Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

FIRST-ORDER LAGRANGIANS AND PATH-INTEGRAL QUANTIZATION IN THE t-J MODEL.

A. Foussats, A. Greco

Published Jan 1, 1999• 11 citations
OpenAlex

Abstract

By using the supersymmetric version of the Faddeev-Jackiw symplectic formalism, a family of first-order constrained Lagrangians for the t-J model is found. In this approach the Hubbard ˆ X-operators are used as field variables. In this framework, we first study the spinless fermion model which satisfies the graded algebra spl(1,1). Later on, in order to satisfy the Hubbard ˆ X-operators commutation rules satisfiying the graded algebra spl(2,1), the number and kind of constraints that must be included in a classical first-order Lagrangian formalism for the t-J model are found. This model is also analyzed in the context of the path- integral formalism, and so the correlation generating functional and the effective Lagrangian are constructed.

Related papers

PERTURBATIVE EXPANSION FOR THE t-J MODEL CONSTRUCTED FROM THE GENERATORS OF THE SUPERSYMMETRIC HUBBARD ALGEBRA

C. Repetto, Oscar P. Zandron

By using the Hubbard [Formula: see text]-operators as field variables along with the supersymmetric version of the Faddeev–Jackiw symplectic formalism, a family of first-order constrained Lagrangians for the t-J model is found. In order to satisfy the Hubbard [Formula: see text]-operator commutation rules satisfying the graded algebra spl(2,1), the number and kind of constraints that must be included in a classical first-order Lagrangian formalism for this model are presented. The model is also analyzed via path-integral formalism, where the correlation-generating functional and the effective Lagrangian are constructed. In this context, the introduction of a proper ghost field is needed to render the model renormalizable. The perturbative Lagrangian formalism is developed and it is shown how propagators and vertices can be renormalized to each order. In particular, the renormalized ferromagnetic magnon propagator arising in the present formalism is discussed. As an example, the thermal softening of the magnon frequency is computed.

International Journal of Modern Physics B•Jun 2, 2009•0 citations

THE HUBBARD OPERATORS AND THE SLAVE-PARTICLES PATH-INTEGRAL REPRESENTATIONS DESCRIBING THE t-J MODEL

O. P. Zandron

In the present work it is shown that the family of first-order Lagrangians for the t-J model and the corresponding correlation generating functional previously found can be exactly mapped into the slave-fermion decoupled representation. Next, by means of the Faddeev-Jackiw symplectic method, a different family of Lagrangians is constructed and it is shown how the corresponding correlation generating functional can be mapped into the slave-boson decoupled representation.

International Journal of Modern Physics B•Apr 30, 2007•0 citations

Connection between the slave-particle andx-operator path-integral representations. A new perturbative approach

A. Foussats, A. Greco, C. Repetto +2 more

In this paper it is shown that the family of first-order Lagrangians for the t - J model and the corresponding correlation-generating functional previously found can be exactly mapped into the slave-fermion decoupled representation. Next, by means of the Faddeev-Jackiw symplectic method, a different family of Lagrangians is constructed and it is shown how the corresponding correlation-generating functional can be mapped into the slave-boson representation. Finally, in order to define the propagation of fermion modes we discuss two alternative ways to treat the fermionic sector in the path-integral formalism for the t - J model.

arXiv:cond-mat/0007018•Journal of Physics A Mathematical and General•Aug 10, 2000•15 citations

Path Integral Methods for Single Band Hubbard Model

N. Heydari, S. Azakov

We review various ways to express the partition function of the single-band Hubard model as a path integral. The emphasis is made on the derivation of the action in the integrand of the path integral and the results obtained from this approach are discussed only briefly. Since the single-band Hubbard model is a pure fermionic model on the lattice and its Hamiltonian is a polynomial in creation and annihilation fermionic operators, with the help of the fermionic coherent states of holomorphic representions the partition function of the model can be straightforwardly expressed as a path integral with respect to Grassmann fields. Then the question arises how to calculate this path integral specially in the most interesting case of the strong coupling, which is described by the term quartic in the fermion fields. The standard way to get rid of this quartic term is to use so-called Hubbard-Stratonovich transformation by introducing auxilary boson field (this procedure is usually called bosonization). Since there are several equivalent forms of the interaction term in the single-band Hubbard model the bosonization procedure is not unique. In the first section of the article we discuss two types of bosoniztions one with two real scalar fields (charge and spin fields) and another with a real vector field. The second section is devoted to a spin-rotation-invariant bosonization procedure invented by Schulz and Weng, Ting and Lee, where an arbitary quantization axis is introduced at each point in space and time and an integration over all possible orientations enters the path integral measure. Spin rotation invariant formulation is necessary to study e.g. spiral magnetization. In the third section we present the contstruction of a path integral for the partition function when the single-band Hubbard Hamiltonian is written in terms of the Hubbard operators, which are elements of the doubly graded semi-simple algebra. In this case one should use generalized coherent states for superalgebra in order to get a path integral formulation. We follow the procedure proposed recently by T ngler and Kopp, to investigate the case of strong coupling.

