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

Abstract

The thermodynamic properties of the Shastry-Sutherland model have posed one of the longestlasting conundrums in frustrated quantum magnetism. Over a wide range on both sides of the quantum phase transition (QPT) from the dimer-product to the plaquette-based ground state, neither analytical nor any available numerical methods have come close to reproducing the physics of the excited states and thermal response. We solve this problem in the dimer-product phase by introducing two qualitative advances in computational physics. One is the use of thermal pure quantum (TPQ) states to augment dramatically the size of clusters amenable to exact diagonalization. The second is the use of tensor-network methods, in the form of infinite projected entangled pair states (iPEPS), for the calculation of finite-temperature quantities. We demonstrate convergence as a function of system size in TPQ calculations and of bond dimension in our iPEPS results, with complete mutual agreement even extremely close to the QPT. Our methods reveal a remarkably sharp and low-lying feature in the magnetic specific heat around the QPT, whose origin appears to lie in a proliferation of excitations composed of two-triplon bound states. The surprisingly low energy scale and apparently extended spatial nature of these states explain the failure of less refined numerical approaches to capture their physics. Both of our methods will have broad and immediate application in addressing the thermodynamic response of a wide range of highly frustrated magnetic models and materials.

A quantum magnetic analogue to the critical point of water

“…As quantified in Fig. 2a, C p (T )/T at low pressures shows an exponential rise to a broad maximum at a temperature, T max , that tracks the gap to the triplon or bound-triplon excitations of the dimer phase [16]. With increasing P , this peak moves gradually lower and becomes proportionately narrower, but between 18 and 20 kbar it becomes extremely narrow and attains a showing initial field-induced suppression of the low-temperature transition followed by a dramatic change in shape to a sharp low-T peak with no broad hump at higher energies.…”

“…We demonstrate by high-precision specific-heat measurements under pressure and applied magnetic field that, like water, the pressure-temperature phase diagram of SrCu 2 (BO 3 ) 2 has an Ising critical point terminating a first-order transition line, which separates phases with different densities of magnetic particles (triplets). We achieve a quantitative explanation of our data by detailed numerical calculations using newly-developed finitetemperature tensor-network methods [16,[18][19][20]. These results open a new dimension in understanding the thermodynamics of quantum magnetic materials, where the anisotropic spin inter-actions producing topological properties [21,22] for spintronic applications drive an increasing focus on first-order QPTs.…”

“…This realizes a S = 1/2 Heisenberg model formulated by Shastry and Sutherland [12] because it has an exact ground state, a product of dimer singlets, for all small and intermediate interaction ratios (J/J D < 0.675 [14]). While the frustration is manifest in many unusual phenomena [15,16,25], our interest in the Shastry-Sutherland model lies in the presence of two QPTs, from the dimer phase to a plaquette phase at J/J D = 0.675(2) and thence to an ordered Néel antiferromagnet (AF) at J/J D = 0.765 (15) [14]; our interest in SrCu 2 (BO 3 ) 2 lies in the remarkable fact that an applied hydrostatic pressure acts to control J/J D , revealing both transitions at respective pressures of . The evolution of peak heights with proximity to the critical coupling ratio, illustrated clearly in the numerical data, is less apparent in experiment.…”

“…The evolution of peak heights with proximity to the critical coupling ratio, illustrated clearly in the numerical data, is less apparent in experiment. We note that the phonon contribution (Cp(T )/T ∝ T 2 ) to the measured specific heat becomes appreciable at higher temperatures; while this can be subtracted for accurate fitting [16], our focus here is on the peak positions at and below 6 K. e, Convergence of the critical coupling ratio obtained in finite-temperature iPEPS calculations as a function of 1/D; the extrapolated value of 0.67(1) agrees well with the zero-temperature value [14]. The finite-temperature critical point has been discussed theoretically in a two-dimensional (2D) Heisenberg spin model, the "fully frustrated bilayer" [27].…”

“…In quantum spin systems, continuous quantum phase transitions (QPTs) [6] have been investigated extensively [7][8][9][10][11], but discontinuous QPTs have received less attention. The frustrated quantum antiferromagnet SrCu 2 (BO 3 ) 2 constitutes a near-exact realization of the paradigmatic Shastry-Sutherland model [12][13][14] and displays exotic phenomena including magnetization plateaux [15], anomalous thermodynamics [16] and discontinuous QPTs [17]. We demonstrate by high-precision specific-heat measurements under pressure and applied magnetic field that, like water, the pressure-temperature phase diagram of SrCu 2 (BO 3 ) 2 has an Ising critical point terminating a first-order transition line, which separates phases with different densities of magnetic particles (triplets).…”