Lorentz Covariance and the Dimensional Crossover of 2d-Antiferromagnets

TL;DR

This paper derives a lattice beta-function for 2d-Antiferromagnetic Heisenberg models, linking lattice interactions to quantum critical points and revealing a chiral doubling of excitation spectra.

Contribution

It introduces a nonperturbative lattice beta-function connecting quantum Monte Carlo data to the nonlinear sigma model's fixed points, highlighting spectral doubling phenomena.

Findings

Relation of lattice couplings to quantum critical points

Chiral doubling of excited state spectra

Renormalization effects near quantum criticality

Abstract

We derive a lattice $\beta$-function for the 2d-Antiferromagnetic Heisenberg model, which allows the lattice interaction couplings of the nonperturbative Quantum Monte Carlo vacuum to be related directly to the zero-temperature fixed points of the nonlinear sigma model in the presence of strong interplanar and spin anisotropies. In addition to the usual renormalization of the gapful disordered state in the vicinity of the quantum critical point, we show that this leads to a chiral doubling of the spectra of excited states.