Perturbative bosonization from two-point correlation functions

Here we address the problem of bosonizing massive fermions without making expansions in the fermion masses in both massive QED(2) and QED(3) with N fermion flavors including also a Thirring coupling. We start from two-point correlators involving the U(1) fermionic current and the gauge field. From the tensor structure of those correlators we prove that the U(1) current must be identically conserved (topological) in the corresponding bosonized theory in both D=2 and D=3 dimensions. We find an effective generating functional in terms of bosonic fields which reproduces these two-point correlators and from that we obtain a map of the Lagrangian density (ψ) over bar (r)(ipartial derivative-m)psi(r) into a bosonic one in both dimensions. This map is nonlocal but it is independent of the electromagnetic and Thirring couplings, at least in the quadratic approximation for the fermionic determinant.

Functional integral bosonization for an impurity in a Luttinger liquid

We use a functional integral formalism developed earlier for the pure Luttinger liquid (LL) to find an exact representation for the electron Green function of the LL in the presence of a single backscattering impurity in the low-temperature limit. This allows us to reproduce results (well known from the bosonization techniques) for the suppression of the electron local density of states (LDOS) at the position of the impurity and for the Friedel oscillations at finite temperature. In addition, we have extracted from the exact representation an analytic dependence of LDOS on the distance from the impurity and shown how it crosses over to that for the pure LL.

Bosonization and entanglement spectrum for one-dimensional polar bosons on disordered lattices

Ultra cold polar bosons in a disordered lattice potential, described by the extended Bose-Hubbard model, display a rich phase diagram. In the case of uniform random disorder one finds two insulating quantum phases-the Mott-insulator and the Haldane insulator-in addition to a superfluid and a Bose glass phase. In the case of a quasiperiodic potential, further phases are found, e.g. the incommensurate density wave, adiabatically connected to the Haldane insulator. For the case of weak random disorder we determine the phase boundaries using a perturbative bosonization approach. We then calculate the entanglement spectrum for both types of disorder, showing that it provides a good indication of the various phases.

Quantum phase analysis of 1D superconducting quantum dot lattice using extended Bose-Hubbard model

We have obtained the quantum phase diagram of a one-dimensional superconducting quantum dot lattice using the extended Bose-Hubbard model for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from the Mott insulating phase to the superconducting phase for integer band fillings of Cooper pairs. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, besides the charge density wave and superconducting phases for half-integer band fillings. We also predict that extended range interactions are necessary to obtain the correct phase boundary of a one-dimensional interacting Cooper system. We have used the density matrix renormalization group method and Abelian bosonization to study our system.

Charge transport in a Tomonaga-Luttinger liquid: Effects of pumping and bias

We study the current produced in a Tomonaga-Luttinger liquid by an applied bias and by weak, pointlike impurity potentials which are oscillating in time. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the dc and ac components of the current have power-law dependences on the bias and pumping frequencies with an exponent 2K-1 for spinless electrons, where K is the interaction parameter. For K < 1/2, the current grows large for special values of the bias. For noninteracting electrons with K=1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1/2 electrons.

One-dimensional fermions with incommensuration close to dimerization

We study a model of fermions hopping on a chain with a weak incommensuration close to dimerization; both q, the deviation of the wave number from pi, and delta, the strength of the incommensuration, are assumed to be small. For free fermions, we show that there are an infinite number of energy bands which meet at zero energy as q approaches zero. The number of states lying inside the q = 0 gap remains nonzero as q/delta --> 0. Thus the limit q --> 0 differs from q = 0, as can be seen clearly in the low-temperature specific heat. For interacting fermions or the XXZ spin-(1/2) chain, we use bosonization to argue that similar results hold. Finally, our results can be applied to the Azbel-Hofstadter problem of particles hopping on a two-dimensional lattice in the presence of a magnetic field.

Non-Abelian chiral gauge theories in two dimensions

An anomalous multiflavor chiral theory, with the gauge group SU(N), is studied using non-Abelian bosonization. The theory can be made gauge invariant by introducing Wess-Zumino fields and it is particularly simple if the Jackiw-Rajaraman parameter equals 2. In the strong-coupling limit, the low-energy effective theory only contains light unconfined fermions which interact weakly.

Conductance of Tomonaga-Luttinger liquid wires and junctions with resistances

We study the effect that resistive regions have on the conductance of a quantum wire with interacting electrons which is connected to Fermi liquid leads. Using the bosonization formalism and a Rayleigh dissipation function to model the power dissipation, we use both scattering theory and Green's function techniques to derive the DC conductance. The resistive regions are generally found to lead to incoherent transport. For a single wire, we find that the resistance adds in series to the contact resistance of h/e(2) for spinless electrons, and the total resistance is independent of the Luttinger parameter K-W of the wire. We numerically solve the bosonic equations to illustrate what happens when a charge density pulse is incident on the wire; the results depend on the parameters of the resistive and interacting regions in interesting ways. For a junction of Tomonaga-Luttinger liquid wires, we use a dissipationless current splitting matrix to model the junction. For a junction of three wires connected to Fermi liquid leads, there are two families of such matrices; we find that the conductance matrix generally depends on K-W for one family but is independent of K-W for the other family, regardless of the resistances present in the system. Copyright (c) EPLA, 2011

