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

Springer proceedings in mathematics & statistics

Fermions Acting on Quasi-local Operators in the XXZ Model

Michio Jimbo, Tetsuji Miwa, Feodor Smirnov

Published Dec 4, 2012• 6 citations
Publisher
DOI
10.1007/978-1-4471-4863-0_10

Related papers

Q-oscillator and correlation functions for XXZ model

Fedor Aleksandrovich Smirnov

Fermionic basis

•Aug 8, 2007•0 citations

Fermionic basis for space of operators in the XXZ model

Herman E. Boos, M. Jimbo, T. Miwa +2 more

In the recent study of correlation functions for the infinite XXZ spin chain, a new pair of anti-commuting operators $b(z), c(z)$ was introduced. They act on the space of quasi-local operators, which are local operators multiplied by the disorder operator. For the inhomogeneous chain with the spectral parameters $ξ_{k}$, these operators have simple poles at $z^2=ξ_{k}^2$. The residues are denoted by $b_{k}, c_{k}$. At $q=i$, we show that the operators $b_{k}, c_{k}$ are cubic monomials in free fermions. In other words, the action of these operators is very simple in the fermion basis. We give an explicit construction of these fermions. Then, we show that the existence of the fermionic basis is a consequence of the Grassmann relation, the equivariance with respect to the action of the symmetric group and the reduction property, which are all valid for the operators $b_{k}, c_{k}$ in the case of generic $q$.

arXiv:hep-th/0702086•Feb 12, 2007•13 citations

Interacting Fermions in Quasi-1D

Ya-Ting Chang, Ruwan Senaratne, Danyel Cavazos-Cavazos +1 more

Bulletin of the American Physical Society•Jun 2, 2021•0 citations

Correlation Functions for Lattice Integrable Models

Fedor Aleksandrovich Smirnov

In this lectures I consider the problem of calculating the correlation functions for XXZ spin chain. First, I explain in details the free fermion case. Then I show that for generic coupling constant the fermionic operators acting on the space of quasi-local fields can be introduced. In the basis generated by these fermionic operators the correlation functions are given by determinants as in the free fermion case.

Acta Polytechnica•Jan 2, 2008•0 citations

Fermion models with quasilocal interaction around polycritical points

Alexander A. Andrianov, V. A. Andrianov

•Jan 1, 1995•0 citations

MODEL HAMILTONIANS WITH FERMION INTERACTION

WORLD SCIENTIFIC eBooks•Aug 19, 2014•0 citations
In the recent study of correlation functions for the infinite XXZ spin chain, a new pair of anti-commuting operators b(z),c(z)b(z), c(z)b(z),c(z) was introduced. They act on the space of quasi-local operators, which are local operators multiplied by the disorder operator. For the inhomogeneous chain with the spectral parameters ξkξ_{k}ξk​, these operators have simple poles at z2=ξk2z^2=ξ_{k}^2z2=ξk2​. The residues are denoted by bk,ckb_{k}, c_{k}bk​,ck​. At q=iq=iq=i, we show that the operators bk,ckb_{k}, c_{k}bk​,ck​ are cubic monomials in free fermions. In other words, the action of these operators is very simple in the fermion basis. We give an explicit construction of these fermions. Then, we show that the existence of the fermionic basis is a consequence of the Grassmann relation, the equivariance with respect to the action of the symmetric group and the reduction property, which are all valid for the operators bk,ckb_{k}, c_{k}bk​,ck​ in the case of generic qqq.