We investigate 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, 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.
We systematically study the effects of higher-order interactions on the
S=23,1 orthogonal dimer chains using exact diagonalization and density matrix renormalization group. Due to frustration and higher spin, there are rich quantum phases, including three Haldane phases, two gapless phases, and several magnetically ordered phases. To characterize these phases and their phase transitions, we study various physical quantities such as energy gap, energy-level crossing, fidelity susceptibility, spin correlation, entanglement spectrum, and central charge. According to our calculations, the biquadratic term can enhance the Haldane phase regions. In particular, we numerically identify that a Haldane phase in
S=23 case is adiabatically connected to the exact AKLT (Affleck, Kennedy, Lieb, and Tasaki) point when adding a bicubic term. Our study on the orthogonal dimer model, which is a 1D version of the Shastry-Sutherland model, provides insights into understanding the possible
S=23,1 Haldane phases in quasi-1D and 2D frustrated magnetic materials.
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 determine the phase diagram of a generalized Shastry-Sutherland model, using a combination of dimer- and quadrumer-boson methods and numerical exact diagonalization techniques. Along special lines in the parameter space the model reduces to the standard Shastry-Sutherland model, the 1/5th depleted square lattice and the two-dimensional plaquette square lattice model. We study the evolution of the ordered phases found in the latter two unfrustrated models under the effect of frustration. Furthermore we present exact diagonalization results for the Shastry-Sutherland model on clusters with up to 32 sites, supporting the existence of an intermediate gapped valence bond crystal phase with plaquette long-range order.
Frustrated spin-1/2 model with all-antiferromagnetic exchange on Shastry-Sutherland lattice (SSL) has been extensively explored, and in this work we study the quantum phase diagram of isotropic Heisenberg spin- 1 / 2 model on the SSL with ferromagnetic exchange interactions along leg, and antiferromagnetic couplings along the diagonal bonds ( J ). Using density matrix renormalization group (DMRG) and exact diagonalization calculations, we identify four distinct ground-state (gs) phases for this frustrated spin-1/2 model: stripe ( π , 0 ) , stripe ( 0 , π ) , ferromagnetic, and spiral-dimer phases. In the spiral-dimer phase the gs can exhibit dimer formation along the diagonal bonds with or without spins spiral along the x axis or y axis in different parameter regime and these states are connected through crossovers. There is a continuous transition between stripe with a long-range spin-spin correlations and spiral-dimer phase with a short-range correlations. An effective spin parameter is introduced to accurately determine the phase boundaries. Our DMRG results differ significantly from previous Schwinger boson mean-field theory predictions. The spiral phase occurs in a narrow range of the parameter space and shows short-range correlations in the system.
We investigate quantum phase transitions in a frustrated orthogonal-dimer chain with an arbitrary spin
S> 1/2. When the ratio of the competing exchange couplings is varied, first-order phase transitions occur
2S times among distinct spin-gap phases. The introduction of single-ion anisotropy further enriches the phase diagram. The phase transitions described by the present model possess most of the essential properties inherent in frustrated quantum spin systems.