We study the excitation spectrum in the dimer phase of the Shastry-Sutherland model by using an unbiased variational method that works in the thermodynamic limit. The method outputs dynamical correlation functions in all possible channels. This output is exploited to identify the order parameters with the highest susceptibility (single or multitriplon condensation in a specific channel) upon approaching a quantum phase transition in the magnetic field versus the $J'/J$ phase diagram. We find four different instabilities: antiferro spin nematic, plaquette spin nematic, stripe magnetic order, and plaquette order, two of which have been reported in previous studies.
We study the Kondo lattice model on the geometrically frustrated Shastry-Sutherland lattice focusing on the quantum phase transition between the valence bond solid and the heavy fermion liquid phase. By explicitly including spinon pairing of local moments at the mean-field level, we establish the emergence of a unique heavy fermion superconducting phase induced by dimer ordering of the local moments coexisting with Kondo hybridization. Furthermore, we demonstrate that for suitable choices of parameters, a partial Kondo-screening phase, where some of the valence bonds are broken, precedes the a…
Thermodynamics of Shastry-Sutherland Model under Magnetic Field
The University of Hong Kong（香港大学）；HK Institute of Quantum Science & Technology, The University of Hong Kong（香港大学量子科学研究所）；State Key Laboratory of Optical Quantum Materials, The University of Hong Kong（香港大学光学量子材料国家重点实验室）
We study the Kondo lattice Shastry-Sutherland model with additional Dzyaloshinskii-Moriya(DM) interactions, exploring the possible magnetic phases in its multi-dimensional parameter space. Treating the local moments as classical spins and using a variational ansatz, we identify the parameter ranges over which various common magnetic orderings are potentially stabilized. Our results reveal that the competing interactions result in a heightened susceptibility towards a wide range of spin configurations including longitudinal ferromagnetic and antiferromagnetic order, coplanar flux configurations…
Exact Demonstration of Magnetization Pleateaus and First Order Dimer-Néel Phase Transitions in a Modified Shastry-Sutherland Model for SrCu$_2$(BO$_3$)$_2$
The Shastry-Sutherland lattice, one of the simplest systems with geometric frustration, which has an exact eigenstate by putting singlets on diagonal bonds, can be realized in a group of layered compounds and rises both theoretical and experimental interest. Most of the previous studies on the Shastry-Sutherland lattice are focusing on the Heisenberg model. Here we opt for the Hubbard model to calculate phase diagrams over a wide range of interaction parameters, and show the competing effects of interaction, frustration and temperature. At low temperature, frustration is shown to favor a param…
The 1/8 fractional plateau phase (1/8-FPP) in Shastry-Sutherland Lattice (SSL) spin systems has been viewed an exemplar of emergence on an Archimedean lattice. Here we explore this phase in the Ising magnet TmB4 using high-resolution specific heat (C) and magnetization (M) in the field-temperature plane. We show that the 1/8-FPP is smoothly connected to the antiferromagnetic (AF) phase on ramping the field from H= 0. Thus, the 1/8-FPP is not a distinct ground state of TmB4. The implication of these results for Heisenberg spins on the SSL is discussed.
