相关论文: $U_q(\mathfrak{sl}_n)$ web models and $\mathbb{Z}_…
Using crystal basis, in the space of symmetric irreducible representations, we explicitly write invertible deforming functionals between the q-deformed universal enveloping algebra and the Lie algebras sl(n) and sp(2n).For sl(2) we obtain…
We consider fractal curves in two-dimensional $Z_N$ spin lattice models. These are N states spin models that undergo a continuous ferromagnetic-paramagnetic phase transition described by the ZN parafermionic field theory. The main…
The U(N) gauge theory on a D-dimensional lattice is reformulated as a theory of lattice strings (a statistical model of random surfaces). The Boltzmann weights of the surfaces can have both signs and are tuned so that the longitudinal modes…
We give a diagrammatic presentation in terms of generators mod relations of the representation category of $U_q(\mathfrak{sl}_n)$. More precisely, we produce all the relations among $\rm{SL}_n$-webs, thus describing the full subcategory…
In this article we give new examples of models in boundary quantum field theory, i.e. local time-translation covariant nets of von Neumann algebras, using a recent construction of Longo and Witten, which uses a local conformal net A on the…
We study the loop $O(n)$ model on the honeycomb lattice. By means of local non-planar deformations of the lattice, we construct a discrete stress-energy tensor. For $n\in [0,2]$, it gives a new observable satisfying a part of Cauchy-Riemann…
The path space of an inhomogeneous vertex model constructed from the vector representation of $U_q\bigl(gl(2|2)\bigr)$ and its dual is studied for various choices of composite vertices and assignments of $gl(2|2)$-weights. At $q=0$, the…
We present a simple lattice formulation of two-dimensional $\mathcal{N}=(2,2)$ $U(k)$ supersymmetric QCD (SQCD) with $N$ matter multiplets in the fundamental representation. The construction uses compact gauge link variables and exactly…
We introduce a numerical linked cluster expansion for square-lattice models whose building block is an L-shape cluster. For the spin-1/2 models studied in this work, we find that this expansion exhibits a similar or better convergence of…
We give general conditions for the existence of a Hamiltonian operator whose discrete time evolution matches the partition function of certain solvable lattice models. In particular, we examine two classes of lattice models: the classical…
We consider the quantum spin ice models in the planar pyrochlore lattice. The models are obtained by perturbing the Ising model with different lattice symmetry preserving quantum fluctuations. We map these models to a compact U(1) lattice…
A treatment of the spin-statistics relation in nonrelativistic quantum mechanics due to Berry and Robbins [Proc. R. Soc. Lond. A (1997) 453, 1771-1790] is generalised within a group-theoretical framework. The construction of Berry and…
We comment on the relationships between several supersymmetric lattice models; the ``orbifold lattice theory'' by Cohen-Kaplan-Katz-Unsal (CKKU), lattice regularization of the topological field theory by Sugino and the ``geometrical…
We consider partition functions on the $N\times N$ square lattice with the local Boltzmann weights given by the $R$-matrix of the $U_{t}(\widehat{sl}(n+1|m))$ quantum algebra. We identify boundary states such that the square lattice can be…
A relation between a class of stationary points of the energy landscape of continuous spin models on a lattice and the configurations of a Ising model defined on the same lattice suggests an approximate expression for the microcanonical…
We present preliminary numerical results from a lattice study of the two-dimensional O(3) non-linear sigma model. In the continuum this model possesses N=2 supersymmetry. The lattice formulation we use retains an exact (twisted)…
It has been conjectured that the two-dimensional N=2 Wess-Zumino model with a quasi-homogeneous superpotential provides the Landau-Ginzburg description of the N=2 superconformal minimal models. For the cubic superpotential W=(lambda)…
We introduce a half-filled Hamiltonian of spin-half lattice fermions that can be studied with the efficient meron-cluster algorithm in any dimension. As with the usual bipartite half-filled Hubbard models, the na\"ive $U(2)$ symmetry is…
Motivated by the prospect of quantum simulation of quantum field theories, we formulate the $O(N)$ nonlinear sigma model as a "qubit" model with an $(N+1)$-dimensional local Hilbert space at each lattice site. Using an efficient worm…
Domain wall junctions are studied in N=2 supersymmetric U(Nc) gauge theory with Nf(>Nc) flavors. We find that all three possibilities are realized for positive, negative and zero junction charges. The positive junction charge is found to be…