Entanglement and classical instabilities: Fingerprints of electron-hole-to-exciton phase transition in a simple model

Abstract

We propose a schematic model to study the formation of excitons in bilayer electron systems. The phase transition is signalized both in the quantum and classical versions of the model. In the present contribution we show that not only the quantum ground state but also higher energy states, up to the energy of the corresponding classical separatrix orbit, "sense" the transition. We also show two types of one-to-one correspondences in this system: On the one hand, between the changes in the degree of entanglement for these low-lying quantum states and the changes in the density of energy levels; on the other hand, between the variation in the expected number of excitons for a given quantum state and the behavior of the corresponding classical orbit.

Inverse Holstein-Primakoff transformation of bosonic operators —Application to a bilayer model

“…1(a) there appear energy spectra for some values of the interaction parameter g, and in fig. 1(b) the ground-state mean value for the number of excitons in the system, b † b = J 2 + J 2z , is shown as a function of g. These results reproduce correctly those obtained previously for this model [17]. In particular, one notes the manifestation of a quantum phase transition in the increase of the number of excitons, for values of the interaction parameter around g = 0.7.…”

“…where the index b is no longer necessary. Once again, and interestingly, this result correctly reproduces the Hamiltonian obtained in [17] using different transformations.…”

“…Moreover, the number of excitons in the system, as shown in Fig. 1(b), can be reproduced by the computation of the area bounded by both the separatrix orbit and the border at p = −1 [16].…”

“…The bosonic excitons were provided indirectly by electron-hole pairs associated with electrons in different layers. Suggested by the experiment, a Hamiltonian was proposed for the interaction of N/2 pairs of fermions (electrons) which can undergo an (electron-hole)-to-exciton quantum phase transition [16].…”

Study of continuous variable entanglement in coupled oscillator systems by means of the dynamical two-step approach

“…Note that the lowest energy eigenstate is an interesting quantum state that has attracted much investigation [37,34]. For instance, the degree of entanglement of the ground state has been used to investigate quantum phase transition [89,90,91].…”