Quantum Phase Transitions in a Model Hamiltonian Exhibiting Entangled Simultaneous Fermion-Pair and Exciton Condensations

TL;DR

This paper identifies quantum phase transitions in a model Hamiltonian with simultaneous fermion-pair and exciton condensations, using geometric analysis of ground-state 2-RDMs to reveal phases and transition orders.

Contribution

It introduces a geometric analysis method of 2-RDMs to characterize quantum phase transitions in a model with entangled fermion-pair and exciton condensates, revealing detailed phase structures.

Findings

Identification of fermion-pair and exciton condensate phases

Discovery of first- and second-order phase transitions

Location of fermion-exciton condensate along the second-order transition

Abstract

Quantum states of a novel Bose-Einstein condensate, in which both fermion-pair and exciton condensations are simultaneously present, have recently been realized theoretically in a model Hamiltonian system. Here we identify quantum phase transitions in that model between fermion-pair and exciton condensations based on a geometric analysis of the convex set of ground-state 2-particle reduced density matrices (2-RDMs). The 2-RDM set provides a finite representation of the infinite parameter space of Hamiltonians that readily reveals a fermion-pair condensate phase and two distinct exciton condensate phases, as well as the emergence of first- and second-order phase transitions as the particle number of the system is increased. The set, furthermore, shows that the fermion-exciton condensate (FEC) lies along the second-order phase transition between the exciton and fermion-pair condensate phases. The detailed information about the exciton and fermion-pair phases, the forces behind these phase, as well as their associated transitions provides additional insight into the formation of the FEC condensate, which we anticipate will prove useful in its experimental realization.