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Springer series in solid-state sciences

Fermion Condensation in Finite Systems

M. Ya. Amusia, Konstantin G. Popov, Vasily R. Shaginyan, V. A. Stephanovich

Published Oct 25, 2014• 1 citation
Publisher
DOI
10.1007/978-3-319-10825-4_12

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Four-particle correlations in fermion systems at finite temperatures are investigated with special attention to the formation of a condensate. Instead of the instability of the normal state with respect to the onset of pairing described by the Gorkov equation, a new equation is obtained which describes the onset of ``quartetting.'' Applying to symmetric nuclear matter, below a critical density, the four-particle condensation ( $\ensuremath{\alpha}$-like quartetting) is found to be favored over deuteron condensation (triplet pairing). This pairing-quartetting competition is expected to be a general feature of interacting fermion systems, such as the exciton-biexciton system in excited semiconductors. Possible experimental consequences are pointed out.
In nature, everything occurs at finite temperature, and quantum phase transitions (QPTs) cannot be an exception. Nevertheless, they are still mainly discussed and formulated at zero temperature. We show that the condensation QPTs recently introduced at zero temperature can naturally be extended to finite temperature just by replacing ground-state energies with corresponding free energies. We illustrate this criterion in the paradigmatic Grover model and in a system of free fermions in a one-dimensional inhomogeneous lattice. In agreement with expected universal features, the two systems show structurally similar phase diagrams. Last, we explain how finite-temperature condensation QPTs can be used to construct quantum annealers having, at finite temperature, output probability exponentially close to 1 in the system size. As examples we consider again the Grover model and the fermionic system, the latter being well within the reach of present heterostructure technology.
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 two-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 phases, 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.