Path-integral bosonization of a non-local interaction and its application to the study of 1d many-body systems

Naón, Carlos M.; Reichenbach, María Cecilia von; Trobo, Marta Liliana

doi:10.1016/0550-3213(94)00534-l

Cited by 25 publications

(52 citation statements)

References 58 publications

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“…Z c is the partition function associated to charge density excitations. It coincides with the spinless NLTM studied in reference [3]. Z s describes spin-density excitations.…”

Section: The Equivalent Bosonic Actionmentioning

confidence: 99%

“…[3]. The bosonized effective action obtained by non Abelian bosonization led to a WZW functional, which was not easy to deal with in order to analyze the physical spectrum.…”

Section: The Model and Its Relationship To A Previous Non Abelian Desmentioning

confidence: 99%

“…Although it provides an elegant framework to analyze the 1d many-body problem, as it stands it is not very practical to consider magnetic properties of Luttinger liquids. This is so because in the original formulation of NLTM [3], the description of spin-flipping (SF) processes, based on non abelian bosonization, is quite involved. In this paper we show how to circumvent this problem by introducing a Thirring-like model with two fermion species.…”

Section: Introductionmentioning

confidence: 99%

“…The simplest theoretical framework that presents this feature is the Tomonaga-Luttinger (TLM) model [2], a many-body system of right and left-moving particles interacting through their charge densities. In recent papers [3] [4] [5] an alternative, field theoretical approach was developed to consider this problem. In these works a non local and non covariant version of the Thirring model was introduced, in which the fermionic densities and currents are coupled through bilocal, distance-dependent potentials.…”

Section: Introductionmentioning

confidence: 99%

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Nonlocal Thirring model with spin flipping interactions

Iucci

Naón

2001

Nuclear Physics B

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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 selfconsistent harmonic approximation we found a formula for the gap of the spin-charge excitations as functional of arbitrary electron-electron potentials.

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“…Z c is the partition function associated to charge density excitations. It coincides with the spinless NLTM studied in reference [3]. Z s describes spin-density excitations.…”

Section: The Equivalent Bosonic Actionmentioning

confidence: 99%

“…[3]. The bosonized effective action obtained by non Abelian bosonization led to a WZW functional, which was not easy to deal with in order to analyze the physical spectrum.…”

Section: The Model and Its Relationship To A Previous Non Abelian Desmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlocal Thirring model with spin flipping interactions

Iucci

Naón

2001

Nuclear Physics B

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“…The model presented in this section was extensively analyzed in (1 + 1)d in the context of the study of many-body physics of quantum wires 21,22,23,24 . It is the purpose of the present paper to extend its analysis to 2 + 1 dimensions .…”

Section: The Modelmentioning

confidence: 99%

Functional Bosonization of Nonrelativistic Fermions in 2+1 Dimensions

Barci¹,

Linhares²,

Queiroz³

et al. 2000

Int. J. Mod. Phys. A

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We analyze the universality of the bosonization rules in non-relativistic fermionic systems in (2 + 1)d. We show that, in the case of linear fermionic dispersion relations, a general fermionic theory can be mapped into a gauge theory in such a way that the fermionic density maps into a magnetic flux and the fermionic current maps into a transverse electric field. These are universal rules in the sense that they remain valid whatever the interaction considered. We also show that these rules are universal in the case of nonlinear dispersion relations provided we consider only density-density interactions. We apply the functional bosonization formalism to a non-relativistic and non-local massive Thirring-like model and evaluate the spectrum of collective excitations in several limits. In the large mass limit, we are able to exactly calculate this spectrum for arbitrary density-density and current-current interactions. We also analyze the massless case and show that it has no collective excitations for any density-density potential in the Gaussian approximation. Moreover, the presence of current interactions may induce a gapless mode with a linear dispersion relation.

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Path-integral formulation of backward and umklapp scattering for one-dimensional spinless fermions

Fernández

Naón

1999

Theor Math Phys

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We present a (1+1)-dimensional fermionic QFT with non-local couplings between currents. This model describes an ensemble of spinless fermions interacting through forward, backward and umklapp scattering processes. We express the vacuum to vacuum functional in terms of a non trivial fermionic determinant. Using path-integral methods we find a bosonic representation for this determinant. Thus we obtain an effective action depending on three scalar fields, two of which correspond to the physical collective excitations whereas the third one is an auxiliary field that is left to be integrated by means of an approximate technique.

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Path-integral bosonization of a non-local interaction and its application to the study of 1d many-body systems

Cited by 25 publications

References 58 publications

Nonlocal Thirring model with spin flipping interactions

Nonlocal Thirring model with spin flipping interactions

Functional Bosonization of Nonrelativistic Fermions in 2+1 Dimensions

Path-integral formulation of backward and umklapp scattering for one-dimensional spinless fermions

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