Critical Behaviour of Mixed Heisenberg Chains

TL;DR

This paper investigates the critical behavior of mixed anisotropic Heisenberg chains, revealing universal properties and conformal field theory descriptions across a phase transition from ferromagnetic to ferrimagnetic states.

Contribution

It provides a numerical analysis of mixed Heisenberg chains, demonstrating universal critical properties and conformal invariance in the entire phase between ferromagnetic and ferrimagnetic regimes.

Findings

The phase $1>\Delta>-1$ is critical with Gaussian conformal field theory.

Critical exponents and conformal dimensions are calculated for various boundary conditions.

Universal behavior is observed across different mixed Heisenberg chain configurations.

Abstract

The critical behaviour of anisotropic Heisenberg models with two kinds of antiferromagnetically exchange-coupled centers are studied numerically by using finite-size calculations and conformal invariance. These models exhibit the interesting property of ferrimagnetism instead of antiferromagnetism. Most of our results are centered in the mixed Heisenberg chain where we have at even (odd) sites a spin-S (S') SU(2) operator interacting with a XXZ like interaction (anisotropy $\Delta$). Our results indicate universal properties for all these chains. The whole phase, $1>\Delta>-1$, where the models change from ferromagnetic $( \Delta=1 )$ to ferrimagnetic $(\Delta=-1)$ behaviour is critical. Along this phase the critical fluctuations are ruled by a c=1 conformal field theory of Gaussian type. The conformal dimensions and critical exponents, along this phase, are calculated by studying these models with several boundary conditions.