•Apr 1, 1997•0 citations

Representation of the t−J model via spin-charge variables

Evgueny Kochetov, Vladimir Sergeevich Yarunin

We show that the $t\ensuremath{-}J$ Hamiltonian is not in general reduced to ${H}_{t\ensuremath{-}J}=H(S\ensuremath{\rightarrow},f)$, where $S\ensuremath{\rightarrow}$ and $f$ stand for independent $([S\ensuremath{\rightarrow},f]=0)$ SU(2) (spin) generators and spinless fermionic (holon) fields, respectively. The proof is based upon an identification of the Hubbard operators with the generators of the su$(2|1)$ superalgebra in the degenerate fundamental representation and ensuing SU$(2|1)$ path-integral representation of the partition function ${Z}_{t\ensuremath{-}J}.$

arXiv:cond-mat/9701220•Physical review. B, Condensed matter•Aug 1, 1997•8 citations

PATH INTEGRAL QUANTIZATION OF LAGRANGIANS WITH LINEAR ACCELERATIONS

Eyad Hasan Hasan

The Lagrangian with linear acceleration can be considered as a model of singular system. The constrained Hamiltonian systems with linear acceleration are investigated by using the Hamilton-Jacobi method. The Hamilton-Jacobi function is constructed by applying the integrability condition on this function to obtain the path integral quantization. It is shown that the equations of motion can be obtained from the action integral

European Scientific Journal ESJ•Jan 31, 2014•1 citation
By using the supersymmetric version of the Faddeev-Jackiw symplectic formalism, a family of first-order constrained Lagrangians for the t-J model is found. In this approach the Hubbard ˆ X-operators are used as field variables. In this framework, we first study the spinless fermion model which satisfies the graded algebra spl(1,1). Later on, in order to satisfy the Hubbard ˆ X-operators commutation rules satisfiying the graded algebra spl(2,1), the number and kind of constraints that must be included in a classical first-order Lagrangian formalism for the t-J model are found. This model is also analyzed in the context of the path- integral formalism, and so the correlation generating functional and the effective Lagrangian are constructed.
By using the Hubbard [Formula: see text]-operators as field variables along with the supersymmetric version of the Faddeev–Jackiw symplectic formalism, a family of first-order constrained Lagrangians for the t-J model is found. In order to satisfy the Hubbard [Formula: see text]-operator commutation rules satisfying the graded algebra spl(2,1), the number and kind of constraints that must be included in a classical first-order Lagrangian formalism for this model are presented. The model is also analyzed via path-integral formalism, where the correlation-generating functional and the effective Lagrangian are constructed. In this context, the introduction of a proper ghost field is needed to render the model renormalizable. The perturbative Lagrangian formalism is developed and it is shown how propagators and vertices can be renormalized to each order. In particular, the renormalized ferromagnetic magnon propagator arising in the present formalism is discussed. As an example, the thermal softening of the magnon frequency is computed.
In this paper it is shown that the family of first-order Lagrangians for the t - J model and the corresponding correlation-generating functional previously found can be exactly mapped into the slave-fermion decoupled representation. Next, by means of the Faddeev-Jackiw symplectic method, a different family of Lagrangians is constructed and it is shown how the corresponding correlation-generating functional can be mapped into the slave-boson representation. Finally, in order to define the propagation of fermion modes we discuss two alternative ways to treat the fermionic sector in the path-integral formalism for the t - J model.
We review various ways to express the partition function of the single-band Hubard model as a path integral. The emphasis is made on the derivation of the action in the integrand of the path integral and the results obtained from this approach are discussed only briefly. Since the single-band Hubbard model is a pure fermionic model on the lattice and its Hamiltonian is a polynomial in creation and annihilation fermionic operators, with the help of the fermionic coherent states of holomorphic representions the partition function of the model can be straightforwardly expressed as a path integral with respect to Grassmann fields. Then the question arises how to calculate this path integral specially in the most interesting case of the strong coupling, which is described by the term quartic in the fermion fields. The standard way to get rid of this quartic term is to use so-called Hubbard-Stratonovich transformation by introducing auxilary boson field (this procedure is usually called bosonization). Since there are several equivalent forms of the interaction term in the single-band Hubbard model the bosonization procedure is not unique. In the first section of the article we discuss two types of bosoniztions one with two real scalar fields (charge and spin fields) and another with a real vector field. The second section is devoted to a spin-rotation-invariant bosonization procedure invented by Schulz and Weng, Ting and Lee, where an arbitary quantization axis is introduced at each point in space and time and an integration over all possible orientations enters the path integral measure. Spin rotation invariant formulation is necessary to study e.g. spiral magnetization. In the third section we present the contstruction of a path integral for the partition function when the single-band Hubbard Hamiltonian is written in terms of the Hubbard operators, which are elements of the doubly graded semi-simple algebra. In this case one should use generalized coherent states for superalgebra in order to get a path integral formulation. We follow the procedure proposed recently by T ngler and Kopp, to investigate the case of strong coupling.
We show that the $t\ensuremath{-}J$ Hamiltonian is not in general reduced to ${H}_{t\ensuremath{-}J}=H(S\ensuremath{\rightarrow},f)$, where $S\ensuremath{\rightarrow}$ and fff stand for independent $([S\ensuremath{\rightarrow},f]=0)$ SU(2) (spin) generators and spinless fermionic (holon) fields, respectively. The proof is based upon an identification of the Hubbard operators with the generators of the su(2∣1)(2|1)(2∣1) superalgebra in the degenerate fundamental representation and ensuing SU(2∣1)(2|1)(2∣1) path-integral representation of the partition function ${Z}_{t\ensuremath{-}J}.$