Ground state phase diagram of a spin-2 antiferromagnet on the square lattice

We use the vertex state model approach to construct optimum ground states for a large class of quantum spin-2 antiferromagnets on the square lattice. Optimum ground states are exact ground states of the model which minimize all local interaction operators. The ground state contains two continuous parameters and exhibits a second order phase transition from a disordered phase with exponentially decaying correlation functions to a Néel ordered phase. The behaviour is very similar to that of the corresponding ground state of a quantum spin-3/2 model on the hexagonal lattice, which has been investigated in an earlier paper. Received 8 April 1999     

Quantum phase transition in spin-3/2 systems on the hexagonal lattice — optimum ground state approach

Optimum ground states are constructed in two dimensions by using so called vertex state models. These models are graphical generalizations of the well-known matrix product ground states for spin chains. On the hexagonal lattice we obtain a one-parametric set of ground states for a five-dimensional manifold of S = 3/2 Hamiltonians. Correlation functions within these ground states are calculated using Monte-Carlo simulations. In contrast to the one-dimensional situation, these states exhibit a parameter-induced second order phase transition. In the disordered phase, two-spin correlations decay exponentially, but in the Néel ordered phase alternating long-range correlations are dominant. We also show that ground state properties can be obtained from the exact solution of a corresponding free-fermion model for most values of the parameter.     

Correlation-induced metal insulator transition in a two-channel fermion-boson model

We investigate charge transport within some background medium by means of an effective lattice model with a novel form of fermion-boson coupling. The bosons describe fluctuations of a correlated background. By analyzing ground state and spectral properties of this transport model, we show how a metal-insulator quantum phase transition can occur for the half-filled band case. We discuss the evolution of a mass-asymmetric band structure in the insulating phase and establish connections to the Mott and Peierls transition scenarios.     

High pressure study of structural and electronic properties of magnesium telluride

The full-potential linear muffin-tin orbital method (FP-LMTO) within the local density approximation (LDA) is used to calculate the electronic band structures and the total energies of MgTe in its stable (NiAs-B8) and high pressure phases. The latter provide us with the ground state properties such us lattice parameter, bulk modulus and its pressure derivatives. The transition pressure at which this compound undergoes the structural phase transition from the NiAs to CsCl phase is calculated. The energy band gaps and their volume and pressure dependence in the stable NiAs-B8 phase are investigated. The ground state properties, the transition pressure are found to agree with the experimental and other theoretical results. The elastic constants at equilibrium in both NiAs and CsCl structure are also determined.     

Spectrum of the non-abelian phase in Kitaev’s honeycomb lattice model

The spectral properties of Kitaev’s honeycomb lattice model are investigated both analytically and numerically with the focus on the non-abelian phase of the model. After summarizing the fermionization technique which maps spins into free Majorana fermions, we evaluate the spectrum of sparse vortex configurations and derive the interaction between two vortices as a function of their separation. We consider the effect vortices can have on the fermionic spectrum as well as on the phase transition between the abelian and non-abelian phases. We explicitly demonstrate the 2ⁿ-fold ground state degeneracy in the presence of 2n well separated vortices and the lifting of the degeneracy due to their short-range interactions. The calculations are performed on an infinite lattice. In addition to the analytic treatment, a numerical study of finite size systems is performed which is in exact agreement with the theoretical considerations. The general spectral properties of the non-abelian phase are considered for various finite toroidal systems.     

Phase transition and critical properties of spin-orbital interacting systems

Phase transition and critical properties of Ising-like spin-orbital interacting systems in 2-dimensional triangular lattice are investigated. We first show that the ground state of the system is a composite spin-orbital ferro-ordered phase. Though Landau effective field theory predicts the second-order phase transition of the composite spin-orbital order, however, the critical exponents obtained by the renormalization group approach demonstrate that the spin-orbital order-disorder transition is far from the second-order, rather, it is more close to the first-order. The unusual critical behavior near the transition point is attributed to the fractionalization of the composite order parameter.     

