clusters and phase with coupled ones when the continuous spectrum gets formed. The eigenstate spatial structure of the model is investigated and it is found that there are localized scar-like states in the delocalized part of the spectrum, that are related to the topologically equivalent nodes in the graph. We also reconsider the localization of the states in the non-perturbative band formed by eigenvalue instantons and find the semi-Poisson level spacing distribution. The Anderson transition for the case of combined ($k$-cycle) structural and diagonal (Anderson) disorders is investigated. It is found that the critical diagonal disorder gets reduced sharply at the clusterization phase transition, but does it unevenly in non-perturbative and mid-spectrum bands, due to the scars, present in the latter. The applications of our findings to $2$d quantum gravity are discussed.

cond-mat.dis-nn↗