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

Abstract

We investigate the minus-sign problem that afflicts quantum Monte Carlo (QMC) simulations of frustrated quantum spin systems, focusing on spin S = 1/2, two spatial dimensions, and the extended Shastry-Sutherland model. We show that formulating the Hamiltonian in the diagonal dimer basis leads to a sign problem that becomes negligible at low temperatures for small and intermediate values of the ratio of the inter-and intra-dimer couplings. This is a consequence of the fact that the product state of dimer singlets is the exact ground state both of the extended Shastry-Sutherland model and of a corresponding "sign-problem-free" model, obtained by changing the signs of all positive off-diagonal matrix elements in the dimer basis. By exploiting this insight, we map the sign problem throughout the extended parameter space from the Shastry-Sutherland to the fully frustrated bilayer model and compare it with the phase diagram computed by tensor-network methods. We use QMC to compute with high accuracy the temperature dependence of the magnetic specific heat and susceptibility of the Shastry-Sutherland model for large systems up to a coupling ratio of 0.526(1) and down to zero temperature. For larger coupling ratios, our QMC results assist us in benchmarking the evolution of the thermodynamic properties by systematic comparison with exact diagonalization calculations and interpolated high-temperature series expansions. arXiv:1808.02043v2 [cond-mat.str-el] FIG. 1. Schematic representations of the extended Shastry-Sutherland model [Eq. (2)] in (a) single-plane and (b) bilayer format.

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

“…6, we focus henceforth on the simple-update approach, which allows us to reach bond dimensions as large as D = 20 in the present problem, rather than the full-update approach, where D = 14 represents a We begin the systematic presentation and comparison of our thermodynamic results by making contact with the previous state of the art, as shown in Ref. [25]. The analysis of these authors, which included ED, QMC, and high-temperature series expansions (HTSEs), terminated at the coupling ratio J/J D = 0.60, where all three methods were beyond their limits.…”

“…In Ref. [25] we showed a schematic illustration of the energy spectrum of the Shastry-Sutherland model as a function of the coupling ratio J/J D , based on Lanczos ED calculations to obtain the lowest levels of a cluster of size N = 36 sites. For more specific insight into the nature of the states revealed by the Lanczos procedure, here we have computed a much larger number of low-energy states, but for smaller clusters (of sizes up to N = 28).…”

“…We stress that, given the large number of states in these calculations, it is not easy to observe the discrete structure of the spectrum even in its lowest-lying regions, and as in Ref. [25] we use shading to indicate the support of these excitations.…”

“…Full exact diagonalization (ED) has been limited to systems of up to 20 sites and, as we will demonstrate in detail here, suffer from significant finite-size limitations at J/J D > 0.6. Quantum Monte Carlo (QMC) methods suffer from extreme sign problems, and despite a recent study by some of us [25] that expands the boundaries of what is possible by QMC, the low-temperature behavior in the regime J/J D > 0.6 remains entirely inaccessible. iPEPS methods work in the thermodynamic limit and are immune to frustration problems, but to date have been limited to ground-state properties.…”

Exact plaquette singlet phases in an orthogonal-plaquette model

“…To this end, apart from exact diagonalizations, series expansions, and iPEPS, for not too large values of J Quantum Monte-Carlo simulations should be possible, due to the exact ground states. This route was recently taken for the SSM in a dimer singlet basis 36 .…”