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Elsevier eBooks

An Elementary Examination of Quantum Phase Transitions Involving Fermions⁎

Jurgen Michael Honig, Józef Spałek

Published Jan 1, 2018• 0 citations
Publisher
DOI
10.1016/b978-0-12-804685-2.00022-x

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We discuss the quantum phase transition that separates a vacuum state with fully gapped fermion spectrum from a vacuum state with topologically protected Fermi points (gap nodes). In the context of condensed-matter physics, such a quantum phase transition with Fermi point splitting may occur for a system of ultracold fermionic atoms in the region of BEC-BCS crossover, provided Cooper pairing occurs in the non- s -wave channel. For elementary particle physics, the splitting of Fermi points may lead to CPT violation, neutrino oscillations, and other phenomena.
We consider the possibility of topological quantum phase transitions of ultracold fermions in optical lattices, which can be studied as a function of interaction strength or atomic filling factor (density). The phase transitions are connected to the topology of the elementary excitation spectrum, and occur only for non-zero angular momentum pairing (p-wave, d-wave and f-wave), while they are absent for s-wave. We construct phase diagrams for the specific example of highly anisotropic optical lattices, where the proposed topological phase transitions are most pronounced. To characterize the existence of these topological transitions, we calculate several measurable quantities including momentum distribution, quasi-particle excitation spectrum, atomic compressibility, superfluid density, and sound velocities.