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 susceptibility (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 pseudo-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 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 these 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.
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 several 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.
We revisit the two-site Hubbard-Holstein model by using extended phonon coherent states. The nontrivial singlet bipolaron is studied exactly in the whole coupling regime. The ground-state (GS) energy and the double occupancy probability are calculated. The linear entropy is exploited successfully to quantify bipartite entanglement between electrons and their environment phonons, displaying a maximum entanglement of the singlet-bipolaron in strong coupling regime. A dramatic drop in the crossover regime is observed in the GS fidelity and its susceptibility. The bipolaron properties is also characterized classically by correlation functions. It is found that the crossover from a two-site to single-site bipolaron is more abrupt and shifts to a larger electron-phonon coupling strength as electron-electron Coulomb repulsion increases.
Speckle interferometric observations made with the 6 m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences in 2000 revealed the triple nature of the nearby ($pi_{Hip}=51.80pm1.74$ mas) low-mass young ($approx200$ Myr) star GJ 900. The configuration of the triple system allowed it to be dynamically unstable. Differential photometry performed from 2000 through 2004 yielded $I$- and $K$-band absolute magnitudes and spectral types for the components to be $I_{A}$=6.66$pm$0.08, $I_{B}$=9.15$pm$0.11, $I_{C}$=10.08$pm$0.26, $K_{A}$=4.84$pm$0.08, $K_{B}$=6.76$pm$0.20, $K_{C}$=7.39$pm$0.31, $Sp_{A}$$approx$K5--K7, $Sp_{B}$$approx$M3--M4, $Sp_{C}$$approx$M5--M6. The ``mass--luminosity relation is used to estimate the individual masses of the components: $mathcal{M}_{A}$$approx0.64mathcal{M}_{odot}$, $mathcal{M}_{B}$$approx0.21mathcal{M}_{odot}$, $mathcal{M}_{C}$$approx0.13mathcal{M}_{odot}$. From the observations of the components relative motion in the period 2000--2006, we conclude that GJ 900 is a hierarchical triple star with the possible orbital periods P$_{A-BC}$$approx$80 yrs and P$_{BC}$$approx$20 yrs. An analysis of the 2MASS images of the region around GJ 900 leads us to suggest that the system can include other very-low-mass components.
