Lattice vs. continuum theory of the periodic Heisenberg chain

TL;DR

This paper analyzes the low-energy excitations of the periodic spin-1/2 XXZ Heisenberg chain, deriving precise asymptotic energy expansions and expressing eigenstates in bosonic modes without solving Bethe Ansatz equations.

Contribution

It provides a perturbative method to compute eigenenergies and eigenstates of the lattice model directly from continuum theory, avoiding Bethe Ansatz solutions.

Findings

Calculated eigenenergies up to order N^-4.

Derived exact coefficients for asymptotic expansions.

Expressed lattice eigenstates in terms of bosonic modes.

Abstract

We consider the detailed structure of low energy excitations in the periodic spin-1/2 XXZ Heisenberg chain. By performing a perturbative calculation of the non-linear corrections to the Gaussian model, we determine the exact coefficients of asymptotic expansions in inverse powers of the system length N for a large number of low-lying excited energy levels. This allows us to calculate eigenenergies of the lattice model up to order order N^-4, without having to solve the Bethe Ansatz equations. At the same time, it is possible to express the exact eigenstates of the lattice model in terms of bosonic modes.