It is shown that there is a hidden connection between the two well-studied sequences of the Temperley-Lieb (TL) integrable models -- the $q$ -state quantum Potts (QP) models at the self-dual points and the staggered ${\rm SU}(n)$ spin- $s$ chains with $n=2s+1$ ( $s \ge 1$ ), in addition to the uniform ${\rm SU}(2)$ spin- $1/2$ Heisenberg model. For each sequence, symmetry group factorization arises, in the sense that if $q$ is factorized into $q_1$ and $q_2$ , then the $q$ -state QP model is unitarily equivalent to a combined QP model with the symmetry group ${\rm S}_{q_1} \times {\rm S}_{q_2}$ or if $n$ is factorized into $n_1$ and $n_2$ , then the staggered ${\rm SU}(n)$ spin- $s$ chain with the symmetry group ${\rm SU}(n)$ is unitarily equivalent to a combined staggered ${\rm SU}(n_1) \times {\rm SU}(n_2)$ spin chain with the symmetry group ${\rm SU}(n_1) \times {\rm SU}(n_2)$ , valid for both ferromagnetic (FM) and antiferromagnetic (AF) cases. Moreover, the FM (AF) staggered ${\rm SU}(n)$ spin- $s$ chain is unitarily equivalent to the AF (FM) $q$ -state QP model with $q=n^2$ , as long as the size of the AF (FM) staggered ${\rm SU}(n)$ spin- $s$ chain is doubled. A combination of the two distinct types of unitary equivalences yields a family of models such that they are essentially identical, but appear in different guises. Some physical implications for unitary equivalence among different TL integrable models are clarified.It is shown that there is a hidden connection between the two well-studied sequences of the Temperley-Lieb (TL) integrable models -- the $q$-state quantum Potts (QP) models at the self-dual points and the staggered ${\rm SU}(n)$ spin-$s$ chains with $n=2s+1$ ($s \ge 1$), in addition to the uniform ${\rm SU}(2)$ spin-$1/2$ Heisenberg model. For each sequence, symmetry group factorization arises, in the sense that if $q$ is factorized into $q_1$ and $q_2$, then the $q$-state QP model is unitarily equivalent to a combined QP model with the symmetry group ${\rm S}_{q_1} \times {\rm S}_{q_2}$ or if $n$ is factorized into $n_1$ and $n_2$, then the staggered ${\rm SU}(n)$ spin-$s$ chain with the symmetry group ${\rm SU}(n)$ is unitarily equivalent to a combined staggered ${\rm SU}(n_1) \times {\rm SU}(n_2)$ spin chain with the symmetry group ${\rm SU}(n_1) \times {\rm SU}(n_2)$, valid for both ferromagnetic (FM) and antiferromagnetic (AF) cases. Moreover, the FM (AF) staggered ${\rm SU}(n)$ spin-$s$ chain is unitarily equivalent to the AF (FM) $q$-state QP model with $q=n^2$, as long as the size of the AF (FM) staggered ${\rm SU}(n)$ spin-$s$ chain is doubled. A combination of the two distinct types of unitary equivalences yields a family of models such that they are essentially identical, but appear in different guises. Some physical implications for unitary equivalence among different TL integrable models are clarified.

arXiv:2603.21242Mar 22, 20260 citations

Integrable laddert-Jmodel with staggered shift of the spectral parameter

Jan Ambjørn A, D. Arnaudon, A. Sedrakyan +2 more

The generalization of the Yang-Baxter equations in the presence of ℤ 2 grading along both chain and time directions is presented and an integrable model of t - J type with staggered disposition of shifts of the spectral parameter along the chain is constructed. The Hamiltonian of the model is computed in the fermionic formulation. It involves three neighbour site interactions and therefore can be considered as a zigzag ladder model. The algebraic Bethe ansatz technique is applied and the eigenstates as well as the eigenvalues of the transfer matrix of the model are found. It is argued that in the thermodynamic limit the lowest energy of the model is formed by the quarter filling of the states by fermions instead of the usual half filling.The generalization of the Yang-Baxter equations in the presence of ℤ 2 grading along both chain and time directions is presented and an integrable model of t - J type with staggered disposition of shifts of the spectral parameter along the chain is constructed. The Hamiltonian of the model is computed in the fermionic formulation. It involves three neighbour site interactions and therefore can be considered as a zigzag ladder model. The algebraic Bethe ansatz technique is applied and the eigenstates as well as the eigenvalues of the transfer matrix of the model are found. It is argued that in the thermodynamic limit the lowest energy of the model is formed by the quarter filling of the states by fermions instead of the usual half filling.

