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

Chinese Physics Letters

Fermion System with Quantum Group Symmetry and Usual Fermion Realizations of Sl q (2)

Sun Changpu, Jianming Li

Published Dec 1, 1992• 0 citations
Publisher

Abstract

The usual fermion realizations of quantum algebra slq (2) defining higher-dimensional representations are built in this letter. Using them, we construct a usual fermion system with quantum group symmetry of slq (2) as a q-deformation of the pairing correlation model in many-body problems. Its energy spectra are exactly solved out from the representation theory of slq (2).

DOI
10.1088/0256-307x/9/12/002

Related papers

Quantum Group and q-Virasoro Symmetries in Fermion Systems

Haru-Tada Sato

We discuss a generalization of the quantum group Uq(sl(2)) to the q-Virasoro algebra in two-dimensional electrons system under uniform magnetic field. It is shown that the integral representations of both algebras are reduced to those in a (1 + 1)-dimensional fermion. As an application of the quantum group symmetry, we discuss a model of quantum group current on the analogy of the Hall current.

Progress of Theoretical Physics•Jan 1, 1995•3 citations

Quantum Group and q-Virasoro Symmetries in Fermion Systems

Haru-Tada Sato

We discuss a generalization of the quantum group Uq(sl(2)) to the q-Virasoro algebra in two-dimensional electrons system under uniform magnetic field. It is shown that the integral representations of both algebras are reduced to those in a (1 + 1)-dimensional fermion. As an application of the quantum group symmetry, we discuss a model of quantum group current on the analogy of the Hall current.

arXiv:hep-th/9312174•Progress of Theoretical Physics•Jan 1, 1995•4 citations

Exactly solvable models for 2D interacting fermions

Edwin Langmann A

I discuss many-body models for correlated fermions in two space dimensions which can be solved exactly using group theory. The simplest example is a model of a quantum Hall system: two-dimensional (2D) fermions in a constant magnetic field and a particular non-local four-point interaction. It is exactly solvable due to a dynamical symmetry corresponding to the Lie algebra gl ∞ ⊕ gl ∞ . There is an algorithm to construct all energy eigenvalues and eigenfunctions of this model. The latter are, in general, many-body states with spatial correlations. The model also has a non-trivial zero temperature phase diagram. I point out that this QH model can be obtained from a more realistic one using a truncation procedure generalizing a similar one leading to mean field theory. Applying this truncation procedure to other 2D fermion models I obtain various simplified models of increasing complexity which generalize mean field theory by taking into account non-trivial correlations but nevertheless are treatable by exact methods.

arXiv:cond-mat/0206045•Journal of Physics A Mathematical and General•Dec 15, 2003•5 citations

A q-deformed oscillator system with quantum group SLq(l) symmetry

Chang-Pu Sun, Xu‐Feng Liu, Jing-fa Lu +1 more

A q-deformed oscillator system with quantum group SL q (l) symmetry is constructed in terms of the q-deformed boson operators. The energy level degeneracy associated with the irreducible representation of SL q (l) is analysed, especially for the case that q is a root of unity.

Journal of Physics A Mathematical and General•Jan 21, 1992•3 citations

Description of nuclear many-body interactions within the framework of quantum deformation theory

E Yaghoubiopour

A fermion realization of compact symplectic algebra provides a natural framework for studying pairing correlations of many-body interactions in nuclei. Here, we use quantum deformation concept in order to describe pairing correlations in atomic nuclei. While the nondeformed limit of the theory provides a reasonable and overall description of certain nuclear properties and fine structure effects, the results show that the q deformation plays a significant role in understanding higher-order effects in the many-body interactions.

