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:2610.03349

Correlation functions of the 19-vertex IRF model and its integrable quantum spin-1 chain

T. S. Tavares, H. B. Abreu, G A P Ribeiro

Published Oct 2, 2026• 0 citations
arXivHTMLPDF

Abstract

We consider the interaction-round-a-face version of the nineteen-vertex model and derive a new quantum spin-$1$ chain. In the isotropic limit, the associated spin chain can be seen as three coupled Babujian-Taktahjan spin chains with different boundary twists. We compute the ground state short-distance correlation functions of the isotropic model in the thermodynamic limit by exploiting the shared integrable structure between the models.

DOI
10.48550/arxiv.2610.03349

Related papers

Correlation functions of the six-vertex IRF model and its quantum spin chain

Thiago Silva Tavares, G A P Ribeiro

We consider the interaction-round-a-face version of the isotropic six-vertex model. The associated spin chain is made of two coupled Heisenberg spin chains with different boundary twists. The phase diagram of the model and the long distance correlations were studied in Tavares and Ribeiro (2023) [43] . Here, we compute the short-distance correlation functions of the model in the ground state for finite system sizes via non-linear integral equations and in the thermodynamic limit. This was possible since the model satisfies the face version of the discrete quantum Knizhnik-Zamolodchikov (qKZ) equation. A suitable ansatz for the density matrix is proposed in the form of a direct sum of two Heisenberg density matrices, which allows us to obtain the discrete functional equation for the two-site function ω ( λ 1 , λ 2 ) . Thanks to the known results on the factorization of correlation functions of the Heisenberg chain, we are able to compute the density matrix of the IRF model for up to four sites and its associated spin chain for up to three sites.

arXiv:2409.05814•Nuclear Physics B•Oct 17, 2024•1 citation

Finite temperature properties of an integrable zigzag ladder chain

Thiago Silva Tavares, G A P Ribeiro

We consider the interaction-round-a-face version of the six-vertex model for arbitrary anisotropy parameter, which allow us to derive an integrable one-dimensional quantum Hamiltonian with three-spin interactions. We apply the quantum transfer matrix approach for the face model version of the six-vertex model. The integrable quantum Hamiltonian shares some thermodynamical properties with the Heisenberg XXZ chain, but has different ordering and critical exponents. Two gapped phases are the dimerized antiferromagnetic order and the usual antiferromagnetic (Néel) order for positive nearest neighbor Ising coupling. In between these, there is an extended critical region, which is a quantum spin-liquid with broken parity symmetry inducing an oscillatory behavior at the long distance <σ1zσℓ+1z> correlation. At finite temperatures, the numerical solution of the non-linear integral equations allows for the determination of the correlation length as well as for the momentum of the oscillation.

arXiv:2307.11279•Nuclear Physics B•Aug 24, 2023•3 citations

On correlation functions of the open XYZ spin 1/2 chain with boundary fields related by a constraint

Giuliano Niccoli, V. Terras

In this paper, we consider the quantum XYZ open spin-1/2 chain with boundary fields. We focus on the particular case in which the six boundary parameters are related by a single constraint enabling us to describe part of the spectrum by standard Bethe equations. We derive for this model exact representations for a set of elementary blocks of correlation functions, hence generalising to XYZ the results obtained in the XXZ open case in [1]. Our approach is also similar to the approach proposed in the XXZ case [1] : we solve the model by Sklyanin’s version of the quantum Separation of Variables, using Baxter’s Vertex-IRF transformation; in this framework, we identify a basis of local operators with a relatively simple action on the transfer matrix eigenstates; we then use the solution of the quantum inverse problem and our recent formulae on scalar products of separate states [2] to compute some of the corresponding matrix elements, which can therefore be considered as elementary building blocks for the correlation functions. The latter are expressed in terms of multiple sums in the finite chain, and as multiple integrals in the thermodynamic limit. Our results evidence that, once the basis of local operators is properly chosen, the corresponding building blocks for correlation functions have a similar structure in the XXX/XXZ/XYZ open chains, and do not require any insertion of non-local ”tail operators”.

arXiv:2507.20299•Nuclear Physics B•Sep 2, 2026•1 citation

Temperley-Lieb lattice models arising from quantum groups

Murray T. Batchelor, Atsuo Kuniba

The authors construct families of solvable quantum spin chains, vertex and interactions round a face (IRF) models from representations of the Temperley-Lieb algebra associated with the quantum groups U q (X n ) for X n =A 1 , B n , C n and D n . They determine a correlation measuring order in the IRF models via the fusion rule in the level l X n (1) . Wess-Zumino-Witten model.

Journal of Physics A Mathematical and General•Jun 7, 1991•39 citations

Solvable nineteen-vertex models and quantum spin chains of spin one

Makoto Idzumi, Tetsuji Tokihiro, M. Arai

We solved the Yang-Baxter equation for the $R$-matrices of three-state vertex models with ice condition, and obtained a complete list of solvable nineteen-vertex models and associated quantum spin Hamiltonians of spin one.

