Magnetic properties of doped Heisenberg chains

TL;DR

This paper analyzes the magnetic susceptibility of doped Heisenberg chains, deriving explicit expressions and sum rules for the contributions of magnetic modes, revealing singular behavior at low doping levels.

Contribution

It provides a new explicit formula for the magnetic susceptibility contribution of gapless modes in doped Heisenberg chains and proves a sum rule applicable at arbitrary hole concentrations.

Findings

Explicit expression for susceptibility contribution at small doping

Singularity in susceptibility as doping approaches zero for large spins

Sum rule for magnetic mode contributions valid for all doping levels

Abstract

The magnetic susceptibility of systems from a class of integrable models for doped spin-$S$ Heisenberg chains is calculated in the limit of vanishing magnetic field. For small concentrations $x_h$ of the mobile spin-$(S-1/2)$ charge carriers we find an explicit expression for the contribution of the gapless mode associated to the magnetic degrees of freedom of these holes to the susceptibility which exhibits a singularity for $x_h\to0$ for sufficiently large $S$. We prove a sum rule for the contributions of the two gapless magnetic modes in the system to the susceptibility which holds for arbitrary hole concentration. This sum rule complements the one for the low temperature specific heat which has been obtained previously.