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

Abstract

Derivation of a reduced effective model allows for a unified treatment and discussion of the J1-J2 Heisenberg model on a triangular and kagome lattice. Calculating thermodynamic quantities, i.e. the entropy s(T ) and uniform susceptibility χ0(T ), numerically on systems up to effectively N = 48 sites we show by comparing to full-model results that low-T properties are well represented within the reduced model. Moreover, we find in the spin-liquid regime similar variation of s(T ) as well as χ0(T ) in both models down to T ≪ J1. In particular, the spin liquid appears to be characterized by Wilson ratio vanishing at low T , indicating on the low-lying singlet dominating over the triplet excitations.

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

“…3 reveal that increasing |J 2 | > 0 suppreses strongly s(T J 1 )) while leaving χ 0 (T ) less affected (at least for T > T f s ). The result for J 2 = ±0.2 indicates on divergent R 0 → ∞ consistent with the emergent magnetic LRO [54,68]. On the other hand, at J 2 = 0, 0.1 the behavior of χ 0 (T ) and s(T ) are consistent with finite triplet gap ∆ t ∼ 0.15 and smaller or even vanishing singlet gap ∆ s < ∆ t .…”

“…The basic HM on KL has been the clearest case for a dominant role of lowlying singlet excitations over the triplet ones [6,50,51]. The latter fact and related large entropy, persistent at low T 1, has been well captured within block-spin [4,5,69] and recently within related reduced-basis approach [54], whereby the singlet excitations can be attributed to chiral fluctuations, distinct from (higher-energy) triplet excitations.…”

“…Besides thermodynamic quantities: uniform magnetic susceptibility χ 0 (T ) and the entropy density s(T ), together with related specific heat C V (T ) = T ds/dT , it is informative to extract also their quotient in the form of temperature-dependent Wilson ratio R(T ), defined as [54],…”

“…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.…”

“…exchange on KL [4-6, 8, 50, 51], that lowest excitations are singlets dominating over the triplet excitations, for which most ED studies reveal a finite spin (triplet) gap ∆ t > 0 although there are numerical indications also for gapless scenario [52,53]. It has been recently shown [54] that the same scenario can be traced via the temperature-dependent Wilson ratio R(T ) in a J 1 -J 2 HM on TL including the next-nearest-neighbor (n.n.n.) exchange J 2 > 0 in the regime where the SL g.s.…”