Semiclassical analysis of spin dynamics in the non-Hermitian Hubbard model

TL;DR

This paper explores the semiclassical spin dynamics in a non-Hermitian Hubbard model, revealing steady states, spin transfer effects, and domain formations influenced by complex interactions.

Contribution

It introduces a semiclassical analysis of a non-Hermitian Hubbard model, highlighting new steady states and spin behaviors due to complex interactions.

Findings

Identification of multiple steady states including decoupled and dimerized configurations

Observation of ferromagnetic domain formation in steady states

Detection of anomalous spin dynamics signatures

Abstract

We investigate a specific limit of the one-dimensional non-Hermitian Hubbard Hamiltonian with complex interactions. In this framework, fermions with different spin quantum numbers are mapped onto two distinct spin species, resulting in two $XY$ spin chains that are coupled through Ising $ZZ$ interaction. The spin ladder model is then examined within the semiclassical limit using a spin-coherent state basis, where the dynamics is governed by a set of coupled Landau-Lifshitz-Gilbert equations. The non-Hermitian interactions in this model generate a spin-transfer torque term. We analyze the system's evolution toward several potential steady states, including a state of decoupled chains that is accessible when each chain has uniform initial conditions. Other possible steady states involve dimerized configurations with decoupled rungs, where the rung spins are either ferromagnetically or antiferromagnetically coupled, depending on the sign of the imaginary interactions. The spin dynamics is then studied in the infinite-temperature limit, which favors dimerized steady states. Despite the decoupled rungs, we observe the formation of ferromagnetic domains along each chain in the steady state. Additionally, we investigate the spin correlation functions and identify signatures of anomalous spin dynamics.