Related papers: Integrable Lattice Models for Conjugate $A^{(1)}_n…
Over the past few years it has been discovered that an "observable" can be set up on the lattice which obeys the discrete Cauchy-Riemann equations. The ensuing condition of discrete holomorphicity leads to a system of linear equations which…
Lattice systems with certain Lie algebraic or quantum Lie algebraic symmetries are constructed. These symmetric models give rise to series of integrable systems. As examples the $A_n$-symmetric chain models and the SU(2)-invariant ladder…
We obtain off-critical (elliptic) Boltzmann weights for lattice models whose continuum limits correspond to massive, $N=2$ supersymmetric, quantum integrable field theories. We also compute the free energies of these models and show that…
In this paper we present a new series of 3-dimensional integrable lattice models with $N$ colors. The case $N=2$ generalizes the elliptic model of our previous paper. The weight functions of the models satisfy modified tetrahedron equations…
We define an infinite class of ``frustration-free'' interacting lattice quantum Hamiltonians for bosons, constructed such that their exact ground states have a density distribution specified by the Boltzmann weight of a corresponding…
Exploiting the quantum integrability condition we construct an ancestor model associated with a new underlying quadratic algebra. This ancestor model represents an exactly integrable quantum lattice inhomogeneous anisotropic model and at…
Some features of integrable lattice models are reviewed for the case of the six-vertex model. By the Bethe ansatz method we derive the free energy of the six-vertex model. Then, from the expression of the free energy we show analytically…
We introduce a class of new integrable lattice models labeled by a pair of positive integers N and r. The integrable model is obtained from the Gauge/YBE correspondence, which states the equivalence of the 4d N=1 S^1 \times S^3/Z_r index of…
In this paper we formulate a new N-state spin integrable model on a three-dimensional lattice with spins interacting round each elementary cube of the lattice. This model can be also reformulated as a vertex type model. Weight functions of…
Given an integral lattice $\Lambda$ of rank $n$ and a finite sequence $m_1 \leq m_2 \leq ... \leq m_k$ of natural numbers we construct a modular form $\Theta_{m_1,m_2,...,m_k,\Lambda}$ of level $N=N(\Lambda)$. The weight of this modular…
In this paper, we explore the relationship between integrability and the discrete holomorphicity of a class of complex lattice observables in the context of the Potts dense loop model and the O(n) dilute loop model. It is shown that the…
A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the…
Applying a unifying Lax operator approach to statistical systems a new class of integrable vertex models based on quantum algebra is proposed, which exhibits a rich variety for generic q, q roots of unity and q -> 1. Exact solutions are…
A standard combinatorial construction, due to Kontsevich, associates to any A-infinity algebra with an invariant inner product, an inhomogeneous class in the cohomology of the moduli spaces of Riemann surfaces with marked points. We…
We study a hermitian $(n+1)$-matrix model with plaquette interaction, $\sum_{i=1}^n MA_iMA_i$. By means of a conformal transformation we rewrite the model as an $O(n)$ model on a random lattice with a non polynomial potential. This allows…
In this paper we introduce a new class of integrable 3D lattice models, possessing continuous families of commuting layer-to-layer transfer matrices. Algebraically, this commutativity is based on a very special construction of local…
We review and give detailed description for ${\rm gl}_{NM}$ Gaudin models related to holomorphic vector bundles of rank $NM$ and degree $N$ over elliptic curve with $n$ punctures. Then we introduce their generalizations constructed by means…
We study a system of functional relations among a commuting family of row-to-row transfer matrices in solvable lattice models. The role of exact sequences of the finite dimensional quantum group modules is clarified. We find a curious…
This note gives a general construction of an integrable lattice model (and a solution of the Yang-Baxter equation with spectral parameter) from a four-dimensional field theory which is a mixture of topological and holomorphic. Spin-chain…
Applying braided Yang-Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and $q$-anyonic models as well as nonlinear…