Nonlinear sigma model approach for phase disorder transitions and the pseudogap phase in chiral Gross-Neveu, Nambu-Jona-Lasinio models and strong-coupling superconductors

We briefly review the nonlinear sigma model approach for the subject of increasing interest: "two-step" phase transitions in the Gross-Neveu and the modified Nambu-Jona-Lasinio models at low $N$ and condensation from pseudogap phase in strong-coupling superconductors. Recent success in describing "Bose-type" superconductors that possess two characterstic temperatures and a pseudogap above $T_c$ is the development approximately comparable with the BCS theory. One can expect that it should have influence on high-energy physics, similar to impact of the BCS theory on this subject. Although first generalizations of this concept to particle physics were made recently, these results were not systematized. In this review we summarize this development and discuss similarities and differences of the appearence of the pseudogap phase in superconductors and the Gross-Neveu and Nambu-Jona-Lasinio - like models. We discuss its possible relevance for chiral phase transition in QCD and color superconductors. This paper is organized in three parts: in the first section we briefly review the separation of temperatures of pair formation and pair condensation in strong - coupling and low carrier density superconductors (i.e. the formation of the {\it pseudogap phase}). Second part is a review of nonlinear sigma model approach to an analogous phenomenon in the Chiral Gross-Neveu model at small N. In the third section we discuss the modified Nambu-Jona-Lasinio model where the chiral phase transition is accompanied by a formation of a phase analogous to the pseudogap phase.Comment: A brief review. Replaced with journal version (some grammatical corrections). The latest updates of this and related papers are also available at the author home page http://www.teorfys.uu.se/PEOPLE/egor

Dual neutral variables and knot solitons in triplet superconductors

In this paper we derive a dual presentation of free energy functional for spin-triplet superconductors in terms of gauge-invariant variables. The resulting equivalent model in ferromagnetic phase has a form of a version of the Faddeev model. This allows one in particular to conclude that spin-triplet superconductors allow formation of stable finite-length closed vortices (the knotted solitons).Comment: Replaced with version published in PRL (added a discussion of the effect of the coupling of the fields {\vec s} and {\vec C} on knot stability). Latest updates of the paper and miscellaneous links related to knotted solitons are also available at the homepage of the author http://www.teorfys.uu.se/PEOPLE/egor/ . Animations of knotted solitons by Hietarinta and Salo are available at http://users.utu.fi/h/hietarin/knots/c45_p2.mp

Characteristic length scales and formation of vortices in the Abelian Higgs model in the presence of a uniform background charge

In this brief report we consider a non-local Abelian Higgs model in the presence of a neutralizing uniform background charge. We show that such a system possesses vortices which key feature is a strong radial electric field. We estimate the basic properties of such an object and characteristic length scales in this model.Comment: Replaced with journal version. Some minor change

Spin-Charge Separation and the Pauli Electron

The separation between the spin and the charge converts the quantum mechanical Pauli Hamiltonian into the Hamiltonian of the non-Abelian Georgi-Glashow model, notorious for its magnetic monopoles and confinement. The independent spin and charge fluctuations both lead to the Faddeev model, suggesting the existence of a deep duality structure and indicating that the fundamental carriers of spin and charge are knotted solitons.Comment: 7 pages; v2: new results added, references update

Possible Pseudogap Phase in QCD

Thermal pion fluctuations, in principle, can completely disorder the phase of the quark condensate and thus restore chiral symmetry. If this happens before the quark condensate melts, strongly-interacting matter will be in the pseudogap state just above the chiral phase transition. The quark condensate does not vanish locally and quarks acquire constituent masses in the pseudogap phase, despite chiral symmetry is restored.Comment: 8 pages, 1 figure; v2: references added; v3: argumerts modified; v4: minor changes; v5: a misprint correcte

Superconductivity in the quasi-two-dimensional Hubbard model

On the basis of spin and pairing fluctuation-exchange approximation, we study the superconductivity in quasi-two-dimensional Hubbard model. The integral equations for the Green's function are self-consistently solved by numerical calculation. Solutions for the order parameter, London penetration depth, density of states, and transition temperature are obtained. Some of the results are compared with the experiments for the cuprate high-temperature superconductors. Numerical techniques are presented in details. With these techniques, the amount of numerical computation can be greatly reduced.Comment: 17 pages, 13 figure

The Influence of an External Chromomagnetic Field on Color Superconductivity

We study the competition of quark-antiquark and diquark condensates under the influence of an external chromomagnetic field modelling the gluon condensate and in dependence on the chemical potential and temperature. As our results indicate, an external chromomagnetic field might produce remarkable qualitative changes in the picture of the color superconducting (CSC) phase formation. This concerns, in particular, the possibility of a transition to the CSC phase and diquark condensation at finite temperature.Comment: 27 pages, RevTex, 8 figures; the version accepted for the publication in PRD (few references added; new numerical results added; main conclusions are not changed

Berezinskii-Kosterlitz-Thouless transition and BCS-Bose crossover in the two-dimensional attractive Hubbard model

We study the two-dimensional attractive Hubbard model using the mapping onto the half-filled repulsive Hubbard model in a uniform magnetic field coupled to the fermion spins. The low-energy effective action for charge and pairing fluctuations is obtained in the hydrodynamic regime. We recover the action of a Bose superfluid where half the fermion density is identified as the conjugate variable of the phase of the superconducting order parameter. By integrating out charge fluctuations, we obtain a phase-only action. In the zero-temperature superconducting state, this action describes a collective phase mode smoothly evolving from the Anderson-Bogoliubov mode at weak coupling to the Bogoliubov mode of a Bose superfluid at strong coupling. At finite temperature, the phase-only action can be used to extract an effective XY model and thus obtain the Berezinskii-Kosterlitz-Thouless (BKT) phase transition temperature. We also identify a renormalized classical regime of superconducting fluctuations above the BKT phase transition, and a regime of incoherent pairs at higher temperature. Special care is devoted to the nearly half-filled case where the symmetry of the order parameter is enlarged to SO(3) due to strong ${\bf q}=(\pi,\pi)$ charge fluctuations. The low-energy effective action is then an SO(3) non-linear sigma model with a (symmetry breaking) magnetic field proportional to the doping. In the strong-coupling limit, the attractive Hubbard model can be mapped onto the Heisenberg model, from which we recover the Gross-Pitaevskii equation in the low-density limit.Comment: 31 pages, 12 figures, RevTex4; (v2) changes following referees' comments, references adde

Criterion for Dominance of Directional over Size Fluctuations in Destroying Order

For systems exhibiting a second-order phase transition with a spontaneously broken continuous O(N)-symmetry at low temperature, we give a criterion for judging at which temperature T_K long-range directional fluctuations of the order field destroy the order when approaching the critical temperature from below. The temperature T_K lies always significantly below the famous Ginzburg temperature T_G at which size fluctuations of finite range in the order field become important.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/re3.html#29

The Coupled Electron-Ion Monte Carlo Method

In these Lecture Notes we review the principles of the Coupled Electron-Ion Monte Carlo methods and discuss some recent results on metallic hydrogen.Comment: 38 pages, 6 figures, Lecture notes for the International School of Solid State Physics, 34th course: "Computer Simulation in Condensed Matter: from Materials to Chemical Biology", 20 July-1 August 2005 Erice (Italy). To appear in Lecture Notes in Physics (2006