Magnetic and Critical Properties of Alternating Spin Heisenberg Chain in a Magnetic Field

TL;DR

This paper investigates the magnetic and critical behavior of an alternating spin Heisenberg chain in a magnetic field, revealing a magnetization plateau and confirming conformal field theory predictions through numerical analysis.

Contribution

It provides a detailed numerical study of the magnetization curve and critical exponents for the alternating spin chain, demonstrating conformal invariance and the universal relation between exponents.

Findings

Magnetization plateau at m=1/4 observed.

Conformal field theory with c=1 describes the system.

Universal relation ηη^z=1 confirmed.

Abstract

We study magnetic and critical properties of the alternating spin antiferromagnetic Heisenberg chain with $S=1/2$ and 1 in a magnetic field at T=0. The numerical diagonalization is applied to the system up to $2N=20$ sites. Checking numerically that magnetic states with the magnetization per site $m$ obey a conformal field theory with conformal anomaly $c=1$ for $1/4<m<3/4$, we use the finite-size scaling of the conformal invariance to obtain a magentization curve in the thermodynamic limit. In the magnetizatin curve a plateau appears at $m=1/4$. We also calculate two critical exponents $\eta$ and $\eta^z$ for $1/4<m<3/4$, which control the asymptotic behavior of the transverse and parallel spin correlation functions. We check the relation $\eta \eta^z=1$, which universally holds for a $c=1$ conformal field theory.