The Lattice $\beta$-function of Quantum Spin Chains

TL;DR

This paper derives the lattice $eta$-function for quantum spin chains, linking finite temperature Monte Carlo data to zero temperature fixed points, and explains the singularity preventing analytic continuation between specific parameters.

Contribution

It introduces the lattice $eta$-function for quantum spin chains and explains its role in the nonintegrable singularity at $ heta$, advancing understanding of continuum limits.

Findings

Lattice $eta$-function derived for quantum spin chains.

Asymptotic freedom causes singularity in $ heta$.

Singularity prevents analytic continuation between $ heta=0$ and $ heta=\pi$.

Abstract

We derive the lattice $\beta$-function for quantum spin chains, suitable for relating finite temperature Monte Carlo data to the zero temperature fixed points of the continuum nonlinear sigma model. Our main result is that the asymptotic freedom of this lattice $\beta$-function is responsible for the nonintegrable singularity in $\theta$, that prevents analytic continuation between $\theta=0$ and $\theta=\pi$.