Decoherence in an infinite range Heisenberg model

TL;DR

This paper investigates decoherence in an infinite range Heisenberg model coupled to phonons, showing that local phonons do not cause decoherence under Markovian dynamics, while global phonons only cause decoherence between states with different total spin z-component.

Contribution

It derives an effective Hamiltonian for IRHM coupled to phonons in strong coupling regimes and analyzes decoherence behavior under different phonon interactions and dynamics.

Findings

Local phonons do not induce decoherence under Markovian dynamics.

Global phonons cause decoherence only between states with different total spin z-component.

Effective Hamiltonian commutes with IRHM, sharing its eigenstates.

Abstract

We study decoherence in an infinite range Heisenberg model (IRHM) in the two situations where the system is coupled to a bath of either local optical phonons or global optical phonons. Using a non-perturbative treatment, we derive an effective Hamiltonian that is valid in the regime of strong spin-phonon coupling under non-adiabatic conditions. It is shown that the effective Hamiltonian commutes with the IRHM and thus has the same eigenstates as the IRHM. By analyzing the dynamics of the system using a quantum master equation approach, we show that the quantum states of the IRHM system do not decohere under Markovian dynamics when the spins interact with local phonons. For interactions with global phonons, the off-diagonal matrix elements of the system's reduced density matrix, obtained for non-Markovian dynamics, do not indicate decoherence only when states with the same $S^z_T$ (i.e., eigenvalue for the z-component of the total spin) are considered.