相关论文: Classification of Solutions to Reflection Equation…
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…
Yang-Baxter integrable vertex models with a generic $\mathbb{Z}_2$-staggering can be expressed in terms of composite $\mathbb{R}$-matrices given in terms of the elementary $R$-matrices. Similarly, integrable open boundary conditions can be…
We consider the six-vertex model on an $N \times N$ square lattice with the domain wall boundary conditions. Boundary one-point correlation functions of the model are expressed as determinants of $N\times N$ matrices, generalizing the known…
We propose a scheme for constructing classical spin Hamiltonians from Hunds coupled spin-fermion models in the limit J_H/t \to \infinity. The strong coupling between fermions and the core spins requires self-consistent calculation of the…
We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r)…
We study the scattering theory for the Gross-Neveu model on the half-line. We find the reflection matrices for the elementary fermions, and by fusion we compute the ones for the two-particle bound-states, showing that they satisfy…
Quantum affine reflection algebras are coideal subalgebras of quantum affine algebras that lead to trigonometric reflection matrices (solutions of the boundary Yang-Baxter equation). In this paper we use the quantum affine reflection…
We use boundary quantum group symmetry to obtain recursion formulas which determine nondiagonal solutions of the boundary Yang-Baxter equation (reflection equation) of the XXZ type for any spin j.
We show that reflection symmetry has a strong influence on quantum transport properties. Using a random S-matrix theory approach, we derive the weak-localization correction, the magnitude of the conductance fluctuations, and the…
A strongly correlated electron system associated with the quantum superalgebra ${U}_q[{osp}(2|2)]$ is studied in the framework of the quantum inverse scattering method. By solving the graded reflection equation, two classes of…
A class of recently introduced su(n) `free-fermion' models has recently been used to construct generalized Hubbard models. I derive an algebra defining the `free-fermion' models and give new classes of solutions. I then introduce a…
It is shown that the eigenproblem of any $2\times 2$ matrix Hamiltonian with discrete eigenvalues is involved with a supersymmetric quantum mechanics. The energy dependence of the superalgebra marks the disparity between the deduced…
It is known that a solution of the tetrahedron equation generates infinitely many solutions of the Yang-Baxter equation via suitable reductions. In this paper this scheme is applied to an oscillator solution of the tetrahedron equation…
The theory of generalized Weyl algebras is used to study the $2\times 2$ reflection equation algebra $\mathcal{A}=\mathcal{A}_q(\operatorname{M}_2)$ in the case that $q$ is not a root of unity, where the $R$-matrix used to define…
Motivated by a study of the crossing symmetry of the `gemini' representation of the affine Hecke algebra we give a construction for crossing tensor space representations of ordinary Hecke algebras. These representations build solutions to…
We prove that the category of systems of sesquilinear forms over a given hermitian category is equivalent to the category of unimodular 1-hermitian forms over another hermitian category. The sesquilinear forms are not required to be…
We analyze the validity of reflection positivity in the classification of invertible phases of quantum spin systems. We provide a mathematical model in which every 2d invertible state admits a reflection-positive representative. We prove…
An asymptotic theory is developed for general non-integrable boundary quantum field theory in 1+1 dimensions based on the Langrangean description. Reflection matrices are defined to connect asymptotic states and are shown to be related to…
It is shown that dimers is Yang-Baxter integrable as a six-vertex model at the free-fermion point with crossing parameter $\lambda=\tfrac{\pi}{2}$. A one-to-many mapping of vertex onto dimer configurations allows the free-fermion solutions…
Large families of Hamiltonians that are non-Hermitian in the conventional sense have been found to have all eigenvalues real, a fact attributed to an unbroken PT symmetry. The corresponding quantum theories possess an unconventional scalar…