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arXiv:2104.08887 · Physical review. B./Physical review. B

Quantum criticality and spin liquid phase in the Shastry-Sutherland model

Jianwei Yang, Anders W. Sandvik, Ling Wang

Published Feb 23, 2022• 88 citations
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Abstract

The two-dimensional quantum spin model proposed by Shastry and Sutherland more than four decades ago is notable for its realization in SrCu${}_{2}$(BO${}_{3}$)${}_{2}$. Here, the authors present numerical evidence of a gapless spin liquid phase in the model and discuss its connection to a deconfined quantum critical point. The new phase exists in a parameter regime where recent high-pressure heat capacity measurements on SrCu${}_{2}$(BO${}_{3}$)${}_{2}$ did not detect any low-temperature order, in contrast to the antiferromagnetic and plaquette-singlet phases existing at higher and lower pressures, respectively. Thus, the elusive spin liquid may exist in SrCu${}_{2}$(BO${}_{3}$)${}_{2}$.

DOI
10.1103/physrevb.105.l060409

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The two-dimensional quantum spin model proposed by Shastry and Sutherland more than four decades ago is notable for its realization in SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​. Here, the authors present numerical evidence of a gapless spin liquid phase in the model and discuss its connection to a deconfined quantum critical point. The new phase exists in a parameter regime where recent high-pressure heat capacity measurements on SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​ did not detect any low-temperature order, in contrast to the antiferromagnetic and plaquette-singlet phases existing at higher and lower pressures, respectively. Thus, the elusive spin liquid may exist in SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​.
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The Shastry-Sutherland model is an effective model of the layered material SrCu_{2}(BO_{3})_{2}, which exhibits an extremely rich phase diagram as a function of pressure and magnetic field. Motivated by the recent controversy regarding its phase diagram at zero magnetic field, we perform large-scale simulations based on infinite projected entangled-pair states, a two-dimensional tensor network Ansatz to represent the ground state directly in the thermodynamic limit. By employing the latest optimization techniques, we obtain variational states with lower energy than previous results obtained from other methods. Using systematic extrapolations to the exact infinite bond dimension limit, our simulations reveal a narrow quantum spin liquid phase between the plaquette and antiferromagnetic phases in the range 0.785(5)≤J^{'}/J≤0.82(1).
We report heat capacity measurements of SrCu_{2}(BO_{3})_{2} under high pressure along with simulations of relevant quantum spin models and map out the (P,T) phase diagram of the material. We find a first-order quantum phase transition between the low-pressure quantum dimer paramagnet and a phase with signatures of a plaquette-singlet state below T=2 K. At higher pressures, we observe a transition into a previously unknown antiferromagnetic state below 4 K. Our findings can be explained within the two-dimensional Shastry-Sutherland quantum spin model supplemented by weak interlayer couplings. The possibility to tune SrCu_{2}(BO_{3})_{2} between the plaquette-singlet and antiferromagnetic states opens opportunities for experimental tests of quantum field theories and lattice models involving fractionalized excitations, emergent symmetries, and gauge fluctuations.
Motivated by the novel phenomena observed in the layered material SrCu_{2}(BO_{3})_{2}, the Shastry-Sutherland model (SSM) has been extensively studied as the minimal model for SrCu_{2}(BO_{3})_{2}. However, the nature of its quantum phase transition from the plaquette valence-bond solid to antiferromagnetic phase is under fierce debate, posing a challenge to understand the underlying quantum criticality. Via the state-of-the-art tensor network simulations, we study the ground state of the SSM on large-scale size up to 20×20 sites. We identify the continuous transition nature accompanied by an emergent O(4) symmetry between the plaquette valence-bond solid and antiferromagnetic phase, which strongly suggests a deconfined quantum critical point (DQCP). Furthermore, we map out the phase diagram of an extended SSM that can be continuously tuned to the SSM, which demonstrates the same DQCP phenomena along a whole critical line. Our results indicate a compelling scenario for understanding the origin of the proposed proximate DQCP in recent experiments of SrCu_{2}(BO_{3})_{2}.
Inspired by recent experimental measurements [Guo et al., Phys. Rev. Lett. 124, 206602 (2020PRLTAO0031-900710.1103/PhysRevLett.124.206602); Jiménez et al., Nature (London) 592, 370 (2021)NATUAS0028-083610.1038/s41586-021-03411-8] on frustrated quantum magnet SrCu_{2}(BO_{3})_{2} under combined pressure and magnetic fields, we study the related spin-1/2 Shastry-Sutherland model using state-of-the-art tensor network methods. By calculating thermodynamics, correlations, and susceptibilities, we find, in zero magnetic field, not only a line of first-order dimer-singlet to plaquette-singlet phase transition ending with a critical point, but also signatures of the ordered plaquette-singlet transition with its critical end point terminating on this first-order line. Moreover, we uncover prominent magnetic barocaloric responses, a novel type of quantum correlation induced cooling effect, in the strongly fluctuating supercritical regime. Under finite fields, we identify a quantum phase transition from the plaquette-singlet phase to the spin supersolid phase that breaks simultaneously lattice translational and spin rotational symmetries. The present findings on the Shastry-Sutherland model are accessible in current experiments and would shed new light on the critical and supercritical phenomena in the archetypal frustrated quantum magnet SrCu_{2}(BO_{3})_{2}.
Motivated by the recent experimental discovery of the TTT-linear specific heat in pressurized and magnetized Shastry-Sutherland Mott insulator SrCu2_22​(BO3_33​)2_22​, we perform the state-of-the-art thermal tensor-network computation on the Shastry-Sutherland model under a magnetic field. Our simulation results suggest the existence of a symmetric intermediate phase with TTT-linear specific heat at low temperature, occupying a large parameter space and between the plaquette-singlet phase and antiferromagnetic phase at low fields and other symmetry-breaking phases at high fields before the system is fully polarized. Such an unexpected novel state bears an astonishing similarity to the experimental findings in the material. It opens the door to further investigations of the possible liberation of deconfined magnetized Dirac spinons by the competing interactions in this highly frustrated quantum magnet model, and by the combined effects of magnetic field and pressure in the associated Shastry-Sutherland Mott insulator SrCu2_22​(BO3_33​)2_22​.