Iranian Journal of Physics Research•Nov 15, 2014•0 citations

Two-dimensional bialgebras and quantum groups: algebraic structures and tensor network realizations

José Garre-Rubio, András Molnár, Germán Sierra

Abstract We introduce a framework to define coalgebra and bialgebra structures on two-dimensional (2D) square lattices, extending the algebraic theory of Hopf algebras and quantum groups beyond the one-dimensional (1D) setting. Our construction is based on defining 2D coproducts through horizontal and vertical maps that satisfy compatibility and associativity conditions, enabling the consistent growth of vector spaces over lattice sites. We present several examples of 2D bialgebras, including group-like and Lie algebra-inspired constructions and a quasi-1D coproduct instance that is applicable to Taft-Hopf algebras and to quantum groups. The approach is further applied to the quantum group U q [ s u ( 2 ) ] , for which we construct 2D generalizations of its generators, analyze q -deformed singlet states, and derive a 2D R-matrix satisfying an intertwining relation in the semiclassical limit. Additionally, we show how tensor network states, particularly projected entangled pair states, naturally induce 2D coalgebra structures when supplemented with appropriate boundary conditions. Our results establish a local and algebraically consistent method to embed quantum group symmetries into higher-dimensional lattice systems, potentially connecting to the emerging theory of fusion 2-categories and categorical symmetries in quantum many-body physics.

arXiv:2507.22541•Journal of Physics A Mathematical and Theoretical•Feb 3, 2026•0 citations
The usual fermion realizations of quantum algebra slq (2) defining higher-dimensional representations are built in this letter. Using them, we construct a usual fermion system with quantum group symmetry of slq (2) as a q-deformation of the pairing correlation model in many-body problems. Its energy spectra are exactly solved out from the representation theory of slq (2).
I discuss many-body models for correlated fermions in two space dimensions which can be solved exactly using group theory. The simplest example is a model of a quantum Hall system: two-dimensional (2D) fermions in a constant magnetic field and a particular non-local four-point interaction. It is exactly solvable due to a dynamical symmetry corresponding to the Lie algebra gl ∞ ⊕ gl ∞ . There is an algorithm to construct all energy eigenvalues and eigenfunctions of this model. The latter are, in general, many-body states with spatial correlations. The model also has a non-trivial zero temperature phase diagram. I point out that this QH model can be obtained from a more realistic one using a truncation procedure generalizing a similar one leading to mean field theory. Applying this truncation procedure to other 2D fermion models I obtain various simplified models of increasing complexity which generalize mean field theory by taking into account non-trivial correlations but nevertheless are treatable by exact methods.
A fermion realization of compact symplectic algebra provides a natural framework for studying pairing correlations of many-body interactions in nuclei. Here, we use quantum deformation concept in order to describe pairing correlations in atomic nuclei. While the nondeformed limit of the theory provides a reasonable and overall description of certain nuclear properties and fine structure effects, the results show that the q deformation plays a significant role in understanding higher-order effects in the many-body interactions.
Abstract We introduce a framework to define coalgebra and bialgebra structures on two-dimensional (2D) square lattices, extending the algebraic theory of Hopf algebras and quantum groups beyond the one-dimensional (1D) setting. Our construction is based on defining 2D coproducts through horizontal and vertical maps that satisfy compatibility and associativity conditions, enabling the consistent growth of vector spaces over lattice sites. We present several examples of 2D bialgebras, including group-like and Lie algebra-inspired constructions and a quasi-1D coproduct instance that is applicable to Taft-Hopf algebras and to quantum groups. The approach is further applied to the quantum group U q [ s u ( 2 ) ] , for which we construct 2D generalizations of its generators, analyze q -deformed singlet states, and derive a 2D R-matrix satisfying an intertwining relation in the semiclassical limit. Additionally, we show how tensor network states, particularly projected entangled pair states, naturally induce 2D coalgebra structures when supplemented with appropriate boundary conditions. Our results establish a local and algebraically consistent method to embed quantum group symmetries into higher-dimensional lattice systems, potentially connecting to the emerging theory of fusion 2-categories and categorical symmetries in quantum many-body physics.