The two-mode quantum Rabi model with bilinear coupling is studied using extended squeezed states. We derive $G$-functions for each Bargmann index $q$% . They share a common structure with the $G$-function of the one-photon and two-photon quantum Rabi
models. The regular spectrum is given by zeros of the $G$-function while the conditions for the presence of doubly degenerate (exceptional) eigenvalues are obtained in closed form through the lifting property. The simple singularity structure of the $G$-function allows to draw conclusions about the distribution of eigenvalues along the real axis and to understand the spectral collapse phenomenon when the coupling reaches a critical value.
Within the numerically exact solution to the Dicke model proposed previously, we study the quantum criticality in terms of the ground-state (GS) energy, fidelity, and the order parameter. The finite size scaling analysis for the average fidelity susc
eptibility (FS) and second derivative of GS energy are performed. The correlation length exponent is obtained to be $ u=2/3$, which is the same as that in Lipkin-Meshkov-Glick model obtained previously, suggesting the same universality. It is observed that average FS and second derivative of GS energy show similar critical behavior, demonstrating the intrinsic relation in the Dicke model. The scaling behavior for the order parameter and the singular part of the GS energy at the critical point are also analyzed and the obtained exponents are consistent with the previous scaling hypothesis in 1/N expansion scheme.
Quantum phase transition in the one-dimensional period-two and uniform quantum compass model are studied by using the pseudo-spin transformation method and the trace map method. The exact solutions are presented, the fidelity, the nearest-neighbor ps
eudo-spin entanglement, spin and pseudo-spin correlation functions are then calculated. At the critical point, the fidelity and its susceptibility change substantially, the gap of pseudo-spin concurrence is observed, which scales as $1/N$ (N is system size). The spin correlation functions show smooth behavior around the critical point. In the period-two chain, the pseudo-spin correlation functions exhibit a oscillating behavior, which is absent in the unform chain. The divergent correlation length at the critical point is demonstrated in the general trend for both cases.
The vortex-lattice melting transitions in two typical iron-based high-Tc superconductor $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$ (122-type) and$Nd(O_{1-x}F_{x})FeAs$ (1111-type) for magnetic fields both parallel and perpendicular to the anisotropy axis are stu
died within the elastic theory. Using the parameters from experiments, the vortex-lattice melting lines in the H-T diagram are located systematically by various groups of Lindemann numbers. It is observed that the theoretical result for the vortex melting on $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$ for parallel fields agrees well the recent experimental data. The future experimental results for the vortex melting can be compared with the present theoretical prediction by tuning reasonable Lindemann numbers.
The instability, so-called the quantum-phase-like transition, in the Dicke model with a rotating-wave approximation for finite $N$ atoms is investigated in terms of the Berry phase and the fidelity. It can be marked by the discontinuous behavior of t
hese quantities as a function of the atom-field coupling parameter. Involving an additional field $A^{2}$ term, it is observed that the instability is not eliminated beyond the characteristic atom-field coupling parameter even for strong interaction of the bosonic fields, contrarily to the previous studies.
Large-scale simulations have been performed on the current-driven two-dimensional XY gauge glass model with resistively-shunted-junction dynamics. It is observed that the linear resistivity at low temperatures tends to zero, providing strong evidence
of glass transition at finite temperature. Dynamic scaling analysis demonstrates that perfect collapses of current-voltage data can be achieved with the glass transition temperature $T_{g}=0.22$, the correlation length critical exponent $ u =1.8$, and the dynamic critical exponent $ z=2.0$. A genuine continuous depinning transition is found at zero temperature. For creeping at low temperatures, critical exponents are evaluated and a non-Arrhenius creep motion is observed in the glass phase.
We calculate the Nernst signal directly in the phenomenological two-dimensional XY model. The obtained numerical results are consistent with the experimental observations in some high-Tc cuprate superconductors qualitatively, where the vortex Nernst
signal has a characteristic tilt-hill profile. It is suggested that the excitations of vortex and anti-vortex in 2D is the possible origin of the anomalous Nernst effect.
We report the theoretical study of the flux-lattice melting in the novel iron-based superconductor $LaO_{0.9}F_{0.1}FeAs$ and $LaO_{0.925}F_{0.075}FeAs$. Using the Hypernetted-Chain closure and an efficient algorithm, we calculate the two-dimensional
one-component plasma pair distribution functions, static structure factors and direct correlation functions at various temperatures. The Hansen-Verlet freezing criterion is shown to be valid for vortex-liquid freezing in type-II superconductors. Flux-lattice meting lines for $LaO_{0.9}F_{0.1}FeAs$ and $LaO_{0.925}F_{0.075}FeAs$ are predicted through the combination of the density functional theory and the mean-field substrate approach.
Dynamics of vortices in strongly type-II superconductors with strong disorder is investigated within the frustrated three-dimensional XY model. For two typical models in [Phys. Rev. Lett. {bf 91}, 077002 (2003)] and [Phys. Rev. B {bf 68}, 220502(R) (
2003)], a strong evidence for the finite temperature vortex glass transition in the unscreened limit is provided by performing large-scale dynamical simulations. The obtained correlation length exponents and the dynamic exponents in both models are different from each other and from those in the three-dimensional gauge glass model. In addition, a genuine continuous depinning transition is observed at zero temperature for both models. A scaling analysis for the thermal rounding of the depinning transition shows a non-Arrhenius type creep motion in the vortex glass phase, contrarily to the recent studies..
By using extended bosonic coherent states, a new technique to solve the Dicke model exactly is proposed in the numerical sense. The accessible system size is two orders of magnitude higher than that reported in literature. Finite-size scaling for sev
eral observables, such as the ground-state energy, Berry phase, and concurrence are analyzed. The existing discrepancy for the scaling exponent of the concurrence is reconciled.
