Magnetism of theN=42kagome lattice antiferromagnet

Abstract

For the paradigmatic frustrated spin-half Heisenberg antiferromagnet on the kagomé lattice we performed large-scale numerical investigation of thermodynamic functions by means of the finitetemperature Lanczos method for system sizes of up to N = 42. We present the dependence of magnetization as well as specific heat on temperature and external field and show in particular that a finite-size scaling of specific heat supports the appearance of a low-temperature shoulder below the major maximum. This seems to be the result of a counterintuitive motion of the density of singlet states towards higher energies. Other interesting features that we discuss are the asymmetric melting of the 1/3 magnetization plateau as well the field dependence of the specific heat that exhibits characteristic features caused by the existence of a flat one-magnon band. By comparison with the unfrustrated square-lattice antiferromagnet the tremendous role of frustration in a wide temperature range is illustrated.

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

“…The largest low-T entropy s(T ) is found for KL with J 2 = 0. Moreover, EM here yields a quantitive agreement with the full HM [48], revealing large remanent s(T ) due to singlet (chirality) excitations down to T ∼ 0.01 [42]. Here, in comparison to EM the SEM fails to distribute the drop of s(T ) over a wider T range, but nevetheless reveals large s(T ) down to T ∼ 0.05.…”

“…the entropy density s(T ) and the uniform susceptibility χ 0 (T ). Both quantities are calculated (see definitions and details in [56]) via the finite-temperature Lanczos method (FTLM) [57][58][59][60], which has been recently used to calculate T > 0 static and dynamical properties of J 1 -J 2 HM of TL up to N = 30 sites [54], as well as thermodynamic T > 0 quantities on KL with up to N = 42 sites [48]. It should be reminded that for thermodynamic quantities involving only conserved quantities [59,60] computer requirements are essentially equal as for ED g.s.…”

“…All results for are for N = 30 sites [54]: a) for entropy density s(T ) and b) uniform susceptibility χ0(T ). c) and d) same quantities for the kagome lattice, compared to full HM, all on N = 42 sites[48].…”

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

“…In the following we will present numerical results for s(T ), χ 0 (T ) and R(T ), which reveal that the vanishing of R(T → 0) is quite generic property of a wide class of isotropic 2D Heisenberg models in their range of (presumable) SL parameter regimes. 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.…”

Finite-Size Scaling of Typicality-Based Estimates

“…In contrast, for lower temperatures, we have shown that (i) the probability distributions can become non-Gaussian and (ii) the scaling of δ(O) can become more complicated and generally depends on the specific model and observable under consideration. While a larger Hilbert-space dimension often leads to an improved accuracy of the random-state approach at low temperatures as well, compare the investigation on kagome lattice antiferromagnets of sizes N = 30 and N = 42 in [35], we have also provided examples where this expectation can break down for too small Z eff , compare also [48].…”