Non-Linear Sigma Model for Inhomogeneous Spin Chains

TL;DR

This paper derives a non-linear sigma model for inhomogeneous antiferromagnetic spin chains, providing explicit gapless conditions based on spin magnitudes and exchange constants, applicable even with impurities.

Contribution

It introduces a generalized NLSM framework for inhomogeneous spin chains with explicit gapless conditions, extending previous models to more complex systems.

Findings

Derived NLSM for inhomogeneous spin chains

Explicit gapless condition depending on system parameters

Applicable to systems with impurities

Abstract

We derive a non-linear sigma model (NLSM) generally representing antiferromagnetic Heisenberg spin chains with inhomogeneous spin magnitudes and inhomogeneous nearest-neighbor exchange constants arrayed in finite periods. Only a restriction is that the average of spin magnitudes on one sublattice is the same as that on the other sublattice. The NLSM gives the gapless condition explicitly written by the spin magnitudes and the exchange constants. We apply this gapless condition to several cases including systems with impurities.