Exact edge singularities and dynamical correlations in spin-1/2 chains

TL;DR

This paper derives exact formulas for the singularities of the dynamical structure factor in the spin-1/2 XXZ chain across all parameters, and combines these with numerical methods to analyze correlations with high precision.

Contribution

It provides the first exact formulas for edge singularities of the dynamical structure factor in the XXZ chain for all q and anisotropy, linking exponents to Bethe ansatz phase shifts.

Findings

Exact formulas for singularities of S^{zz}(q,omega) across all parameters.

High-precision calculations of dynamical correlations combining analytical and numerical methods.

Insights into long-time asymptotics of spin correlations.

Abstract

Exact formulas for the singularities of the dynamical structure factor, S^{zz}(q,omega), of the S=1/2 xxz spin chain at all q and any anisotropy and magnetic field in the critical regime are derived, expressing the exponents in terms of the phase shifts which are known exactly from the Bethe ansatz solution. We also study the long time asymptotics of the self-correlation function <0|S_j^z(t)S_j^z(0)|0>. Utilizing these results to supplement very accurate time-dependent Density Matrix Renormalization Group (DMRG) for short to moderate times, we calculate S^{zz}(q,omega) to very high precision.