Journal de Physique I•Aug 1, 1994•25 citations

Interaction-round-a-face density-matrix renormalization-group method applied to rotational-invariant quantum spin chains

Tatsuaki Wada

An interaction-round-a-face density-matrix renormalization-group (IRF-DMRG) method is developed for higher integer spin chain models which are rotational invariant. The expressions of the IRF weights associated with the nearest-neighbor spin-$S$ interaction ${\mathbf{S}}_{i}\ensuremath{\cdot}{\mathbf{S}}_{i+1}$ are explicitly derived. Using the IRF-DMRG with these IRF weights, the Haldane gaps $\ensuremath{\Delta}$ and the ground state energy densities ${e}_{0}$ for both $S=1$ and $S=2$ isotropic antiferromagnetic Heisenberg quantum spin chains are calculated by keeping up to only $m=90$ states.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Mar 1, 2000•34 citations
We consider the interaction-round-a-face version of the nineteen-vertex model and derive a new quantum spin-111 chain. In the isotropic limit, the associated spin chain can be seen as three coupled Babujian-Taktahjan spin chains with different boundary twists. We compute the ground state short-distance correlation functions of the isotropic model in the thermodynamic limit by exploiting the shared integrable structure between the models.
We consider the interaction-round-a-face version of the isotropic six-vertex model. The associated spin chain is made of two coupled Heisenberg spin chains with different boundary twists. The phase diagram of the model and the long distance correlations were studied in Tavares and Ribeiro (2023) [43] . Here, we compute the short-distance correlation functions of the model in the ground state for finite system sizes via non-linear integral equations and in the thermodynamic limit. This was possible since the model satisfies the face version of the discrete quantum Knizhnik-Zamolodchikov (qKZ) equation. A suitable ansatz for the density matrix is proposed in the form of a direct sum of two Heisenberg density matrices, which allows us to obtain the discrete functional equation for the two-site function ω ( λ 1 , λ 2 ) . Thanks to the known results on the factorization of correlation functions of the Heisenberg chain, we are able to compute the density matrix of the IRF model for up to four sites and its associated spin chain for up to three sites.
We consider the interaction-round-a-face version of the six-vertex model for arbitrary anisotropy parameter, which allow us to derive an integrable one-dimensional quantum Hamiltonian with three-spin interactions. We apply the quantum transfer matrix approach for the face model version of the six-vertex model. The integrable quantum Hamiltonian shares some thermodynamical properties with the Heisenberg XXZ chain, but has different ordering and critical exponents. Two gapped phases are the dimerized antiferromagnetic order and the usual antiferromagnetic (Néel) order for positive nearest neighbor Ising coupling. In between these, there is an extended critical region, which is a quantum spin-liquid with broken parity symmetry inducing an oscillatory behavior at the long distance <σ1zσℓ+1z> correlation. At finite temperatures, the numerical solution of the non-linear integral equations allows for the determination of the correlation length as well as for the momentum of the oscillation.
In this paper, we consider the quantum XYZ open spin-1/2 chain with boundary fields. We focus on the particular case in which the six boundary parameters are related by a single constraint enabling us to describe part of the spectrum by standard Bethe equations. We derive for this model exact representations for a set of elementary blocks of correlation functions, hence generalising to XYZ the results obtained in the XXZ open case in [1]. Our approach is also similar to the approach proposed in the XXZ case [1] : we solve the model by Sklyanin’s version of the quantum Separation of Variables, using Baxter’s Vertex-IRF transformation; in this framework, we identify a basis of local operators with a relatively simple action on the transfer matrix eigenstates; we then use the solution of the quantum inverse problem and our recent formulae on scalar products of separate states [2] to compute some of the corresponding matrix elements, which can therefore be considered as elementary building blocks for the correlation functions. The latter are expressed in terms of multiple sums in the finite chain, and as multiple integrals in the thermodynamic limit. Our results evidence that, once the basis of local operators is properly chosen, the corresponding building blocks for correlation functions have a similar structure in the XXX/XXZ/XYZ open chains, and do not require any insertion of non-local ”tail operators”.
We solved the Yang-Baxter equation for the RRR-matrices of three-state vertex models with ice condition, and obtained a complete list of solvable nineteen-vertex models and associated quantum spin Hamiltonians of spin one.
An interaction-round-a-face density-matrix renormalization-group (IRF-DMRG) method is developed for higher integer spin chain models which are rotational invariant. The expressions of the IRF weights associated with the nearest-neighbor spin-SSS interaction ${\mathbf{S}}_{i}\ensuremath{\cdot}{\mathbf{S}}_{i+1}$ are explicitly derived. Using the IRF-DMRG with these IRF weights, the Haldane gaps $\ensuremath{\Delta}$ and the ground state energy densities e0{e}_{0}e0​ for both S=1S=1S=1 and S=2S=2S=2 isotropic antiferromagnetic Heisenberg quantum spin chains are calculated by keeping up to only m=90m=90m=90 states.