Abstract
We present numerical results for finite-temperature $T>0$ thermodynamic quantities, entropy $s(T)$, uniform susceptibility $\chi_0(T)$ and the Wilson ratio $R(T)$, for several isotropic $S=1/2$ extended Heisenberg models which are prototype models for planar quantum spin liquids. We consider in this context the frustrated $J_1$-$J_2$ model on kagome, triangular, and square lattice, as well as the Heisenberg model on triangular lattice with the ring exchange. Our analysis reveals that typically in the spin-liquid parameter regimes the low-temperature $s(T)$ remains considerable, while $\chi_0(T)$ is reduced consistent mostly with a triplet gap. This leads to vanishing $R(T \to 0)$, being the indication of macroscopic number of singlets lying below triplet excitations. This is in contrast to $J_1$-$J_2$ Heisenberg chain, where $R(T \to 0)$ either remains finite in the gapless regime, or the singlet and triplet gap are equal in the dimerized regime.
Highlights
Various frustrated S = 1/2 Heisenberg models (HMs) have been the subject of intensive theoretical studies in last decades in connection with the possibility of a spin-liquid (SL) ground state (g.s.)
In the following we use two finite-temperature Lanczos method (FTLM) codes for the considered models: (a) To calculate the largest systems with N = 36 sites for the 2D triangular lattice (TL), kagome lattice (KL) as well as square lattice (SQL) J1-J2 HM with Nst ∼ 1010, we develop a code that equips a technique to save the memory for the Hamiltonian by dividing H into two subsystems
We considered here prototype 2D isotropic S = 1/2 HM, which are at least in some parameter regimes best candidates for the SL g.s
Summary
Various frustrated S = 1/2 Heisenberg models (HMs) have been the subject of intensive theoretical studies in last decades in connection with the possibility of a spin-liquid (SL) ground state (g.s.) These efforts have been recently strengthened by the discovery of several classes of insulating materials, revealing low-energy spin excitations behaving as a quantum SL without any magnetic order down to low temperatures (for reviews see [1,2,3]). Among measurable spin properties are thermodynamic quantities such as the uniform magnetic susceptibility χ0(T ), magnetic (contribution to) specific heat CV (T ), and related spin entropy density s(T ) They are crucial to pinpointing the different characters and scenarios of SL behavior, in partic-
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