Finite-temperature properties of the extended Heisenberg model on a triangular lattice

TL;DR

This study investigates the finite-temperature behavior of the frustrated $J_1$-$J_2$ Heisenberg model on a triangular lattice, revealing a sharp specific heat maximum and signs of spin-liquid states at certain frustration levels.

Contribution

It provides numerical analysis of the $J_1$-$J_2$ Heisenberg model at finite temperatures, highlighting the emergence of spin-liquid behavior and dynamical properties on a triangular lattice.

Findings

Sharp low-temperature maximum in specific heat.

Evidence of spin-liquid ground state at $J_2/J_1 \, \sim \, 0.1$.

Spin-lattice relaxation rate follows $1/T_1 \propto T^{\alpha}$ with $\alpha \geq 1$.

Abstract

We present numerical results for the $J_1$-$J_2$ Heisenberg model on a triangular lattice at finite temperatures $T>0$. In contrast to unfrustrated lattices we reach much lower $T \sim 0.15 J_1$. In static quantities the novel feature is a quite sharp low-$T$ maximum in the specific heat. Dynamical spin structure factor $S({\bf q},\omega)$ allows for the extraction of the effective spin-wave energies $\omega_{\bf q}(T)$ and their damping $\gamma_{\bf q}(T)$. While for $J_2=0$ our results are consistent with $T=0$ spin ordering, $J_2/J_1 \sim 0.1 $ induces additional frustration with a signature of spin liquid ground state. In the latter case, results for spin-lattice relaxation rate indicate in the low-$T$ accesible regime on $1/T_1 \propto T^{\alpha}$ with $\alpha \geq 1$, as observed in recent spin-liquid materials on a triangular lattice.