Propagation of Disturbances in Degenerate Quantum Systems

TL;DR

This paper investigates how disturbances propagate in finite degenerate quantum systems, specifically in the J1-J2 Heisenberg model near the Majumdar-Ghosh point, revealing entanglement-driven propagation without energy transfer.

Contribution

It demonstrates that in degenerate quantum systems, local disturbances can propagate via entanglement, even in finite clusters and away from the exact degeneracy point.

Findings

Disturbances carry quantum entanglement throughout the system.

Energy remains localized despite disturbance propagation.

Propagation persists even with approximate degeneracy.

Abstract

Disturbances in gapless quantum many-body models are known to travel an unlimited distance throughout the system. Here, we explore this phenomenon in finite clusters with degenerate ground states. The specific model studied here is the one-dimensional J1-J2 Heisenberg Hamiltonian at and close to the Majumdar-Ghosh point. Both open and periodic boundary conditions are considered. Quenches are performed using a local magnetic field. The degenerate Majumdar-Ghosh ground state allows disturbances which carry quantum entanglement to propagate throughout the system, and thus dephase the entire system within the degenerate subspace. These disturbances can also carry polarization, but not energy, as all energy is stored locally. The local evolution of the part of the system where energy is stored drives the rest of the system through long-range entanglement. We also examine approximations for the ground state of this Hamiltonian in the strong field limit, and study how couplings away from the Majumdar-Ghosh point affect the propagation of disturbances. We find that even in the case of approximate degeneracy, a disturbance can be propagated throughout a finite system.