Abstract
Fermi condensation is usually a phenomena of strongly correlated system. In this letter, we point out a novel mechanism for condensation of Dirac fermions due to Weyl anomaly. The condensation has its physical origin in the nontrivial response of the fermion vacuum to changes in the background spacetime (either boundary location or the background metric), and can be felt when a background scalar field is turned on. The scalar field can be, for example, the Higgs field in a fundamental theory or the phonon in condensed matter system. For a spacetime with boundaries, the induced Fermi condensate is inversely proportional to the proper distance from the boundary. For a conformally flat spacetime without boundaries, Fermi condensation depends on the conformal factor and its derivatives. We also generalize the Banks-Casher relation which relates the Fermi condensate to the zero mode density of the Dirac operator to a local form. Due to its universal nature, this anomaly induced Fermi condensate can be expected to have a wide range of applications in physics.
Highlights
Fermi condensation hψψi ≠ 0 is an interesting quantum phenomena and has a wide range of applications
The condensation of fermion is usually attributed to the effects of strongly coupled dynamics and it can be used as an order parameter characterizing the phases of the theory
We show that, in addition to currents, Weyl anomaly can give rises to Fermi condensation if a background scalar field is turned on
Summary
Fermi condensation hψψi ≠ 0 is an interesting quantum phenomena and has a wide range of applications. Generalization of the result (2) to higher dimensions and the result (3) for arbitrary finite σ can be found in [6,7,8] respectively We remark that these anomalous currents do not rely on the presence of a material system, but is a pure vacuum phenomena. As for (3), it arises from the fact that the vacuum of the theory is different for different σ and a nonvanishing vev for the current operator is resulted due to nontrivial Bogoliubov transformation This is similar to the process of particle creation during cosmological expansion or the Hawking radiation [17]. For more general Dirac operator, we show that the Fermi condensate obeys an elegant generalized form of the Bank-Casher relation, see (24) and (25) below
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