相关论文: $U_q(\mathfrak{sl}_n)$ web models and $\mathbb{Z}_…

In our recent work [Phys. Rev. Lett. 102, 230502 (2009)] we showed that the partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), can be…

A connected set in a graph is a non-empty set of vertices that induces a connected subgraph. In an infinite lattice, a connected set is often referred to as a lattice animal, whose enumeration up to isomorphism is a classical problem in…

The diagonalisation of the transfer matrices of solvable vertex models with alternating spins is given. The crystal structure of (semi-)infinite tensor products of finite-dimensional $U_q(\hat{sl}_2)$ crystals with alternating dimensions is…

The work contains a detailed study of the scaling limit of a certain critical, integrable inhomogeneous six-vertex model subject to twisted boundary conditions. It is based on a numerical analysis of the Bethe ansatz equations as well as…

The flow of U(1) charge through dense fishnet diagrams, in a non-hermitian matrix scalar field theory g_1Tr(\Sigma^\dagger\Sigma)^2 + 2g_1vTr\Sigma^{\dagger 2}\Sigma^2, is described by a 6-vertex model on a ``diamond'' lattice [1]. We give…

Based on the tensor network state representation, we develop a nonlinear dynamic theory coined as network contractor dynamics (NCD) to explore the thermodynamic properties of two-dimensional quantum lattice models. By invoking the rank-$1$…

We establish and analyze a new relationship between the matrices describing an arbitrary component of a spin $s$, where $2s\in \mathbb{Z}^+$, and the matrices of $\mathbb{C}P^{2s}$ two-dimensional Euclidean sigma models. The spin matrices…

The random-cluster model with parameters $(p,q)$ is a random graph model that generalizes bond percolation ($q=1$) and the Ising and Potts models ($q\geq 2$). We study its Glauber dynamics on $n\times n$ boxes $\Lambda_{n}$ of the integer…

Two $q$-analogs of the hypercube graph are introduced and shown to be related through a graph quotient. The roles of the subspace lattice graph, of a twisted primitive elements of $U_q(\mathfrak{su}(2))$ and of the dual $q$-Krawtchouk…

We report on the utility of using Shannons Sampling theorem to solve Quantum Mechanical systems. We show that by extending the logic of Shannons interpolation theorem we can define a Universal Lattice Basis, which has superior interpolating…

We calculate the partition function of the $q$-state Potts model on arbitrary-length cyclic ladder graphs of the square and triangular lattices, with a generalized external magnetic field that favors or disfavors a subset of spin values…

We consider a SU(2) lattice gauge theory on the square lattice, with a single fundamental complex fermion and a single fundamental complex boson on each lattice site. Projective symmetries of the gauge-charged fermions are chosen so that…

We employ appropriate realizations of the affine Hecke algebra and we recover previously known non-diagonal solutions of the reflection equation for the $U_{q}(\hat{gl_n})$ case. With the help of linear intertwining relations involving the…

The $N$-state chiral Potts model in lattice statistical mechanics can be obtained as a ``descendant'' of the six-vertex model, via an intermediate ``$Q$'' or ``$\tau_2 (t_q)$'' model. Here we generalize this to obtain a column-inhomogeneous…

In this study, an integrable vertex model based on the quantum affine superalgebra $U_q\bigl(\hat{gl}(2|2)\bigr)$ is constructed. The model is characterized by a particular assignment of spectral parameters and lowest as well as highest…

We use numerical bootstrap techniques to study correlation functions of traceless symmetric tensors of $O(N)$ with two indexes $t_{ij}$. We obtain upper bounds on operator dimensions for all the relevant representations and several values…

We review the construction of exactly solvable lattice models whose continuum limits are $N=2$ supersymmetric models. Both critical and off-critical models are discussed. The approach we take is to first find lattice models with natural…

We formulate a model of relativistic fermions moving in two Euclidean dimensions based on a tight-binding model of graphene. The eigenvalue spectrum of the resulting Dirac operator is solved numerically in smooth U(1) gauge field…

Starting from a Hecke $R-$matrix, Jing and Zhang constructed a new deformation $U_{q}(sl_{2})$ of $U(sl_{2})$, and studied its finite dimensional representations in \cite{JZ}. Especically, this algebra is proved to be just a bialgebra, and…

We introduce a new rotation-invariant web basis for a family of Specht modules $S^{(d^3, 1^{n-3d})}$, indexed by normal plabic graphs satisfying a degree condition and resembling $A_2$ webs. We show that the $\mathfrak{S}_n$ action on our…