Thermodynamic properties of highly frustrated quantum spin ladders: Influence of many-particle bound states

Abstract

Quantum antiferromagnets have proven to be some of the cleanest realizations available for theoretical, numerical, and experimental studies of quantum fluctuation effects. At finite temperatures, however, the additional effects of thermal fluctuations in the restricted phase space of a low-dimensional system have received much less attention, particularly the situation in frustrated quantum magnets, where the excitations may be complex collective (bound or even fractionalized) modes. We investigate this problem by studying the thermodynamic properties of the frustrated two-leg S = 1/2 spin ladder, with particular emphasis on the fully frustrated case. We present numerical results for the magnetic specific heat and susceptibility, obtained from exact diagonalization and quantum Monte Carlo studies, which we show can be rendered free of the sign problem even in a strongly frustrated system and which allow us to reach unprecedented sizes of L = 200 ladder rungs. We find that frustration effects cause an unconventional evolution of the thermodynamic response across the full parameter regime of the model. However, close to the first-order transition they cause a highly anomalous reduction in temperature scales with no concomitant changes in the gap; the specific heat shows a very narrow peak at very low energies and the susceptibility rises abruptly at extremely low temperatures. Unusually, the two quantities have different gaps over an extended region of the parameter space. We demonstrate that these results reflect the presence of large numbers of multi-particle bound-state excitations, whose energies fall below the one-triplon gap in the transition region.

Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations

“…For this reason, we have not performed simulations for still larger values of N , although this would be completely feasible due to the rather mild sign problem in this parameter regime. In the limit J = 0, we recover the result for decoupled dimers, which is known analytically [29,[49][50][51] and is represented by the dashed lines. As the ratio J/J D is increased, χ(T ) shows a flattening of its maximum accompanied by a downward shift of its low-temperature flank [ Fig.…”

“…The emergence of this distinctive maximum at a temperature scale very low in comparison with the coupling constants constitutes the dominant thermodynamic feature as one approaches the first-order transition from the dimer-singlet to the plaquette phase at J/J D ≈ 0.675 [40]. This behavior is analogous to that observed on approaching the boundary of the rung-singlet phase in highly frustrated spin ladders [29,32], where its origin was traced to the presence of many low-lying bound rung-triplet excitations. Our results suggest that the same type of boundstate mechanism is at work in the less constrained 2D system, and that the emergence of the low-temperature maximum in the specific heat is its clearest thermodynamic fingerprint.…”

“…Closing this section with a brief technical summary, we perform stochastic series expansion [44] QMC simulations in the dimer basis [29,30] with directed loop updates [45,46] to compute the thermodynamic properties of the Shastry-Sutherland model (1) and to characterize the sign problem in the extended model (2). These simulations perform an unrestricted sampling of the configuration space, meaning one not constrained to any subset of the Hilbert space defined by the S z and D z operators of the total system.…”

“…In this paper, we show that knowing the exact ground state of the Shastry-Sutherland model is indeed a considerable advantage, provided that one formulates QMC simulations in the dimer basis [29][30][31][32][33] rather than the conventional site basis. Unlike a number of fully frustrated models studied recently, in which the minus sign disappears completely in the dimer basis, we illustrate the extent to which the sign problem is still present throughout the generalized phase diagram that connects the Shastry-Sutherland model to the fully frustrated bilayer.…”

Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase

“…IV, it is helpful to compare and contrast the Shastry-Sutherland model with the fully frustrated two-leg spin ladder. In this 1D model, some of us [76,80] also found a striking thermodynamic response at low temperatures, which could be traced to a proliferation of low-energy multimagnon bound states upon approaching a first-order QPT. While it is clear that the proliferation of low-lying states is the origin of the low-temperature properties of the Shastry-Sutherland model, there are some important differences between the 1D and 2D systems, most notably concerning the mechanism behind the formation of these states.…”