arXiv:hep-th/0006243Journal of Physics A Mathematical and GeneralJul 20, 200115 citations

Integrable generalized Thirring model

Korkut Bardakci, Luis M. Bernardo, Nir Sochen

arXiv:hep-th/9607018Nuclear Physics BMar 1, 19979 citations

Integrable Ladder t-J Model with Staggered Shift of the Spectral Parameter

Jan Ambjørn A, D. Arnaudon, A. Sedrakyan +2 more

The generalization of the Yang-Baxter equations (YBE) in the presence of Z_2 grading along both chain and time directions is presented and an integrable model of t-J type with staggered disposition along a chain of shifts of the spectral parameter is constructed. The Hamiltonian of the model is computed in fermionic formulation. It involves three neighbour site interactions and therefore can be considered as a zig-zag ladder model. The Algebraic Bethe Ansatz technique is applied and the eigenstates, along with eigenvalues of the transfer matrix of the model are found. In the thermodynamic limit, the lowest energy of the model is formed by the quarter filling of the states by fermions instead of usual half filling.The generalization of the Yang-Baxter equations (YBE) in the presence of Z_2 grading along both chain and time directions is presented and an integrable model of t-J type with staggered disposition along a chain of shifts of the spectral parameter is constructed. The Hamiltonian of the model is computed in fermionic formulation. It involves three neighbour site interactions and therefore can be considered as a zig-zag ladder model. The Algebraic Bethe Ansatz technique is applied and the eigenstates, along with eigenvalues of the transfer matrix of the model are found. In the thermodynamic limit, the lowest energy of the model is formed by the quarter filling of the states by fermions instead of usual half filling.

Jan 1, 20011 citation

Multi-leg integrable ladder models

D. Arnaudon, A. Sedrakyan, Tigran Sedrakyan

arXiv:hep-th/0210087Nuclear Physics BDec 2, 20035 citations

It is shown that there is a hidden connection between the two well-studied sequences of the Temperley-Lieb (TL) integrable models -- the

q

-state quantum Potts (QP) models at the self-dual points and the staggered

{\rm SU}(n)

spin-

s

chains with

n=2s+1

(

s \ge 1

), in addition to the uniform

{\rm SU}(2)

spin-

1/2

Heisenberg model. For each sequence, symmetry group factorization arises, in the sense that if

q

is factorized into

q_1

and

q_2

, then the

q

-state QP model is unitarily equivalent to a combined QP model with the symmetry group

{\rm S}_{q_1} \times {\rm S}_{q_2}

or if

n

is factorized into

n_1

and

n_2

, then the staggered

{\rm SU}(n)

spin-

s

chain with the symmetry group

{\rm SU}(n)

is unitarily equivalent to a combined staggered

{\rm SU}(n_1) \times {\rm SU}(n_2)

spin chain with the symmetry group

{\rm SU}(n_1) \times {\rm SU}(n_2)

, valid for both ferromagnetic (FM) and antiferromagnetic (AF) cases. Moreover, the FM (AF) staggered

{\rm SU}(n)

spin-

s

chain is unitarily equivalent to the AF (FM)

q

-state QP model with

q=n^2

, as long as the size of the AF (FM) staggered

{\rm SU}(n)

spin-

s

chain is doubled. A combination of the two distinct types of unitary equivalences yields a family of models such that they are essentially identical, but appear in different guises. Some physical implications for unitary equivalence among different TL integrable models are clarified.