Domain formation and orbital ordering transition in a doped Jahn-Teller insulator

The ground state of a double-exchange model for orbitally degenerate e(g) electrons with Jahn-Teller lattice coupling and weak disorder is found to be spatially inhomogeneous near half filling. Using a real-space Monte Carlo method we show that doping the half-filled orbitally ordered insulator leads to the appearance of hole-rich disordered regions in an orbitally ordered environment. The doping driven orbital order to disorder transition is accompanied by the emergence of metallic behavior. We present results on transport and optical properties along with spatial patterns for lattice distortions and charge densities, providing a basis for an overall understanding of the low-doping phase diagram of La1 - xCaxMnO3.     

Superfluid to Mott‐insulator transition in an anisotropic two‐dimensional optical lattice

We study the superfluid to Mott‐insulator transition of bosons in an optical anisotropic lattice by employing the Bose‐Hubbard model living on a two‐dimensional lattice with anisotropy parameter κ. The compressible superfluid state and incompressible Mott‐insulator (MI) lobes are efficiently described analytically, using the quantum U(1) rotor approach. The ground state phase diagram showing the evolution of the MI lobes is quantified for arbitrary values of κ, corresponding to various kind of lattices: from square, through rectangular to almost one‐dimensional.     

Symmetry Breaking Ground States of Bose-Einstein Condensates in 1D Double Square Well and Optical Lattice Well

We investigate the phenomena of symmetry breaking and phase transition in the ground state of Bose-Einstein condensates (BECs) trapped in a double square well and in an optical lattice well, respectively. By using standing-wave expansion method, we present symmetric and asymmetric ground state solutions of nonlinear Schrödinger equation (NLSE) with a symmetric double square well potential for attractive nonlinearity. In particular, we study the ground state wave function's properties by changing the depth of potential and atomic interactions (here we restrict ourselves to the attractive regime). By using the Fourier grid Hamiltonian method, we also reveal a phase transition of BECs trapped in one-dimensional optical lattice potential.     

Pair superfluidity of three-body constrained bosons in two dimensions

We examine the equilibrium properties of lattice bosons with attractive on-site interactions in the presence of a three-body hard-core constraint that stabilizes the system against collapse and gives rise to a dimer superfluid phase. Employing quantum Monte Carlo simulations, the ground state phase diagram of this system on the square lattice is analyzed. In particular, we study the quantum phase transition between the atomic and dimer superfluid regime and analyze the nature of the superfluid-insulator transitions. Evidence is provided for the existence of a tricritical point along the saturation transition line, where the transition changes from being first order to a continuous transition of the dilute Bose gas of holes. The Berzinskii-Kosterlitz-Thouless transition from the dimer superfluid to the normal fluid is found to be consistent with an anomalous stiffness jump, as expected from the unbinding of half-vortices.     

Theoretical study of ground state and high-pressure phase of platinum carbide

We report local density-functional calculations using the full-potential linearized muffin-tin orbital method (FP-LMTO) for platinum carbide (PtC) in the, rock-salt (B1), zinc-blende (B3), wurtzite (B4), nickel-arsenide (B8) and PbO (B10) structures. The ground state properties such as the equilibrium lattice constant, elastic constants, the bulk modulus and its pressure derivative of PtC in these phases are determined and compared with available experimental and theoretical data.Our calculations show that the ground state phase of PtC to be zinc-blende (B3) structure at zero pressure and the nickel-arsenide (B8) structure is a high-pressure phase. The transition pressures at which this compound undergoes the structural phase transition from (B3) to (B8) and from (B3) to (B1) are found to be 34.25 and 51.28 GPa, respectively. The highest bulk modulus values in the nickel-arsenide (B8), zinc-blende (B3), rock-salt (B1) and PbO (B10) structures indicate that PtC is a hard material.     

