Functional integral approach to multipoint correlators in 2d critical systems

We extend a previously developed technique for computing spin-spin critical correlators in the 2d Ising model, to the case of multiple correlations. This enables us to derive Kadanoff-Ceva's formula in a simple and elegant way. We also exploit a doubling procedure in order to evaluate the critical exponent of the polarization operator in the Baxter model. Thus we provide a rigorous proof of the relation between different exponents, in the path-integral framework.Comment: 10 pages, LaTex, no figure

Heat transport through quantum Hall edge states: Tunneling versus capacitive coupling to reservoirs

We study the heat transport along an edge state of a two-dimensional electron gas in the quantum Hall regime, in contact to two reservoirs at different temperatures. We consider two exactly solvable models for the edge state coupled to the reservoirs. The first one corresponds to filling $\nu=1$ and tunneling coupling to the reservoirs. The second one corresponds to integer or fractional filling of the sequence $\nu=1/m$ (with $m$ odd), and capacitive coupling to the reservoirs. In both cases we solve the problem by means of non-equilibrium Green function formalism. We show that heat propagates chirally along the edge in the two setups. We identify two temperature regimes, defined by $\Delta$, the mean level spacing of the edge. At low temperatures, $T< \Delta$, finite size effects play an important role in heat transport, for both types of contacts. The nature of the contacts manifest themselves in different power laws for the thermal conductance as a function of the temperature. For capacitive couplings a highly non-universal behavior takes place, through a prefactor that depends on the length of the edge as well as on the coupling strengths and the filling fraction. For larger temperatures, $T>\Delta$, finite-size effects become irrelevant, but the heat transport strongly depends on the strength of the edge-reservoir interactions, in both cases. The thermal conductance for tunneling coupling grows linearly with $T$, whereas for the capacitive case it saturates to a value that depends on the coupling strengths and the filling factors of the edge and the contacts.Comment: 15 pages, 5 figure

Path-integral fermion-boson decoupling at finite temperature

We show how to extend the standard functional approach to bosonisation, based on a decoupling change of path-integral variables, to the case in which a finite temperature is considered. As examples, in order to both illustrate and check the procedure, we derive the thermodynamical partition functions for the Thirring and Schwinger models.Comment: 12 pages, latex, no figure

Duality and bosonization in Schwinger-Keldysh formulation

We present a path-integral bosonization approach for systems out of equilibrium based on a duality transformation of the original Dirac fermion theory combined with the Schwinger-Keldysh time closed contour technique, to handle the non-equilibrium situation. The duality approach to bosonization that we present is valid for $D \geq 2$ space-time dimensions leading for $D=2$ to exact results. In this last case we present the bosonization rules for fermion currents, calculate current-current correlation functions and establish the connection between the fermionic and bosonic distribution functions in a generic, nonequilibrium situation.Comment: 16 pages, 1 figur

Path-integral Bosonization of d=2d=2 PT symmetric models

We discuss bosonization of non-Hermitian PT invariant fermion models in $d=2$ space-time dimensions within the path-integral approach in which the generating functionals associated to the fermion and boson models can be related. We first discuss the PT symmetric Thirring-sine-Gordon connection and then extend the treatment to bosonize the Gross-Neveu model.Comment: 12 pages, no figure

Non local Thirring model with spin flipping interactions

We extend a non local and non covariant version of the Thirring model in order to describe a many-body system with spin-flipping interactions By introducing a model with two fermion species we are able to avoid the use of non abelian bosonization which is needed in a previous approach. We obtain a bosonized expression for the partition function, describing the dynamics of the collective modes of this system. By using the self-consistent harmonic approximation we found a formula for the gap of the spin-charge excitations as functional of arbitrary electron-electron potentials

Vacuum properties of a Non-Local Thirring-Like Model

We use path-integral methods to analyze the vacuum properties of a recently proposed extension of the Thirring model in which the interaction between fermionic currents is non-local. We calculate the exact ground state wave functional of the model for any bilocal potential, and also study its long-distance behavior. We show that the ground state wave functional has a general factored Jastrow form. We also find that it posess an interesting symmetry involving the interchange of density-density and current-current interactions.Comment: 25 pages, latex, no figure

Friedel oscillations in a Luttinger liquid with long-range interactions

We introduce a path-integral approach that allows to compute charge density oscillations in a Luttinger liquid with impurities. We obtain an explicit expression for the envelope of Friedel oscillations in the presence of arbitrary electron-electron potentials. As examples, in order to illustrate the procedure, we show how to use our formula for contact and Coulomb potentials.Comment: 11 pages, no figures, latex. Revised version to appear in PR