Abstract
We review various connections between condensed matter systems with the Nambu–Jona-Lasinio model and nonlinear sigma models. The field theoretical description of interacting systems offers a systematic framework to describe the dynamical generation of condensates. Recent findings of a duality between the Nambu–Jona-Lasinio model and nonlinear sigma models enables us to investigate various properties underlying both theories. In this review, we mainly focus on inhomogeneous condensations in static situations. The various methods developed in the Nambu–Jona-Lasinio model reveal the inhomogeneous phase structures and also yield new inhomogeneous solutions in nonlinear sigma models owing to the duality. The recent progress on interacting systems in finite systems is also reviewed.
Highlights
Fermionic systems with many body interactions affect the ground state structure
A connection between the Nambu and Jona-Lasinio (NJL) model and nonlinear σ (NLσ) models was recognized (In this article, we focus on the O(N) sigma model and the C P N −1 model
We have presented the connections between the condensed matter systems and the NJL and nonlinear σ models
Summary
Fermionic systems with many body interactions affect the ground state structure. In the case of repulsive interaction, the vacuum state and the low energy excited states are well described by the. The BCS scenario has been reinterpreted as a spontaneous symmetry breaking by Nambu and Jona-Lasinio (NJL) [10,11] In their model, the chiral symmetry is spontaneously broken, and the mass of Fermions, which is zero in the unbroken phase, is dynamically generated. There is a huge area of the cross-section between condensed matter physics and high energy physics, we leave those issues for other articles and focus on topics about systems described by the NJL model. We show the discretized model, which describes superconducting or superfluid phenomena in materials or cold atom systems As another important example, we introduce a polyacetylene system.
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