相关论文: Spectral Decomposition of Path Space in Solvable L…

We study one-dimensional reaction-diffusion models described by master equations and their associated two-state quantum Hamiltonians. By choosing appropriate rates, the equations of motion decouple into certain subsets. We solve the first…

We consider a tensor product $V(b)= \otimes_{i=1}^n\C^N(b_i)$ of the Yangian $Y(gl_N)$ evaluation vector representations. We consider the action of the commutative Bethe subalgebra $B^q \subset Y(gl_N)$ on a $gl_N$-weight subspace…

Planar N=4 super Yang-Mills appears to be integrable. While this allows to find this theory's exact spectrum, integrability has hitherto been of no direct use for scattering amplitudes. To remedy this, we deform all scattering amplitudes by…

Lattice modes are intrinsic to the periodic structures and their occurrence can be easily tuned and controlled by changing the lattice constant of the structural array. Previous studies have revealed excitation of sharp absorption…

We study a new integrable probabilistic system, defined in terms of a stochastic colored vertex model on a square lattice. The main distinctive feature of our model is a new family of parameters attached to diagonals rather than to rows or…

A path-integral representation for the kernel of the evolution operator of general Hamiltonian systems is reviewed. We study the models with bosonic and fermionic degrees of freedom. A general scheme for introducing boundary conditions in…

By ungauging a recently discovered lattice rotor model for Chern-Simons theory, we create an exactly soluble path integral on spacetime lattice for $U^\kappa(1)$ Symmetry Protected Topological (SPT) phases in $2+1$ dimensions with a…

A lattice model of interacting q-oscillators, proposed in [V. Bazhanov, S. Sergeev, arXiv:hep-th/0509181], is the quantum mechanical integrable model in 2+1 dimensional space-time. Its layer-to-layer transfer-matrix is a polynomial of two…

We study spaces of conformal blocks associated with line bundles over elliptic curves, with coefficients in a vertex algebra. For vertex algebras satisfying suitable finiteness and semisimplicity conditions, which are met by all admissible…

We present results from lattice simulations of ${\cal N}=2$ super Yang-Mills theory in two dimensions. The lattice formulation we use was developed in \cite{2dpaper} and retains both gauge invariance and an exact (twisted) supersymmetry for…

We derive a bosonic formula for the character of the principal space in the level $k$ vacuum module for $\widehat{\mathfrak{sl}}_{n+1}$, starting from a known fermionic formula for it. In our previous work, the latter was written as a sum…

A doublet of three-dimensional Dirac fermions can effectively describe the low energy spectrum of a fermionic cubic lattice. We employ this fermion doubling to encode a non-Abelian SU(2) charge in the fundamental representation. We…

Overlap fermions preserve a remnant of chiral symmetry on the lattice. They are a powerful tool to investigate the topological structure of the vacuum of Yang-Mills theory and full QCD. Recent results concerning the localization of…

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…

We investigate the spectral properties and dynamical features of a time-periodic PT-symmetric Hamiltonian on a one-dimensional tight-binding lattice. It is shown that a high-frequency modulation can drive the system under a transition…

I choose the Lee-Yang model and go through different approaches to analyze it using the form factor approach and the bootstrap program, the lattice description and the lattice TBA equations for a full understanding of the model. The…

We obtain a closed form expression for the energy spectrum of $\mathcal{P}\mathcal{T}$-symmetric superlattice systems with complex potentials of periodic sets of two $\delta$-potentials in the elementary cell. In the presence of periodic…

In this paper, we introduce a combinatorial path model of representation of the quantum affine algebra of type $D_n$, inspired by Mukhin and Young's combinatorial path models of representations of the quantum affine algebras of types $A_n$…

We address the novel structures arising in quantum and string integrable theories, as well as construct methods to obtain them and provide further analysis. Specifically, we implement the automorphic symmetries on periodic lattice systems…

Efficient deterministic algorithms to construct representations of lattice path matroids over finite fields are presented. They are built on known constructions of hierarchical secret sharing schemes, a recent characterization of…