Thermodynamics of the one-dimensional frustrated Heisenberg ferromagnet with arbitrary spin

TL;DR

This study investigates the thermodynamic behavior of the one-dimensional frustrated J1-J2 Heisenberg ferromagnet with arbitrary spin, revealing critical behavior changes at the quantum critical point and frustration-induced low-temperature maxima in specific heat for certain spins.

Contribution

It provides a detailed analysis of thermodynamic quantities across different spins and identifies how frustration affects low-temperature behavior near the quantum critical point.

Findings

Susceptibility and correlation length follow specific temperature power laws.

Critical behavior changes at the quantum critical point J2=|J1|/4.

Frustration induces low-temperature maxima in specific heat for S=1/2 and S=1.

Abstract

The thermodynamic quantities (spin-spin correlation functions <{\bf S}_0{\bf S}_n>, correlation length {\xi}, spin susceptibility {\chi}, and specific heat C_V) of the frustrated one-dimensional J1-J2 Heisenberg ferromagnet with arbitrary spin quantum number S below the quantum critical point, i.e. for J2< |J1|/4, are calculated using a rotation-invariant Green-function formalism and full diagonalization as well as a finite-temperature Lanczos technique for finite chains of up to N=18 sites. The low-temperature behavior of the susceptibility {\chi} and the correlation length {\xi} is well described by \chi = (2/3)S^4 (|J1|-4J2) T^{-2} + A S^{5/2} (|J1|-4J2)^{1/2} T^{-3/2} and \xi = S^2 (|J1|-4J2) T^{-1} + B S^{1/2} (|J1|-4J2)^{1/2} T^{-1/2} with A \approx 1.1 ... 1.2 and B \approx 0.84 ... 0.89. The vanishing of the factors in front of the temperature at J2=|J1|/4 indicates a change of the critical behavior of {\chi} and {\xi} at T \to 0. The specific heat may exhibit an additional frustration-induced low-temperature maximum when approaching the quantum critical point. This maximum appears for S=1/2 and S=1, but was not found for S>1.