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Thermodynamic characteristics of Fermi systems are investigated in the vicinity of a phase transition where the effective mass diverges and the single-particle spectrum becomes flat. It is demonstrated that at extremely low temperatures…
Strong repulsive interactions in a one-dimensional electron system suppress the exchange coupling J of electron spins to a value much smaller than the Fermi energy E_F. The conventional theoretical description of such systems based on the…
We propose a simple bose-fermi model in two dimensions, with a coupling that converts pairs of opposite spin fermions into localized bosons and vice versa. We show that tracing out one of the degrees, either the bosons or fermions,…
We analyze how the logarithmic renormalizations in the Cooper channel affect the non-analytic temperature dependence of the specific heat coefficient \gamma (T) - \gamma (0)=A(T)T in a 2D Fermi liquid. We show that A(T) is expressed exactly…
We explore the weak-strong-coupling Bose-Fermi duality in a model of a single-channel integer or fractional quantum Hall edge state with a finite-range interaction. The system is described by a chiral Luttinger liquid with non-linear…
We show that a two-dimensional (2D) spin-polarised Fermi gas immersed in a 3D Bose-Einstein condensate (BEC) constitutes a very promising system to realise a $p_x+ip_y$ superfluid. The fermions attract each other via an induced interaction…
We explain recently observed linear temperature dependence of the nodal Fermi velocity $v_F (T)$ in near-optimally doped cuprates. We argue that it originates from electron-electron interaction, and is a fundamental property of an arbitrary…
We present results for the long-distance asymptotics of correlation functions of mesoscopic one-dimensional systems with periodic and open (Dirichlet) boundary conditions, as well as at finite temperature in the thermodynamic limit. The…
This article is written as a Lecture given in the 2006 Varenna Summer School on "Ultracold Fermi Gases". Here we present a review of BCS--Bose Einstein condensation (BEC) crossover theory with emphasis on finite temperature effects. We…
We discuss the technique of bosonization for studying systems of interacting fermions in one dimension. After briefly reviewing the low-energy properties of Fermi and Luttinger liquids, we present some of the relations between bosonic and…
The critical behavior of one-dimensional interacting Fermi systems is expected to display universality features, called Luttinger liquid behavior. Critical exponents and certain thermodynamic quantities are expected to be related among each…
We study spin-dependent heat transport in quantum gases, focusing on transport phenomena related to pure spin currents and spin-dependent temperatures. Using the Boltzmann equation, we compute the coupled spin and heat transport…
We revisit the issue of the leading nonanalytic corrections to the temperature dependence of the specific heat coefficient, $\gamma (T)=C(T)/T,$ for a system of interacting fermions in three dimensions. We show that the leading temperature…
We use the Kotliar-Ruckenstein slave-boson formalism to study the temperature dependence of paramagnetic phases of the one-band Hubbard model for a variety of band structures. We calculate the Fermi liquid quasiparticle spectral weight $Z$…
It is shown that it is possible to bosonize fermions in any number of dimensions using the hydrodynamic variables, namely the velocity potential and density. The slow part of the Fermi field is defined irrespective of dimensionality and the…
We investigate the one-dimensional Hubbard model with an additional bond-charge interaction, recently considered in the description of compounds that exhibit strong 1D features above the temperature of ordered phases. The partition function…
We consider a one-dimensional mixture of bosons and spinless fermions with contact interactions. In this system, the elementary excitations at low energies are described by four linearly dispersing modes characterized by two excitation…
We theoretically investigate normal-state properties of a unitary Bose-Fermi mixture. Including strong hetero-pairing fluctuations, we evaluate the Bose and Fermi chemical potential, internal energy, pressure, entropy, as well as specific…
We briefly discuss recent experiments on the BCS-BEC crossover with ultracold alkali-metal atoms both in three-dimensional configurations and two-dimensional ones. Then we analyze the quantum-field-theory formalism used to describe an…
We calculate the damping of the Bogoliubov-Anderson mode in a one-dimensional two-component attractive Fermi gas for arbitrary coupling strength within a quantum hydrodynamic approach. Using the Bethe-Ansatz solution of the 1D BCS-BEC…