Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries

TL;DR

This paper introduces symmetry-preserving matrix product state methods to accurately compute excitation spectra and reveal the topological nature of spinons and holons in one-dimensional quantum systems.

Contribution

The authors develop a variational MPS approach incorporating symmetries to determine dispersion relations and topological properties of elementary excitations.

Findings

Accurate excitation spectra for XXZ spin chain, Hubbard, and extended Hubbard models.

Explicit demonstration of the topological nature of spinons and holons.

Efficient calculation of magnetic field or chemical potential for target ground states.

Abstract

We develop variational matrix product state (MPS) methods with symmetries to determine dispersion relations of one dimensional quantum lattices as a function of momentum and preset quantum number. We test our methods on the XXZ spin chain, the Hubbard model and a non-integrable extended Hubbard model, and determine the excitation spectra with a precision similar to the one of the ground state. The formulation in terms of quantum numbers makes the topological nature of spinons and holons very explicit. In addition, the method also enables an easy and efficient direct calculation of the necessary magnetic field or chemical potential required for a certain ground state magnetization or particle density.