Quantum Phase Transitions in the Shastry-Sutherland Model forSrCu2(BO3)2

Abstract

We investigate the quantum phase transitions in the frustrated antiferromagnetic Heisenberg model for SrCu2(BO3)2 by using the series expansion method. It is found that a novel spin-gap phase, which is adiabatically connected to the plaquette-singlet phase, exists between the dimer and the magnetically ordered phases known so far. When the ratio of the competing exchange couplings α(= J ′ /J) is varied, this spin-gap phase exhibits the first-(second-) order quantum phase transition to the dimer (the magnetically ordered) phase at the critical point αc1 = 0.677(2) (αc2 = 0.86(1)). Our results shed light on some controversial arguments about the nature of the quantum phase transitions in this model. PACS numbers: 75.10Jm, 75.40CxTwo-dimensional (2D) antiferromagnetic quantum spin systems with the spin gap have been the subject of considerable interest. A typical compound found recently is SrCu 2 (BO 3 ) 2 [1], in which the characteristic lattice structure of the Cu 2+ spins (see Fig. 1) stabilizes the singlet ground state. This system has been providing a variety of interesting phenomena such as the plateaus in the magnetization curve observed at 1/3, 1/4 and 1/8 of the full moment [1,2]. The spin system may be described by the 2D Heisenberg model on the square lattice with some diagonal bonds which is referred to as the ShastrySutherland model [3], as pointed out by Miyahara and Ueda [4]. The key structure with the orthogonal dimers shown in Fig. 1 makes the system unique and particularly interesting among 2D spin-gap compounds. In this frustrated system, there may occur non-trivial quantum phase transitions when the nearest-neighbor coupling J and the next-nearest-neighbor coupling J ′ are varied. Albrecht and Mila [5] discussed the possibility of a helical phase between the dimer and the magnetically ordered phases by means of the Schwinger boson mean-field theory. Recent theoretical studies, however, have suggested that there may not be such a helical phase, but the first-order phase transition occurs from the dimer to the ordered phases [4,6]. Furthermore, more recent study [7] claims that the phase transition should be of the second order with a non-trivial critical exponent ν = 0.45(2). These controversial conclusions may come from the fact that the quantum phase transition in the Shastry-Sutherland model suffers from the strong frustration due to the competing exchange interactions J and J ′ , and therefore a careful treatment should be necessary to figure out the correct nature of the phase transition. In particular, we have to keep in mind that such a strong frustration may possibly stabilize another spin-gap phase distinct from the dimer phase.In this paper, by calculating the ground state energy, the staggered susceptibility and the spin gap by means of the series expansion method, we find that there should exist a novel spin-gap phase with the disordered ground state, which is stabilized by the strong frustration, between the dimer and the magnetically ordered phases. The spin-gap phase found in this...

Magnon dispersion and anisotropies inSrCu2(BO3)2

“…If only isotropic interactions are considered, SrCu 2 ͑BO 3 ͒ 2 is very close in parameter space ͑JЈ / J = 0.62͒ to a quantum critical point, 4 ͑JЈ / J = 0.68͒, which separates the dimer phase ͑which is known exactly͒ from a phase that is not known exactly but may be quadrumerized. [22][23][24] Perturbative approaches to the excitations may therefore turn out to be inaccurate. For instance, the splitting of the q = 0 triplet energy is given by ␦ = D Ќ Ј g͑JЈ / J͒, which is linear in D Ќ Ј and involves a function g͑JЈ / J͒ with g͑0͒ = 4, but g͑JЈ / J͒ = 2.0 for JЈ / J = 0.62.…”

Low-Lying Magnetic Excitation of the Shastry-Sutherland Model

“…[4], it was pointed out that SrCu 2 (BO 3 ) 2 may be modeled by the S = 1/2 Heisenberg model on the Shastry-Sutherland (SS) lattice [5] (Shastry-Sutherland model, hereafter). This sparked experimental-and theoretical researches on interesting features of the ShastrySutherland model [6][7][8][9][10][11].Strong geometrical frustration of the SS model allows a simple dimer-product to be the exact ground state [5]. In the zeroth-order approximation, a triplet excitation above the dimer-singlet ground state is created by promoting one of the dimer singlets to triplet.…”

High-order study of the quantum critical behavior of a frustrated spin- 12 antiferromagnet on a stacked honeycomb bilayer

“…(4), (5), and the ES wave function considered, as in Eq. (16). In the present case we restrict attention to the lowest-lying spin-triplet excitation, so that ∆ e now becomes equal to the spintriplet gap, which we denote by ∆.…”

“…Various theoretical studies (see, e.g., Refs. [16,17]) yield (J ′ /J) c ≈ 1.48. In the Shastry-Sutherland material SrCu 2 (BO 3 ) 2 , for which (J ′ /J) ≈ 1.6, the triplon crystalline phases show up as a series of magnetization plateaux at unconventional filling fractions [11,12] that are stabilized by complex manybody interactions among the triplons [9,12,18,19].…”