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

Abstract

We present numerical results for the J1-J2 Heisenberg model on a triangular lattice at finite temperatures T > 0. In contrast to unfrustrated lattices we reach much lower T ∼ 0.15J1. In static quantities the novel feature is a quite sharp low-T maximum in the specific heat. Dynamical spin structure factor S(q, ω) allows for the extraction of the effective spin-wave energies ωq(T ) and their damping γq(T ). While for J2 = 0 our results are consistent with T = 0 spin ordering, J2/J1 ∼ 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/T1 ∝ T α with α 1, as observed in recent spin-liquid materials on a triangular lattice.for local spins S = 1/2 with AFM nearest-neighbor spin exchange J 1 and next-nearest neighbor exchange J 2 0. J 2 introduces additional frustration. Further on we set J 1 = 1 as an energy scale. We consider the model on 2D lattices with periodic boundary conditions with up to N = 30 sites according to minimal imperfection [35][36][37] and the possibility to contain particular wavevector arXiv:1804.04819v1 [cond-mat.str-el]

Vanishing Wilson ratio as the hallmark of quantum spin-liquid models

“…Results, presented in Fig. 5, are qualitatively consistent with previous ones for N = 30 [24] but due to larger size and consequently smaller T f s more clearly reveal the small entropy s(T ) and related diverging R(T ) below T ∼ 0.2 for J 2 ∼ 0, where the g.s. possesses magnetic LRO.…”

“…In any case, due to frustration and consequently enhanced s(T J 1 ) in SL models FTLM generally allows to reach lower effective T f s . E.g., while for HM on a (unfrustrated) SQL (even at largest N = 36) T f s ∼ 0.4J 1 [62,63], SL models allow for considerably lower T f s ≤ 0.1 [24,56]. b) For systems with only short-range spin correlations one can reach situation where spin correlation length (even at T → 0) is shorter that the system length, ξ ≤ L. In such a case, FTLM has no obvious restrictions even at T → 0, so T f s ∼ 0.…”

“…Thermodynamic (and some dynamic) quantities for the J 1 -J 2 HM, Eq. (7), on TL have been recently calculated using FTLM [24] up to N = 30 sites and employing the reduced-basis approach [54], whereby the similarity of Here we upgrade previous FTLM studies with the calculation of J 1 -J 2 HM on TL to N = 36 sites. Results, presented in Fig.…”

“…In this context we generalise previous numerical T > 0 studies of HM on KL [55,56] to include also the n.n.n. exchange J 2 = 0 and upgrade results for the J 1 -J 2 HM on TL [24], now studying also the HM on TL with the ring exchange, as well as another standard model of SL, i.e., frustrated J 1 -J 2 HM on SQL. Results in the SL regimes confirm the singlets as dominating low-energy excitations.…”

Similarity of thermodynamic properties of the Heisenberg model on triangular and kagome lattices

“…In Figs. 1a,b we present s(T ) and χ 0 (T ), respectively, as obtained on TL for J 2 = 0.1 on N = 30 via FTLM on EM and SEM, compared with the full HM on the same size [54]. The qualitative behavior of both quantities within EM and SEM is quite similar at low T < 0.4, although EM (SEM) miss (as expected) s(T ) with increasing T , but apparently also some part of spin fluctuations reducing the value of χ 0 (T ).…”