A continuum approximation for the excitations of the (1,1,...,1) interface in the quantum Heisenberg model

TL;DR

This paper demonstrates that, under proper scaling, the low-energy excitations of a specific interface in the quantum Heisenberg model can be approximated by the spectrum of a lower-dimensional Laplacian, linking quantum spin models to classical differential operators.

Contribution

The paper introduces a continuum approximation for the low-lying excitations of the (1,1,...,1) interface in the quantum Heisenberg model, connecting quantum spin excitations to classical Laplacian spectra.

Findings

Low-lying excitation energies correspond to the spectrum of a (d-1)-dimensional Laplacian.

The approximation holds under an appropriate scaling regime.

Provides a bridge between quantum spin models and classical differential operators.

Abstract

It is shown that, with an appropriate scaling, the energy of low-lying excitations of the (1,1,...,1) interface in the $d$-dimensional quantum Heisenberg model are given by the spectrum of the $d-1$-dimensional Laplacian on an suitable domain.