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arXiv:hep-th/0601049 · Journal of Physics A Mathematical and General

From relativistic quantum fields to condensed matter and back again: updating the Gross–Neveu phase diagram

Michael Thies

Published Sep 27, 2006• 149 citations
arXivHTMLPDF

Abstract

During the last few years, the phase diagram of the large N Gross–Neveu model in 1 + 1 dimensions at finite temperature and chemical potential has undergone a major revision. Here, we present a streamlined account of this development, collecting the most important results. Quasi-one-dimensional condensed matter systems like conducting polymers provide real physical systems which can be approximately described by the Gross–Neveu model and have played some role in establishing its phase structure. The kink–antikink phase found at low temperatures is closely related to inhomogeneous superconductors in the Larkin–Ovchinnikov–Fulde–Ferrell phase. With the complete phase diagram at hand, the Gross–Neveu model can now serve as a firm testing ground for new algorithms and theoretical ideas.

DOI
10.1088/0305-4470/39/41/s04

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During the last few years, the phase diagram of the large N Gross–Neveu model in 1 + 1 dimensions at finite temperature and chemical potential has undergone a major revision. Here, we present a streamlined account of this development, collecting the most important results. Quasi-one-dimensional condensed matter systems like conducting polymers provide real physical systems which can be approximately described by the Gross–Neveu model and have played some role in establishing its phase structure. The kink–antikink phase found at low temperatures is closely related to inhomogeneous superconductors in the Larkin–Ovchinnikov–Fulde–Ferrell phase. With the complete phase diagram at hand, the Gross–Neveu model can now serve as a firm testing ground for new algorithms and theoretical ideas.
During the last few years, the phase diagram of the large N Gross-Neveu model in 1+1 dimensions at finite temperature and chemical potential has undergone a major revision. Here we present a streamlined account of this development, collecting the most important results. Quasi-one-dimensional condensed matter systems like conducting polymers provide real physical systems which can be approximately described by the Gross-Neveu model and have played some role in establishing its phase structure. The kink-antikink phase found at low temperatures is closely related to inhomogeneous superconductors in the Larkin-Ovchinnikov-Fulde-Ferrell phase. With the complete phase diagram at hand, the Gross-Neveu model can now serve as a firm testing ground for new algorithms and theoretical ideas.
There is substantial evidence that the ground state of the 2D chiral Gross-Neveu model, in the presence of a U(1) fermion number chemical potential μ and in the large N limit, is given by a "chiral spiral" phase, namely an inhomogeneous phase with a chiral condensate having a spatially periodic phase. We show that the chiral spiral configuration persists at finite N and T=0 for any μ>0. Our analysis is based on nonabelian bosonization, that relates the model to a U(N)_{1} Wess-Zumino-Witten model deformed by current-current interactions. In this description, the appearance of the inhomogeneous phase is surprisingly simple. We also rederive the phase diagram of the large N chiral Gross-Neveu model via a direct diagrammatic computation, finding agreement with previous results in the literature.
Abstract Ultracold two-component Fermi gases with a tunable population imbalance have provided an excellent opportunity for studying the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, which have been of great interest in condensed matter physics. However, the FFLO states have not been observed experimentally in Fermi gases in three dimensions (3D), possibly due to their small phase space volume and extremely low temperature required for an equal-mass Fermi gas. Here we explore possible effects of mass imbalance, mainly in a 6Li–40K mixture, on the one-plane-wave FFLO phases for a 3D homogeneous case at the mean-field level. We present various phase diagrams related to the FFLO states at both zero and finite temperatures, throughout the BCS-BEC crossover, and show that a large mass ratio may enhance substantially FFLO type of pairing.
The Fulde-Ferrell Larkin-Ovchinnikov (FFLO) type superconductor is an exotic form of matter known as a supersolid because it simultaneously supports superfluid and magnetic order. In both condensed matter and ultracold atomic gases, this phase has yet to be conclusively observed despite long interest in both theory and experiment. In one-dimension (1D), unlike expectations for higher dimensions, the FFLO phase is found in a large region of the phase diagram [1]. The effect of quantum and thermal fluctuations, however, are expected to be reduced in higher dimensions. These considerations motivated the proposal to search for FFLO near the 1D-3D dimensional crossover [2], which we have identified and characterized [3]. We confine a spin-imbalanced Fermi gas of lithium 6 to an array of 1D tubes using a 2D optical lattice. We bring the system into the dimensional crossover by increasing the inter-tube tunneling rate and using a Feshbach resonance to tune interactions. The periodicity of these domain walls, which depends on the magnitude of the polarization, is a definitive signature of the FFLO phase. In this work, we develop new experimental and analytical methods to extract periodic signals that, if they indeed are domain walls, lay the foundation for full confirmation of the FFLO phase. [1] Y. A. Liao, A. S. C. Rittner, T. Paprotta, W. Li, G. B. Partridge, R. G. Hulet, S. K. Baur, and E. J. Mueller, “Spin-imbalance in a one-dimensional Fermi gas,” Nature 467, 567 (2010). [2] M. M. Parish, S. K. Baur, E. J. Mueller, and D. A. Huse, “Quasi-One- Dimensional Polarized Fermi Superfluids,” Phys. Rev. Lett. 99, 250403 (2007). [3] M. C. Revelle, J. A. Fry, B. A. Olsen, and R. G. Hulet, “1D to 3D Crossover of a Spin-Imbalanced Fermi Gas,” Physical Review Letters 117 (2016).
Providing a broad review of many techniques and their application to condensed matter systems, this book begins with a review of thermodynamics and statistical mechanics, before moving onto real and imaginary time path integrals and the link between Euclidean quantum mechanics and statistical mechanics. A detailed study of the Ising, gauge-Ising and XY models is included. The renormalization group is developed and applied to critical phenomena, Fermi liquid theory and the renormalization of field theories. Next, the book explores bosonization and its applications to one-dimensional fermionic systems and the correlation functions of homogeneous and random-bond Ising models. It concludes with Bohm–Pines and Chern–Simons theories applied to the quantum Hall effect. Introducing the reader to a variety of techniques, it opens up vast areas of condensed matter theory for both graduate students and researchers in theoretical, statistical and condensed matter physics.