A matrix product state based algorithm for determining dispersion relations of quantum spin chains with periodic boundary conditions

TL;DR

This paper introduces a matrix product state algorithm for efficiently approximating the dispersion relations of quantum spin chains with periodic boundary conditions, achieving high accuracy in benchmark models.

Contribution

The authors develop a momentum eigenstate ansatz within the MPS framework for periodic systems, enabling precise dispersion relation calculations for quantum spin chains.

Findings

Accurately approximates dispersion relations for quantum spin chains.

Benchmark results show high precision compared to exact solutions.

Effective for models like quantum Ising and Heisenberg spin chains.

Abstract

We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of \"Ostlund and Rommer [1], we separate the Hilbert space of the system into subspaces with different momentum. This gives rise to a direct sum of effective Hamiltonians, each one corresponding to a different momentum, and we determine their spectrum by solving a generalized eigenvalue equation. Surprisingly, many branches of the dispersion relation are approximated to a very good precision. We benchmark the accuracy of the algorithm by comparison with the exact solutions of the quantum Ising and the antiferromagnetic Heisenberg spin-1/2 model.