Coherent motion in the interaction model of cold glasses

We have studied the collective phenomena of multicomponent glasses at ultra low temperatures [Strehlow, et. al, Phys. Rev. Lett 80, 5361 (1998)] by taking into account the proper interaction between tunneling centers. We have considered both double and triple well potentials with different types of interactions. We show that a phase with coherent motion appears for a range of parameters when the path of tunneling is coursed by an interaction of the XY type, while the usual Ising like interaction does not lead to the expected collective phenomena. In the phase of coherent motion, the dipole moment and the low-energy levels oscillate with a frequency proportional to the number of tunneling centers in the system. Simultaneous level crossing occurs between the ground and first excited states. The effects of long-range interactions and also of random couplings have been also studied for a one- and two-dimensional array of tunneling centers. We find that long-range interactions do not affect the coherent motion, while a wide distribution of random couplings destroys the collective effects.Comment: 11 pages, 11 figures, shorter version appears in Phys. rev.

Phase diagram of J1-J2 transverse field Ising model on the checkerboard lattice: a plaquette-operator approach

We study the effect of quantum fluctuations by means of a transverse magnetic field ($\Gamma$) on the antiferromagnetic $J_1-J_2$ Ising model on the checkerboard lattice, the two dimensional version of the pyrochlore lattice. The zero-temperature phase diagram of the model has been obtained by employing a plaquette operator approach (POA). The plaquette operator formalism bosonizes the model, in which a single boson is associated to each eigenstate of a plaquette and the inter-plaquette interactions define an effective Hamiltonian. The excitations of a plaquette would represent an-harmonic fluctuations of the model, which lead not only to lower the excitation energy compared with a single-spin flip but also to lift the extensive degeneracy in favor of a plaquette ordered solid (RPS) state, which breaks lattice translational symmetry, in addition to a unique collinear phase for $J_2>J_1$. The bosonic excitation gap vanishes at the critical points to the N\'{e}el ($J_2 < J_1$) and collinear ($J_2 > J_1$) ordered phases, which defines the critical phase boundaries. At the homogeneous coupling ($J_2=J_1$) and its close neighborhood, the (canted) RPS state, established from an-harmonic fluctuations, lasts for low fields, $\Gamma/J_1\lesssim 0.3$, which is followed by a transition to the quantum paramagnet (polarized) phase at high fields. The transition from RPS state to the N\'{e}el phase is either a deconfined quantum phase transition or a first order one, however a continuous transition occurs between RPS and collinear phases.Comment: To appear in EPJB, 12 pages, 15 figures, 1 tabl

Thermodynamic Properties of XXZ model in a Transverse Field

We have numerically studied the thermodynamic properties of the spin 1/2 XXZ chain in the presence of a transverse (non commuting) magnetic field. The thermal, field dependence of specific heat and correlation functions for chains up to 20 sites have been calculated. The area where the specific heat decays exponentially is considered as a measure of the energy gap. We have also obtained the exchange interaction between chains in a bulk material using the random phase approximation and derived the phase diagram of the three dimensional material with this approximation. The behavior of the structure factor at different momenta verifies the antiferromagnetic long range order in y-direction for the three dimensional case. Moreover, we have concluded that the Low Temperature Lanczos results [M. Aichhorn et al., Phys. Rev. B 67, 161103(R) (2003)] are more accurate for low temperatures and closer to the full diagonalization ones than the results of Finite Temperature Lanczos Method [J. Jaklic and P. Prelovsek, Phys. Rev. B 49, 5065 (1994)].Comment: 7 pages, 10 eps figure

Ground-state fidelity of the spin-1 Heisenberg chain with single ion anisotropy: quantum renormalization group and exact diagonalization approaches

We study the phase diagram of the anisotropic spin-1 Heisenberg chain with single ion anisotropy (D) using a ground-state fidelity approach. The ground-state fidelity and its corresponding susceptibility are calculated within the quantum renormalization group scheme where we obtained the renormalization of fidelity preventing to calculate the ground state. Using this approach, the phase boundaries between the antiferromagnetic N\'{e}el, Haldane and large-D phases are obtained for the whole phase diagram, which justifies the application of quantum renormalization group to trace the symmetery protected topological phases. In addition, we present numerical exact diagonalization (Lanczos) results in, which we employ a recently introduced non-local order parameter to locate the transition from Haldane to large-D phase accurately.Comment: 9 pages, 11 figures, 1 table, to appear in JPC