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Using the density-matrix renormalization group method for the ground state and excitations of the Shastry-Sutherland spin model, we demonstrate the existence of a narrow quantum spin liquid phase between the previously known plaquette-singlet and antiferromagnetic states. Our conclusions are based on finite-size scaling of excited level crossings and order parameters. Together with previous results on candidate models for deconfined quantum criticality and spin liquid phases, our results point to a unified quantum phase diagram where the deconfined quantum-critical point separates a line of first-order transitions and a gapless spin liquid phase. The frustrated Shastry-Sutherland model is close to the critical point but slightly inside the spin liquid phase, while previously studied unfrustrated models cross the first-order line. We also argue that recent heat capacity measurements in SrCu$_2$(BO$_3$)$_2$ show evidence of the proposed spin liquid at pressures between 2.6 and 3 GPa.
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We investigate classical Heisenberg spins on the Shastry-Sutherland lattice and under an external magnetic field. A detailed study is carried out both analytically and numerically by means of classical Monte-Carlo simulations. Magnetization pseudo-plateaux are observed around 1/3 of the saturation magnetization for a range of values of the magnetic couplings. We show that the existence of the pseudo-plateau is due to an entropic selection of a particular collinear state. A phase diagram that shows the domains of existence of those pseudo-plateaux in the $(h, T)$ plane is obtained.
The thermodynamic properties of the Shastry-Sutherland model have posed one of the longest-lasting 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.
We revisit the critical behavior of the sub-ohmic spin-boson model. Analysis of both the leading and subleading terms in the temperature dependence of the inverse static local spin susceptibility at the quantum critical point, calculated using a numerical renormalization-group method, provides evidence that the quantum critical point is interacting in cases where the quantum-to-classical mapping would predict mean-field behavior. The subleading term is shown to be consistent with an w/T scaling of the local dynamical susceptibility, as is the leading term. The frequency and temperature dependences of the local spin susceptibility in the strong-coupling (delocalized) regime are also presented. We attribute the violation of the quantum-to-classical mapping to a Berry-phase term in a continuum path-integral representation of the model. This effect connects the behavior discussed here with its counterparts in models with continuous spin symmetry.
Using inelastic neutron scattering, x-ray, neutron diffraction, and the first-principle calculation techniques, we show that the crystal structure of the two-dimensional quantum spin system (CuCl)LaNb$_2$O$_7$ is orthorhombic with $Pbam$ symmetry in which CuCl$_4$O$_2$ octahedra are tilted from their high symmetry positions and the Cu$^{2+} (s = 1/2)$ ions form a distorted square lattice. The dominant magnetic interactions are the fourth nearest neighbor antiferromagnetic interactions with a Cu-Cl--Cl-Cu exchange path, which lead to the formation of spin singlets. The two strongest interactions between the singlets are ferromagnetic, which makes (CuCl)LaNb$_2$O$_7$ the first system of ferromagnetically coupled Shastry-Sutherland quantum spin singlets.
We report the microscopic magnetic model for the spin-1/2 Heisenberg system CdCu2(BO3)2, one of the few quantum magnets showing the 1/2-magnetization plateau. Recent neutron diffraction experiments on this compound [M. Hase et al., Phys. Rev. B 80, 104405 (2009)] evidenced long-range magnetic order, inconsistent with the previously suggested phenomenological magnetic model of isolated dimers and spin chains. Based on extensive density-functional theory band structure calculations, exact diagonalizations, quantum Monte Carlo simulations, third-order perturbation theory, as well as high-field magnetization measurements, we find that the magnetic properties of CdCu2(BO3)2 are accounted for by a frustrated quasi-2D magnetic model featuring four inequivalent exchange couplings: the leading antiferromagnetic coupling J_d within the structural Cu2O6 dimers, two interdimer couplings J_t1 and J_t2, forming magnetic tetramers, and a ferromagnetic coupling J_it between the tetramers. Based on comparison to the experimental data, we evaluate the ratios of the leading couplings J_d : J_t1 : J_t2 : J_it = 1 : 0.20 : 0.45 : -0.30, with J_d of about 178 K. The inequivalence of J_t1 and J_t2 largely lifts the frustration and triggers long-range antiferromagnetic ordering. The proposed model accounts correctly for the different magnetic moments localized on structurally inequivalent Cu atoms in the ground-state magnetic configuration. We extensively analyze the magnetic properties of this model, including a detailed description of the magnetically ordered ground state and its evolution in magnetic field with particular emphasis on the 1/2-magnetization plateau. Our results establish remarkable analogies to the Shastry-Sutherland model of SrCu2(BO3)2, and characterize the closely related CdCu2(BO3)2 as a material realization for the spin-1/2 decorated anisotropic Shastry-Sutherland lattice.
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