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

arXiv:1204.4777

A note on path integral formulism of $Z_{2}$ slave-spin representation of Hubbard model

Yin Zhong, Hong‐Gang Luo

Published Apr 21, 2012• 0 citations
arXivHTMLPDF

Abstract

This is a note on the derivation of path integral formulism for $Z_{2}$ slave-spin representation of Hubbard model and may be helpful for further study in related works. We are rather happy to receive any comments and other discussions are welcome.

DOI
10.48550/arxiv.1204.4777

Related papers

Superconducting and Antiferromagnetic Instabilities in the Slave Boson Approach to the Hubbard Model: Functional Integral Formulation

P. Wróbel

Springer eBooks•Jan 1, 1990•0 citations

More about path integrals for spin

Kunio Funahashi, Tarō Kashiwa, Shuji Nima +1 more

arXiv:hep-th/9504125•Nuclear Physics B•Oct 1, 1995•17 citations

Comment on “ Z2 -slave-spin theory for strongly correlated fermions”

Álvaro Antônio Bandeira Ferraz, E. A. Kochetov

The authors of Ref. 1 introduced a new slave-spin (SS) \nmean-field (MF) approach to the Hubbard model of strongly \ncorrelated electrons in terms of Ising spins and standard \nfermion operators by constructing an enlarged Hilbert space \nwith both physical and unphysical states. The purpose of \nthis construction is clear: this formulation involves a much \nsmaller number of slave fields, compared with more standard \nslave particle frameworks. In this way, the complexity of the \noriginal model is reduced to a more readily tractable system \nof Ising spins in a transverse field coupled to free fermions. \nIn this Comment, we show that the unphysical states are not \nproperly excluded, and despite the claimed good agreement \nwith previous results, the consistency of their MF theory is \nunjustified

arXiv:1301.4508•Physical Review B•Jan 2, 2013•1 citation

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

Path Integrals and Product Integrals

John F. Hamilton, Lawrence S. Schulman

The product integral is shown to be the appropriate mathematical tool for implementing the path integral for spin in its simplest form.

Journal of Mathematical Physics•Jan 1, 1971•18 citations

First order Lagrangians and path integral quantization for Hubbard operators

Oscar P. Zandron, Patrick Turner

Advanced Studies in Theoretical Physics•Jan 1, 2016•0 citations
A note on path integral formulism of Z2Z_{2}Z2​ slave-spin representation of Hubbard model
This is a note on the derivation of path integral formulism for Z2Z_{2}Z2​ slave-spin representation of Hubbard model and may be helpful for further study in related works. We are rather happy to receive any comments and other discussions are welcome.
The authors of Ref. 1 introduced a new slave-spin (SS) \nmean-field (MF) approach to the Hubbard model of strongly \ncorrelated electrons in terms of Ising spins and standard \nfermion operators by constructing an enlarged Hilbert space \nwith both physical and unphysical states. The purpose of \nthis construction is clear: this formulation involves a much \nsmaller number of slave fields, compared with more standard \nslave particle frameworks. In this way, the complexity of the \noriginal model is reduced to a more readily tractable system \nof Ising spins in a transverse field coupled to free fermions. \nIn this Comment, we show that the unphysical states are not \nproperly excluded, and despite the claimed good agreement \nwith previous results, the consistency of their MF theory is \nunjustified
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.