Shastry-Sutherland lattice was observed as alternative ground state in Rare Earth intermetallic with Mo$_2$B$_2$Fe and U$_2$Pt$_2$Sn anisotropic structures where magnetic frustration is favored. In the case of Ce$_2$Pd$_2$Sn, it was shown that such phase can be suppressed by the application of magnetic field and, in this work, its stability is studied as a function of the electronic concentration by doping the Sn(4+) lattice with In(3+) atoms. Magnetic and specific heat measurements show that around 50\% substitution the Shastry Sutherland lattice vanishes in a critical point. This result conf…
Considerable recent theoretical and experimental efforts have been devoted to the study of quantum criticality and novel phases of antiferromagnetic heavy-fermion metals. In particular, quantum phase transitions have been discovered in the compound Yb$_2$Pt$_2$Pb. These developments have motivated us to study the competition between the RKKY and Kondo interactions on the Shastry-Sutherland lattice. We determine the zero-temperature phase diagram as a function of magnetic frustration and Kondo coupling within a slave-fermion approach. Pertinent phases include the Shastry-Sutherland valence bond…
We study topological properties of one-triplon bands in an extended Shastry-Sutherland model relevant for the frustrated quantum magnet SrCu_2(BO_3)_2. To this end perturbative continuous unitary transformations are applied about the isolated dimer limit allowing to calculate the one-triplon dispersion up to high order in various couplings including intra and inter Dzyaloshinskii-Moriya interactions and a general uniform magnetic field. We determine the Berry curvature and the Chern number of the different one-triplon bands. We demonstrate the occurance of Chern numbers $\pm 1$ and $\pm 2$ for…
The temperature dependence of the gapped triplet excitations (triplons) in the 2D Shastry-Sutherland quantum magnet SrCu$_2$(BO$_3$)$_2$ is studied by means of inelastic neutron scattering. The excitation amplitude rapidly decreases as a function of temperature while the integrated spectral weight can be explained by an isolated dimer model up to 10~K. Analyzing this anomalous spectral line-shape in terms of damped harmonic oscillators shows that the observed damping is due to a two-component process: one component remains sharp and resolution limited while the second broadens. We explain the …
Magnetization Plateaus in the Shastry-Sutherland Model for SrCu_2(BO_3)_2: Results of Fourth-Order Perturbation Expansion with a Low-Density Approximation
Motivated by the intriguing properties of the Shastry-Sutherland compound SrCu2(BO3)2 under pressure, with a still debated intermediate plaquette phase appearing at around 20 kbar and a possible deconfined critical point at higher pressure upon entering the antiferromagnetic phase, we have investigated its high-field properties in this pressure range using tunnel diode oscillator (TDO) measurements. The two main new phases revealed by these measurements are fully consistent with those identified by infinite Projected Entangled Pair states (iPEPS) calculations of the Shastry-Sutherland model, a…
It is known that for a topologically ordered state the area law for the entanglement entropy shows a negative universal additive constant contribution, $-γ$, called the topological entanglement entropy. We theoretically study the entanglement entropy of the two-dimensional Shastry-Sutherland quantum antiferromagnet using exact diagonalization on clusters of 16 and 24 spins. By utilizing the Kitaev-Preskill construction [A. Kitaev and J. Preskill, Phys. Rev. Lett. {\bf 96}, 110404 (2006)] we extract a finite topological term, $-γ$, in the region of bond-strength parameter space corresponding to…
The small-cluster exact-diagonalization calculations and the projector quantum Monte Carlo method are used to examine the competing effects of geometrical frustration and interaction on ferromagnetism in the Hubbard model on the Shastry-Sutherland lattice. It is shown that the geometrical frustration stabilizes the ferromagnetic state at high electron concentrations ($n \gtrsim 7/4$), where strong correlations between ferromagnetism and the shape of the noninteracting density of states are observed. In particular, it is found that ferromagnetism is stabilized only for these values of frustrati…
The minimal effective model for the magnetisation plateaus below 1/2 in the Shastry-Sutherland model is derived to be an Ising model of certain unit-cell hard-core bosons with anisotropic repulsive interactions on isosceles triangular lattice. It unambiguously gives the prominent plateaus at 1/8, 1/6, 1/4, 1/3 and an additional one at 3/8, related through a particle-hole (p-h) transformation. The Dzyaloshinsky-Moriya (DM) interaction dresses it up with an inhomogeneous transverse field that also causes p-h asymmetry due to an in-plane component of the inter-dimer DM vector. This explains the a…
