Fine structures in the spectrum of the open-boundary Heisenberg chain at large anisotropies

TL;DR

This paper investigates the detailed spectral band structures of the open-boundary Heisenberg XXZ chain at large anisotropies, revealing intricate fine structures and their dynamical implications using perturbation theory.

Contribution

It provides a detailed characterization and explanation of the fine spectral structures and substructures in the open-boundary XXZ chain at large anisotropies, using degenerate perturbation theory.

Findings

Identification of richer band structures with open boundaries

Explanation of fine structures via perturbation theory

Demonstration of dynamical effects from sub-band structures

Abstract

At large anisotropies, the spectrum of the Heisenberg XXZ spin chain separates into `bands' with energies largely determined by the number of domain walls. The band structure is richer with open boundary conditions: there are more bands and the bands develop intricate fine structures. We characterize and explain these structures and substructures in the open-boundary chain. The fine structures are explained using degenerate perturbation theory. We also present some dynamical consequences of these sub-band structures, through explicit time evolution of the wavefunction from initial states motivated by the fine structure analysis.