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arXiv:cond-mat/0003435 · Physical Review Letters

Quantum Phase Transitions in the Shastry-Sutherland Model for SrCu2(BO3)2

Akihisa Koga, Norio Kawakami

Published May 8, 2000• 239 citations
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Abstract

We investigate quantum phase transitions in the frustrated antiferromagnetic Heisenberg model for $\mathrm{Sr}{\mathrm{Cu}}_{2}({\mathrm{BO}}_{3}{)}_{2}$ by using the series expansion method. It is found that a novel spin-gap phase, adiabatically connected to the plaquette-singlet phase, exists between the dimer and the magnetically ordered phases known thus far. When the ratio of the competing exchange couplings $\ensuremath{\alpha}({\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}J}^{\ensuremath{'}}/J)$ is varied, this spin-gap phase exhibits a first- (second-) order quantum phase transition to the dimer (the magnetically ordered) phase at the critical point ${\ensuremath{\alpha}}_{c1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.677(2)$ [ ${\ensuremath{\alpha}}_{c2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.86(1)$]. Our results shed light on some controversial arguments about the nature of quantum phase transitions in this model.

DOI
10.1103/physrevlett.84.4461

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We investigate quantum phase transitions in the frustrated antiferromagnetic Heisenberg model for SrCu2(BO3)2\mathrm{Sr}{\mathrm{Cu}}_{2}({\mathrm{BO}}_{3}{)}_{2}SrCu2​(BO3​)2​ by using the series expansion method. It is found that a novel spin-gap phase, adiabatically connected to the plaquette-singlet phase, exists between the dimer and the magnetically ordered phases known thus far. When the ratio of the competing exchange couplings \ensuremathα(=J\ensuremath′/J)\ensuremath{\alpha}({\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}J}^{\ensuremath{'}}/J)\ensuremathα(=J\ensuremath′/J) is varied, this spin-gap phase exhibits a first- (second-) order quantum phase transition to the dimer (the magnetically ordered) phase at the critical point \ensuremathαc1=0.677(2){\ensuremath{\alpha}}_{c1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.677(2)\ensuremathαc1​=0.677(2) [ \ensuremathαc2=0.86(1){\ensuremath{\alpha}}_{c2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.86(1)\ensuremathαc2​=0.86(1)]. Our results shed light on some controversial arguments about the nature of quantum phase transitions in this model.
We give a short review of our recent works on the first-order quantum phase transitions in frustrated spin chains with orthogonal-dimer structure. When the ratio of the competing antiferromagnetic exchange couplings is varied, a first-order transition occurs between the dimer phase and the plaquette phase, which is accompanied by the discontinuity in the spin excitation gap. We further show that strong frustration triggers the phase transitions in a magnetic field, which exhibit plateaus and jumps in the magnetization curve. The hole-doping effect is also addressed for the orthogonal-dimer chain with linked-tetrahedra structure. It is found that the competing antiferromagnetic interactions result in a firstorder metal-insulator transition upon hole doping. Recently antiferromagnetic quantum spin systems with strong frustration have been studied intensively. A typical example is SrCu2(BO3)2 1) where the spin-1/2 magnetic Cu ions are located on the orthogonal-dimer lattice (the so-called Shastry-Sutherland model). 2) Various interesting phenomena were observed for this compound
We investigate the low-energy properties of the orthogonal-dimer spin chain characterized by a frustrated dimer-plaquette structure. When the competing antiferromagnetic couplings are varied, the first-order quantum phase transition occurs between the dimer and the plaquette phases, which is accompanied by nontrivial features due to frustration: besides the discontinuity in the lowest excitation gap at the transition point, a sharp level crossing occurs for the spectrum in the plaquette phase. We further reveal that the plateau in the magnetization curve at 1/4 of the full moment dramatically changes its character in the vicinity of the critical point. It is argued that the first-order phase transition in this system captures some essential properties found in the two-dimensional orthogonal-dimer model proposed for SrCu2(BO3)2.{\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}.SrCu2​(BO3​)2​.
Recent experiments [Guo et al., Phys. Rev. Lett. 124 206602 (2020)] on thermodynamic properties of the frustrated layered quantum magnet SrCu2(BO3)2 — the Shastry–Sutherland material — have provided strong evidence for a low-temperature phase transition between plaquette-singlet and antiferromagnetic order as a function of pressure. Further motivated by the recently discovered unusual first-order quantum phase transition with an apparent emergent O(4) symmetry of the antiferromagnetic and plaquette-singlet order parameters in a two-dimensional “checkerboard J-Q” quantum spin model [Zhao et al., Nat. Phys. 15 678 (2019)], we here study the same model in the presence of weak inter-layer couplings. Our focus is on the evolution of the emergent symmetry as the system crosses over from two to three dimensions and the phase transition extends from strictly zero temperature in two dimensions up to finite temperature as expected in SrCu2(BO3)2. Using quantum Monte Carlo simulations, we map out the phase boundaries of the plaquette-singlet and antiferromagnetic phases, with particular focus on the triple point where these two ordered phases meet the paramagnetic phase for given strength of the inter-layer coupling. All transitions are first-order in the neighborhood of the triple point. We show that the emergent O(4) symmetry of the coexistence state breaks down clearly when the interlayer coupling becomes sufficiently large, but for a weak coupling, of the magnitude expected experimentally, the enlarged symmetry can still be observed at the triple point up to significant length scales. Thus, it is likely that the plaquette-singlet to antiferromagnetic transition in SrCu2(BO3)2 exhibits remnants of emergent O(4) symmetry, which should be observable due to additional weakly gapped Goldstone modes.
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}.
The two dimensional Heisenberg model for SrCu2(BO3)2{\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}SrCu2​(BO3​)2​ has an exact dimer ground state which was proven by Shastry and Sutherland almost twenty years ago. The critical value of the quantum phase transition from the dimer state to the N\'eel ordered state is determined. Analysis of the experimental data shows that SrCu2(BO3)2\mathrm{SrCu}{}_{2}(\mathrm{BO}{}_{3}{)}_{2}SrCu2​(BO3​)2​ has the dimer ground state but its coupling constants are close to the transition point, which leads to an unusual temperature dependence of the susceptibility. The almost localized nature of the triplet excitations explains the plateaus observed in the magnetization curve.
We study a generalized Shastry-Sutherland model for the material SrCu2(BO3)(2). Along a line in the parameter space, we show rigorously that the model has a first-order phase transition between dimerized and Neel-ordered ground states. Furthermore, when a magnetic field is applied in the dimerized phase, magnetization plateaus develop at commensurate values of the magnetization. We also discuss various aspects of the phase diagram and properties of this model away from this exactly soluble line, which include gap-closing continuous transitions between dimerized and magnetically ordered phases.