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arXiv:1012.5177 · Physical Review B

Emergence of one-dimensional physics from the distorted Shastry-Sutherland lattice

Marion Moliner, Ioannis Rousochatzakis, Frédéric Mila

Published Apr 28, 2011• 14 citations
arXivHTMLPDF

Abstract

Motivated by the ongoing investigation of SrCu${}_{2}$(BO${}_{3}$)${}_{2}$ under pressure, we study a variant of the two-dimensional Shastry-Sutherland (SS) spin-$1/2$ model with two types of dimers. Combined with the frustration of the SS model, this modification induces, in a large parameter range, a dimensional reduction at low energies, with nearly decoupled effective $S=1$ Haldane chains forming along one of the diagonals of the lattice. We also present evidence that the intermediate plaquette solid phase of the undistorted SS model remains stable in a finite region of the phase diagram.

DOI
10.1103/physrevb.83.140414

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Motivated by the ongoing investigation of SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​ under pressure, we study a variant of the two-dimensional Shastry-Sutherland (SS) spin-1/21/21/2 model with two types of dimers. Combined with the frustration of the SS model, this modification induces, in a large parameter range, a dimensional reduction at low energies, with nearly decoupled effective S=1S=1S=1 Haldane chains forming along one of the diagonals of the lattice. We also present evidence that the intermediate plaquette solid phase of the undistorted SS model remains stable in a finite region of the phase diagram.
The layered material SrCu _2 2 (BO _3 3 ) _2 2 has long been studied because of its fascinating physics in a magnetic field and under pressure. Many of its properties are remarkably well described by the Shastry-Sutherland model (SSM) - a two-dimensional frustrated spin system. However, the extent of the intermediate plaquette phase discovered in SrCu _2 2 (BO _3 3 ) _2 2 under pressure is significantly smaller than predicted in theory, which is likely due to the weak interlayer coupling that is present in the material but neglected in the model. Using state-of-the-art tensor network methods we study the SSM with a weak interlayer coupling and show that the intermediate plaquette phase is destabilized already at a smaller value around J''/J\sim0.04-0.05 J ″ / J ∼ 0.04 − 0.05 than previously predicted from series expansion. Based on our phase diagram we estimate the effective interlayer coupling in SrCu _2 2 (BO _3 3 ) _2 2 to be around J''/J\sim 0.027 J ″ / J ∼ 0.027 at ambient pressure.
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.
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​.
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}.
Exact results in frustrated quantum many-body systems are rare, especially in dimensions higher than one. The Shastry-Sutherland (SS) model stands out as a rare example of a two-dimensional spin system with an exactly solvable dimer singlet ground state. In this work, we introduce a three-dimensional analogue of the SS lattice, constructed by deforming the pyrochlore lattice to preserve the local SS geometry. Despite the dimensional increase and altered topology, the ground-state phase diagrams of classical Ising and Heisenberg spins, remain analytically tractable and closely follow their 2D counterparts, including the existence of a 1/3 magnetization plateau and umbrella states. Most notably, for quantum spins S = 1/2, the dimer singlet state survives as an exact ground state over a finite region of the phase diagram. We argue, using exact diagonalization, that the singlet phase is stabilized beyond its 2D counterpart, suggesting enhanced robustness in three dimensions. These results offer a rare, controlled platform to explore the impact of dimensionality on quantum frustration, exact solvability, and potential spin liquid behavior in 3D, with relevance to emergent topological and magnetic phases.
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}.