Exact nonequilibrium hole dynamics, magnetic polarons and string excitations in antiferromagnetic Bethe lattices

TL;DR

This paper provides an exact solution for the nonequilibrium dynamics of a single hole in an antiferromagnetic Bethe lattice, revealing bound states, oscillations, and detailed spectral properties of magnetic polarons and string excitations.

Contribution

It introduces an exactly solvable model for nonequilibrium hole dynamics on Bethe lattices, leveraging fractal self-similarity to analyze magnetic polarons and string excitations.

Findings

Hole remains localized with aperiodic oscillations

Eigenenergy spectrum of magnetic polarons is irregular

Exact characterization of string excitations

Abstract

We investigate a rare instance of an exactly solvable nonequilibrium many-body problem. In particular, we derive an exact solution for the nonequilibrium dynamics of an initially localized single hole in a fully anisotropic antiferromagnetic Bethe lattice, described by the $t$-$J_z$ model. The solvability of the model relies on the fractal self-similarity of Bethe lattices, making it possible to compute the full motion of the hole as it moves through the lattice, as well as exactly characterizing the resulting effect on spin-spin correlation functions. We find that the hole remains bound to its initial position with large aperiodic oscillations in the hole density distribution. We track this back to the irregular pattern of the eigenenergies of the magnetic polaron ground state and string excitations, which we also determine exactly.