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arXiv:0807.0922 · Physical Review A

Polarized superfluids near their tricritical point

Daniel E. Sheehy

Published Mar 6, 2009• 10 citations
arXivHTMLPDF

Abstract

We obtain a variety of predictions for the properties of population-imbalanced (or polarized) fermionic superfluids near their tricritical point. In the vicinity of the high-symmetry tricritical point, observable quantities such as the cloud shape, heat capacity, local polarization, and correlation length should exhibit distinct behavior arising from the tricritical scaling laws, as well as logarithmic corrections to scaling reflecting the marginal nature of interactions.

DOI
10.1103/physreva.79.033606

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We obtain a variety of predictions for the properties of population-imbalanced (or polarized) fermionic superfluids near their tricritical point. In the vicinity of the high-symmetry tricritical point, observable quantities such as the cloud shape, heat capacity, local polarization, and correlation length should exhibit distinct behavior arising from the tricritical scaling laws, as well as logarithmic corrections to scaling reflecting the marginal nature of interactions.
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Differential renormalization equation for the qqq-state Potts model are proposed, and the critical behavior of the model near q=qcq={q}_{c}q=qc​ discussed. The equations give rise to critical and tricritical fixed points which merge at q=qcq={q}_{c}q=qc​ when a dilution field becomes marginal, to an essential singularity in the latent heat as a function of q=qcq={q}_{c}q=qc​, in accordance with the exact result of Baxter, and, for q=qcq={q}_{c}q=qc​, to a logarithm correction to the power-law behavior of the free energy as a function of $T\ensuremath{-}{T}_{c}$.
Many-body systems undergoing quantum phase transitions reveal substantial growth of nonclassical correlations between different parties of the system. This behavior is manifested by characteristic divergences of the von Neumann entropy. Here we show that very similar features may be observed in one-dimensional systems of a few strongly interacting atoms when the structural transitions between different spatial orderings are driven by a varying shape of an external potential. When the appropriate adaptation of the finite-size scaling approach is performed in the vicinity of the transition point, few-fermion systems display a characteristic power-law invariance of divergent quantities.