Abstract Yang–Baxter integrable vertex models with a generic Z 2 -staggering can be expressed in terms of composite R -matrices given in terms of the elementary R-matrices. Similarly, integrable open boundary conditions can be constructed through generalized reflection algebras based on these objects and their representations in terms of composite boundary matrices K ± . We show that only two types of staggering yield a local Hamiltonian with integrable open boundary conditions in this approach. The staggering in the underlying model allows for a second hierarchy of commuting integrals of motion (in addition to the one including the Hamiltonian obtained from the usual transfer matrix), starting with the so-called quasi momentum operator. In this paper, we show that this quasi momentum operator can be obtained together with the Hamiltonian for both periodic and open models in a unified way from enlarged Yang–Baxter or reflection algebras in the composite picture. For the special case of the staggered six-vertex model, this allows constructing an integrable spectral flow between the two local cases.Abstract Yang–Baxter integrable vertex models with a generic Z 2 -staggering can be expressed in terms of composite R -matrices given in terms of the elementary R-matrices. Similarly, integrable open boundary conditions can be constructed through generalized reflection algebras based on these objects and their representations in terms of composite boundary matrices K ± . We show that only two types of staggering yield a local Hamiltonian with integrable open boundary conditions in this approach. The staggering in the underlying model allows for a second hierarchy of commuting integrals of motion (in addition to the one including the Hamiltonian obtained from the usual transfer matrix), starting with the so-called quasi momentum operator. In this paper, we show that this quasi momentum operator can be obtained together with the Hamiltonian for both periodic and open models in a unified way from enlarged Yang–Baxter or reflection algebras in the composite picture. For the special case of the staggered six-vertex model, this allows constructing an integrable spectral flow between the two local cases.

arXiv:2209.06182Journal of Physics A Mathematical and TheoreticalJan 12, 20238 citations

Aspects of Integrable Models

Costas John Efthimiou

Jan 1, 19940 citations

Open boundary conditions of the $D^{(2)}_3$ spin chain and sectors of conformal field theoriesOpen boundary conditions of the $D^{(2)}_3$ spin chain and sectors of conformal field theories

Pete Rigas

We study open boundary conditions for the $D^{(2)}_3$ spin chain, which shares connections with the six-vertex model, under staggering, and also to the antiferromagnetic Potts model. By formulating a suitable transfer matrix that is related to $K$ matrices and to the Jimbo $R$ -matrix, we obtain an analytical expression for the Hamiltonian, as a logarithmic derivative of the transfer matrix, under open boundary conditions. Such computations have connections with several objects studied in Integrable Probability, which underlie exactly solvable structures.We study open boundary conditions for the $D^{(2)}_3$ spin chain, which shares connections with the six-vertex model, under staggering, and also to the antiferromagnetic Potts model. By formulating a suitable transfer matrix that is related to $K$ matrices and to the Jimbo $R$-matrix, we obtain an analytical expression for the Hamiltonian, as a logarithmic derivative of the transfer matrix, under open boundary conditions. Such computations have connections with several objects studied in Integrable Probability, which underlie exactly solvable structures.

arXiv:2310.18499Oct 27, 20230 citations

Integrable models of coupled Heisenberg chains

Jan 1, 19950 citations

Open boundary conditions of the

D^{(2)}_3

spin chain and sectors of conformal field theories

We study open boundary conditions for the

D^{(2)}_3

spin chain, which shares connections with the six-vertex model, under staggering, and also to the antiferromagnetic Potts model. By formulating a suitable transfer matrix that is related to

K

matrices and to the Jimbo

R

-matrix, we obtain an analytical expression for the Hamiltonian, as a logarithmic derivative of the transfer matrix, under open boundary conditions. Such computations have connections with several objects studied in Integrable Probability, which underlie exactly solvable structures.