Ferromagnetically coupled Shastry-Sutherland quantum spin singlets in (CuCl)LaNb$_2$O$_7$
利用非弹性中子散射、X射线、中子衍射和第一性原理计算技术，我们证明了二维量子自旋系统（CuCl）$_2$的晶体结构是正交的，具有$Pbam$对称性，其中$_4$八面体从它们的高对称位置倾斜，Cu $^{2+} (s = 1/2)$离子形成畸变的正方形晶格.主要的磁相互作用是第四近邻反铁磁相互作用，具有Cu-Cl--Cl-Cu交换路径，这导致自旋单线态的形成。单态之间的两个最强相互作用是铁磁性的，这使得（CuCl）LaNb $_2$ O $_7$成为第一个铁磁耦合Shastry-Sutherland量子自旋单态系统。
Insulator-metal transition is investigated self-consistently on the frustrated Shastry-Sutherland lattice in the framework of Slave-Boson mean-field theory. Due to the presence of quasi-flat band structure characteristic, the system displays a spin-density-wave (SDW) insulating phase at the weak doping levels, which is robust against frustration, and it will be transited into an SDW metallic phase at high doping levels. As further increasing the doping, the temperature or the frustration on the diagonal linking bonds, the magnetic order $m$ will be monotonically suppressed, resulting in the ap…
We look into the quantum phase diagram of a spin-$\frac{1}{2}$ antiferromagnet on the square lattice with degenerate Shastry-Sutherland ground states, for which only a schematic phase diagram is known so far. Many exotic phases were proposed in the schematic phase diagram by the use of exact diagonalization on very small system sizes. In our present work, an important extension of this antiferromagnet is introduced and investigated in the thermodynamic limit using triplon mean-field theory. Remarkably, this antiferromagnet shows a stable plaquette spin-gapped phase like the original Shastry-Su…
Using infinite projected entangled-pair states (iPEPS), we show that the Shastry-Sutherland model in an external magnetic field has low-magnetization plateaus which, in contrast to previous predictions, correspond to crystals of bound states of triplets, and {\it not} to crystals of triplets. The first sizable plateaus appear at magnetization 1/8, 2/15 and 1/6, in agreement with experiments on the orthogonal-dimer antiferromagnet SrCu$_2$(BO$_3$)$_2$, and they can be naturally understood as regular patterns of bound states, including the intriguing 2/15 one. We also show that, even in a confin…
We investigate the physical properties of the Shastry-Sutherland lattice material BaNd$_2$ZnO$_5$. Neutron diffraction, magnetic susceptibility, and specific heat measurements reveal antiferromagnetic order below 1.65 K. The magnetic order is found to be a 2-$\boldsymbol{Q}$ magnetic structure with the magnetic moments lying in the Shastry-Sutherland lattice planes comprising the tetragonal crystal structure of BaNd$_2$ZnO$_5$. The ordered moment for this structure is 1.9(1) $μ_B$ per Nd ion. Inelastic neutron scattering measurements reveal that the crystal field ground state doublet is well s…
Anomalous thermal broadening in the Shastry-Sutherland model and SrCu$_2($BO$_3)_2$
University of Munich（慕尼黑大学）；Arnold Sommerfeld Center for Theoretical Physics, University of Munich（慕尼黑大学阿诺德·索末菲尔德理论物理中心）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Laboratoire Léon Brillouin, CEA, CNRS, Université Paris-Saclay（巴黎萨克雷大学CEA-CNRS莱昂·布里渊实验室）；Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, CY Cergy Paris Université（CY塞吉巴黎大学CNRS 8089号理论与建模物理实验室）
Motivated by intertwined crystal symmetries and topological phases, we study the possible realization of topological insulator in nonsymmorphic crystals at integer fillings. In particular, we consider spin orbit coupled electronic systems of two-dimensional crystal Shastry-Sutherland lattice at integer filling where the gapless line degeneracy is protected by glide reflection symmetry. Based on a simple tight-binding model, we investigate how the topological insulating phase is stabilized by breaking nonsymmorphic symmetries but in the presence of time reversal symmetry and inversion symmetry.…
Quantum Monte Carlo (QMC) simulations constitute nowadays one of the most powerful methods to study strongly correlated quantum systems, provided that no "sign problem" arises. However, many systems of interest, including highly frustrated magnets, suffer from an average sign that is close to zero in standard QMC simulations. Nevertheless, a possible sign problem depends on the simulation basis, and here we demonstrate how a suitable choice of cluster basis can be used to eliminate or at least reduce the sign problem in highly frustrated magnets that were so far inaccessible to efficient QMC s…