Supersolid Phase in One-Dimensional Bose-Hubbard Model With Extended Range Interactions: DMRG And Field Theoretic Study at Different Densities

We use the Density Matrix Renormalization Group and the Abelian bosonization method to study the effect of density on quantum phases of one-dimensional extended Bose-Hubbard model. We predict the existence of supersolid phase and also other quantum phases for this system. We have analyzed the role of extended range interaction parameters on solitonic phase near half-filling. We discuss the effects of dimerization in nearest neighbor hopping and interaction as well as next nearest neighbor interaction on the plateau phase at half-filling.

Model of resistances in systems of Tomonaga-Luttinger liquid wires

In a recent paper, we combined the technique of bosonization with the concept of a Rayleigh dissipation function to develop a model for resistances in one-dimensional systems of interacting spinless electrons Europhys. Lett. 93, 57007 (2011)]. We also studied the conductance of a system of three wires by using a current splitting matrix M at the junction. In this paper, we extend our earlier work in several ways. The power dissipated in a three-wire system is calculated as a function of M and the voltages applied in the leads. By combining two junctions of three wires, we examine a system consisting of two parallel resistances. We study the conductance of this system as a function of the M matrices and the two resistances; we find that the total resistance is generally quite different from what one expects for a classical system of parallel resistances. We do a sum over paths to compute the conductance of this system when one of the two resistances is taken to be infinitely large. We study the conductance of a three-wire system of interacting spin-1/2 electrons, and show that the charge and spin conductances can generally be different from each other. Finally, we consider a system of two wires that are coupled by a dissipation function, and we show that this leads to a current in one wire when a voltage bias is applied across the other wire.

Majorana modes and transport across junctions of superconductors and normal metals

We study Majorana modes and transport in one-dimensional systems with a p-wave superconductor (SC) and normal metal leads. For a system with an SC lying between two leads, it is known that there is a Majorana mode at the junction between the SC and each lead. If the p-wave pairing Delta changes sign or if a strong impurity is present at some point inside the SC, two additional Majorana modes appear near that point. We study the effect of all these modes on the sub-gap conductance between the leads and the SC. We derive an analytical expression as a function of Delta and the length L of the SC for the energy shifts of the Majorana modes at the junctions due to hybridization between them; the shifts oscillate and decay exponentially as L is increased. The energy shifts exactly match the location of the peaks in the conductance. Using bosonization and the renormalization group method, we study the effect of interactions between the electrons on Delta and the strengths of an impurity inside the SC or the barriers between the SC and the leads; this in turn affects the Majorana modes and the conductance. Finally, we propose a novel experimental realization of these systems, in particular of a system where Delta changes sign at one point inside the SC.

Teoria de campos aplicada ao grafeno:um estudo

Este trabalho visa a um estudo de bosonização de sistemas fermiônicos. As relações entre a bosonização e matéria condensada, notoriamente o caso do Grafeno, são apresentados e depois discutimos as possíveis implicações do mecanismo de i-particles na existência de correlatores de 4 correntes. Cálculos em D = 4 também são realizados para que se possa observar o diferente comportamento da ação bosonizada em diferentes dimensões.

Equivalence between supersymmetric self-dual and Maxwell-Chern-Simons models coupled to a matter spinor superfield

We study the duality of the supersymmetric self-dual and Maxwell-Chern-Simons theories coupled to a fermionic matter superfield, using a master action. This approach evades the difficulties inherent to the quartic couplings that appear when matter is represented by a scalar superfield. The price is that the spinorial matter superfield represents a unusual supersymmetric multiplet, whose main physical properties we also discuss. (C) 2009 Elsevier B.V. All rights reserved.

On duality of the noncommutative supersymmetric Maxwell-Chern-Simons theory

We study the possibility of establishing the dual equivalence between the noncommutative supersymmetric Maxwell-Chern-Simons theory and the noncommutative supersymmetric self-dual theory. It turns to be that whereas in the commutative case the Maxwell-Chern-Simons theory can be mapped into the sum of the self-dual theory and the Chern-Simons theory, in the noncommutative case such a mapping is possible only for the theory with modified Maxwell term. (c) 2008 Elsevier B.V. All rights reserved.

Pareamento BCS em um Líquido de Luttinger em 1D

In this work we investigate the effect of a BCS-type pairing term for free spinless fermions, with a propensity to form a condensate of pairs in a 1+1 dimension. Using the of bosonization technique we explore the possible condition of existence of quasiparticles in a superconducting state. Although there is no spontaneous breaking of chiral symmetry the propagator of one-particle fermion is massive and, in fact, resembles the one-particle Green s function of conventional quasiparticles