A simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation

We present a simple quantum many-body system - a two-dimensional lattice of qubits with a Hamiltonian composed of nearest-neighbor two-body interactions - such that the ground state is a universal resource for quantum computation using single-qubit measurements. This ground state approximates a cluster state that is encoded into a larger number of physical qubits. The Hamiltonian we use is motivated by the projected entangled pair states, which provide a transparent mechanism to produce such approximate encoded cluster states on square or other lattice structures (as well as a variety of other quantum states) as the ground state. We show that the error in this approximation takes the form of independent errors on bonds occurring with a fixed probability. The energy gap of such a system, which in part determines its usefulness for quantum computation, is shown to be independent of the size of the lattice. In addition, we show that the scaling of this energy gap in terms of the coupling constants of the Hamiltonian is directly determined by the lattice geometry. As a result, the approximate encoded cluster state obtained on a hexagonal lattice (a resource that is also universal for quantum computation) can be shown to have a larger energy gap than one on a square lattice with an equivalent Hamiltonian.Comment: 5 pages, 1 figure; v2 has a simplified lattice, an extended analysis of errors, and some additional references; v3 published versio

Persistent superfluid phase in a three-dimensional quantum XY model with ring exchange

We present quantum Monte Carlo simulation results on a quantum S=1/2 XY model with ring exchange (the J-K model) on a three-dimensional simple cubic lattice. We first characterize the ground state properties of the pure XY model, obtaining estimations for the energy, spin stiffness and spin susceptibility at T=0 in the superfluid phase. With the ring exchange, we then present simulation data on small lattices which suggests that the superfluid phase persists to very large values of the ring exchange K, without signatures of a phase transition. We comment on the consequences of this result for the search for various exotic phases in three dimensions.Comment: 4 pages, 4 figure

Competing Spin-Gap Phases in a Frustrated Quantum Spin System in Two Dimensions

We investigate quantum phase transitions among the spin-gap phases and the magnetically ordered phases in a two-dimensional frustrated antiferromagnetic spin system, which interpolates several important models such as the orthogonal-dimer model as well as the model on the 1/5-depleted square lattice. By computing the ground state energy, the staggered susceptibility and the spin gap by means of the series expansion method, we determine the ground-state phase diagram and discuss the role of geometrical frustration. In particular, it is found that a RVB-type spin-gap phase proposed recently for the orthogonal-dimer system is adiabatically connected to the plaquette phase known for the 1/5-depleted square-lattice model.Comment: 6 pages, to appear in JPSJ 70 (2001

Generalised Shastry-Sutherland Models in three and higher dimensions

We construct Heisenberg anti-ferromagnetic models in arbitrary dimensions that have isotropic valence bond crystals (VBC) as their exact ground states. The d=2 model is the Shastry-Sutherland model. In the 3-d case we show that it is possible to have a lattice structure, analogous to that of SrCu_2(BO_3)_2, where the stronger bonds are associated with shorter bond lengths. A dimer mean field theory becomes exact at d -> infinity and a systematic 1/d expansion can be developed about it. We study the Neel-VBC transition at large d and find that the transition is first order in even but second order in odd dimensions.Comment: Published version; slightly expande

Spin-S bilayer Heisenberg models: Mean-field arguments and numerical calculations

Spin-S bilayer Heisenberg models (nearest-neighbor square lattice antiferromagnets in each layer, with antiferromagnetic interlayer couplings) are treated using dimer mean-field theory for general S and high-order expansions about the dimer limit for S=1, 3/2,...,4. We suggest that the transition between the dimer phase at weak intraplane coupling and the Neel phase at strong intraplane coupling is continuous for all S, contrary to a recent suggestion based on Schwinger boson mean-field theory. We also present results for S=1 layers based on expansions about the Ising limit: In every respect the S=1 bilayers appear to behave like S=1/2 bilayers, further supporting our picture for the nature of the order-disorder phase transition.Comment: 6 pages, Revtex 3.0, 8 figures (not embedded in text

Novel approach to description of spin liquid phases in low-dimensional quantum antiferromagnets

We consider quantum spin systems with dimerization, which at strong coupling have singlet ground states. To account for strong correlations, the excitations are described as dilute Bose gas of degenerate triplets with infinite on-site repulsion. This approach is applied to the two-layer Heisenberg model at zero temperature with general couplings. Our analytic results for the triplet gap, the excitation spectrum and the location of the quantum critical point are in excellent agreement with numerical results, obtained by dimer series expansions.Comment: 4 pages, REVTex, 3 Postscript figure

Ab Initio Calculation of Spin Gap Behavior in CaV4O9

Second neighbor dominated exchange coupling in CaV4O9 has been obtained from ab initio density functional (DF) calculations. A DF-based self-consistent atomic deformation model reveals that the nearest neighbor coupling is small due to strong cancellation among the various superexchange processes. Exact diagonalization of the predicted Heisenberg model yields spin-gap behavior in good agreement with experiment. The model is refined by fitting to the experimental susceptibility. The resulting model agrees very well with the experimental susceptibility and triplet dispersion.Comment: 4 pages; 3 ps figures included in text; Revte

Two-Triplet-Dimer Excitation Spectra in the Shastry-Sutherland Model for SrCu_2(BO_3)_2

By using the perturbation expansion up to the fifth order, we study the two-triplet-dimer excitation spectra in the Shastry-Sutherland model, where the localized nature of a triplet-dimer, the propagation of a triplet-dimer pair by the correlated hopping and the long-range interactions between triplet-dimers play an essential role. It is found that the dispersion relations for first-neighbor triplet-dimer pair excitations with S=1 and p-type symmetry qualitatively explain the second-lowest branch observed in the neutron inelastic scattering experiment. It is also predicted that the second-lowest branch consists of two components, p_x- and p_y-states, with slightly different excitation energies. The origin of the singlet mode at 3.7meV observed in the Raman scattering experiment is also discussed.Comment: 5 pages, 3 figure

Nonmagnetic Insulating States near the Mott Transitions on Lattices with Geometrical Frustration and Implications for κ\kappa-(ET)2_2Cu2(CN)3_2(CN)_3

We study phase diagrams of the Hubbard model on anisotropic triangular lattices, which also represents a model for $\kappa$-type BEDT-TTF compounds. In contrast with mean-field predictions, path-integral renormalization group calculations show a universal presence of nonmagnetic insulator sandwitched by antiferromagnetic insulator and paramagnetic metals. The nonmagnetic phase does not show a simple translational symmetry breakings such as flux phases, implying a genuine Mott insulator. We discuss possible relevance on the nonmagnetic insulating phase found in $\kappa$-(ET)$_2$Cu$_2(CN)_3$.Comment: 4pages including 7 figure

A self-consistent perturbative evaluation of ground state energies: application to cohesive energies of spin lattices

The work presents a simple formalism which proposes an estimate of the ground state energy from a single reference function. It is based on a perturbative expansion but leads to non linear coupled equations. It can be viewed as well as a modified coupled cluster formulation. Applied to a series of spin lattices governed by model Hamiltonians the method leads to simple analytic solutions. The so-calculated cohesive energies are surprisingly accurate. Two examples illustrate its applicability to locate phase transition.Comment: Accepted by Phys. Rev.