Two-stage melting in systems of strongly interacting Rydberg atoms

We analyze the ground state properties of a one-dimensional cold atomic system in a lattice, where Rydberg excitations are created by an external laser drive. In the classical limit, the ground state is characterized by a complete devil's staircase for the commensurate solid structures of Rydberg excitations. Using perturbation theory and a mapping onto an effective low-energy Hamiltonian, we find a transition of these commensurate solids into a floating solid with algebraic correlations. For stronger quantum fluctuations the floating solid eventually melts within a second quantum phase transition and the ground state becomes paramagnetic.     

Pairwise entanglement and geometric phase in high dimensional free-Fermion lattice systems

The pairwise entanglement, measured by concurrence and geometric phase in high dimensional free-Fermion lattice systems have been studied in this paper. When the system stays at the ground state, their derivatives with the external parameter show the singularity closed to the phase transition points, and can be used to detect the phase transition in this model. Furthermore our studies show for the free-Fermion model that both concurrence and geometric phase show the intimate connection with the correlation functions. The possible connection between concurrence and geometric phase has been also discussed.     

Ground-state phases and quantum phase transitions in a two-dimensional spin-1/2 XY model with four-spin interactions

We discuss the ground state phase transition between an antiferromagnet and a valence-bond solid in a two-dimensional spin-1/2 XY model with a four-spin interaction. This transition has been proposed as a candidate for a deconfined quantum-critical point. We analyze quantum Monte Carlo data in order to accurately characterize the transition. The central question that remains to be answered is whether the transition really is continuous, or whether it is actually weakly first-order. We present the current status of both ground state and finite-temperature calculations. Based on the results, we discuss possible scenarios for the transition, none of which is consistent with deconfined quantum-criticality. However, we argue that a deconfined quantum-critical point may be located nearby in an extended parameter space.We also discuss the staggered Ising phase obtaining in the limit of strong four-spin coupling.     

Fermi-surface reconstruction without breakdown of Kondo screening at the quantum critical point

Motivated by recent Hall-effect experiment in YbRh(2)Si(2), we study ground state properties of a Kondo lattice model in a two-dimensional square lattice using variational Monte Carlo method. We show that there are two types of phase transition, an antiferromagnetic transition and a topological one (Fermi-surface reconstruction). In a wide region of parameters, these two transitions occur simultaneously without the breakdown of Kondo screening, accompanied by a discontinuous change of the Hall coefficient. This result is consistent with the experiment and gives a novel theoretical picture for the quantum critical point in heavy-fermion systems.     

Properties of the ground state in a spin-2 transverse Ising model with the presence of a crystal field

The properties of the ground state in the spin-2 transverse Ising model with the presence of a crystal field are studied by using the effective-field theory with correlations. The longitudinal and transverse magnetizations, the phase diagram and the internal energy in the ground state are given numerically for a honeycomb lattice (z=3).     

Magnetic properties and spin waves of bilayer magnets in a uniform field

The two-layer square lattice quantum antiferromagnet with spins 12 shows a zero-field magnetic order-disorder transition at a critical ratio of the inter-plane to intra-plane couplings. Adding a uniform magnetic field tunes the system to canted antiferromagnetism and eventually to a fully polarized state; similar behavior occurs for ferromagnetic intra-plane coupling. Based on a bond operator spin representation, we propose an approximate ground state wavefunction which consistently covers all phases by means of a unitary transformation. The excitations can be efficiently described as independent bosons; in the antiferromagnetic phase these reduce to the well-known spin waves, whereas they describe gapped spin-1 excitations in the singlet phase. We compute the spectra of these excitations as well as the magnetizations throughout the whole phase diagram. Received 23 April 2001     

Pinning of vortices in a Bose-Einstein condensate by an optical lattice

We consider the ground state of vortices in a Bose-Einstein condensate. We show that turning on a weak optical periodic potential leads to a transition from the triangular Abrikosov vortex lattice to phases where the vortices are pinned by the optical potential. We discuss the phase diagram of the system for a two-dimensional optical periodic potential with one vortex per optical lattice cell. We also discuss the influence of a one-dimensional optical periodic potential on the vortex ground state. The latter situation has no analog in other condensed-matter systems.