Phase Diagrams of Mixed Spin Chains with Period 4 by the Nonlinear $\sigma$ Model

TL;DR

This paper analyzes the phase diagrams of mixed quantum spin chains with period 4 using a nonlinear sigma model, revealing complex phase boundaries and structures based on spin magnitudes.

Contribution

It introduces a nonlinear sigma model approach to map mixed spin chains with period 4, providing a detailed phase diagram and explaining phases via an extended valence-bond-solid picture.

Findings

Identifies phase boundaries in mixed spin chains with period 4.

Reveals a rich phase structure dependent on spin magnitudes.

Provides a unified framework for understanding phases in inhomogeneous spin chains.

Abstract

We study mixed quantum spin chains consisting of two kinds of spins with magnitudes, s_a and s_b. The spins are arrayed as s_a-s_a-s_b-s_b in a unit cell and the exchange couplings are accordingly periodic with period 4. The spin Hamiltonian is mapped onto a nonlinear $\sigma$ model based on the general formula for periodic inhomogeneous spin chains. The gapless condition given by the nonlinear $\sigma$ model determines boundaries between disordered phases in the space of the exchange parameters. The phase diagram has a rich phase structure characterized by the values of s_a and s_b. We explain all phases in the singlet-cluster-solid picture which is an extension of the valence-bond-solid picture.