Thermal entanglement of Hubbard dimers in the nonextensive statistics

Abstract

The thermal entanglement of the Hubbard dimer (two-site Hubbard model) has been studied with the nonextensive statistics. We have calculated the auto-correlation ($O_q$), pair correlation ($L_q$), concurrence ($\Gamma_q$) and conditional entropy ($R_q$) as functions of entropic index $q$ and the temperature $T$. The thermal entanglement is shown to considerably depend on the entropic index. For $q < 1.0$, the threshold temperature where $\Gamma_q$ vanishes or $R_q$ changes its sign is more increased and the entanglement may survive at higher temperatures than for $q=1.0$. Relations among $L_q$, $\Gamma_q$ and $R_q$ are investigated. The physical meaning of the entropic index $q$ is discussed with the microcanonical and superstatistical approaches. The nonextensive statistics is applied also to Heisenberg dimers.Comment: 28 pages, 6 figures; the final version accepted in Physica

Hubbard pair cluster in the external fields. Studies of the polarization and susceptibility

“…At the same time, it has been noticed that the exact solutions to the model can be obtained for small clusters, consisting of several lattice sites [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84]. Intensive investigations of such systems have been carried out both from the point of view of static properties [48-50, 52, 58, 62, 64, 66-68, 71-73, 75-80, 82, 83, 85-88], as well as for dynamical description [54,59,61,70,81,84].…”

Hubbard pair cluster in the external fields. Studies of the chemical potential

“…The magnetic field has been taken into account in [22], however, the influence of the external electric field on the cluster properties has not been studied there.Motivated by such a possibility, we undertake the exact study of the Hubbard simplest cluster, namely the pair (or dimer), embedded simultaneously in the external magnetic and electric fields. We note that such system has already attracted some attention [28][29][30][31][32][33][34][35]. Also the effect of the electric field on the properties of the Hubbard model was studied [36,37].…”

Correlation Paradox of the Dissociation Limit: A Quantum Information Perspective

“…As a matter of fact, this almost completes the diagonalization, and it remains to diagonalize Ĥ 0,0,– on the corresponding two-dimensional space . The details of those calculations are presented in Appendix A, and we just present here the well-known results for the six eigenenergies (with U ≡ 1) It is crucial to notice that the ground state is always nondegenerate, and the first excited energy corresponds to the 3-fold degenerate triplet states. The energy spectrum (eq ) is also shown in Figure (recall t = exp­(− r )), and the corresponding six eigenstates are listed in Appendix A.…”

“…At finite temperature, the state of interest is the thermal Gibbs state (we set for simplicity k B ≡ 1), where is the partition function. In addition to the standard Boltzmann-Gibbs statistics which we use here, there have also been proposals of other distributions for systems of nonextensive size. , Although it is somewhat debatable to say which statistics is more appropriate for a small system like ours, we stick to the Boltzmann–Gibbs distribution and use the thermal equilibrium state as defined in eq .…”