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We discuss the extent to which solutions to one-phase free boundary problems can be characterized according to their topological complexity. Our questions are motivated by fundamental work of Luis Caffarelli on free boundaries and by…
We study operators with large internal charge in boundary conformal field theories (BCFTs) with internal symmetries. Using the state-operator correspondence and the existence of a macroscopic limit, we find a non-trivial relation between…
We present some open problems in the field of exactly solvable models. Two of the problems are related to the correlation functions of the XXX spin chain and the XXZ spin chain, one to the entropy of subsystems and one to the six vertex…
Intertwiners between \ade lattice models are presented and the general theory developed. The intertwiners are discussed at three levels: at the level of the adjacency matrices, at the level of the cell calculus intertwining the face…
An interacting spin-fermion model is exactly solved on an open chain. In a certain representation, it is the nearest-neighbor Hubbard model in the limit of infinite $U$ (local interaction). Exact solution of its complete energy…
This short paper proposes to learn models of satisfiability modulo theories (SMT) formulas during solving. Specifically, we focus on infinite models for problems in the logic of linear arithmetic with uninterpreted functions (UFLIA). The…
This thesis considers massive field theories in 1+1 dimensions known as affine Toda quantum field theories. We first consider the boundary sine-Gordon model, deriving a complete picture of the boundary bound state structure for general…
Fusion rules among irreducible modules of the free bosonic orbifold vertex operator algebra are completely determined.
Exact expressions of the boundary state and the form factors of the Ising model are used to derive differential equations for the one-point functions of the energy and magnetization operators of the model in the presence of a boundary…
A systematic procedure to derive exact solutions of the associated Lame equation for an arbitrary value of the energy is presented. Supersymmetric transformations in which the seed solutions have factorization energies inside the gaps are…
In this paper the exact solution and correlation functions for a double-chain Ising model with multi-spin interactions and symmetric Hamiltonian density are obtained. The study employs the transfer matrix method to derive fundamental…
Grand Unified Theories based on the group SO(10) generically provide interesting and testable relations between the charged fermions and neutrino sector masses and mixings. In the light of the recent neutrino data, we reexamine these…
We study the conformal field theory of a free massless scalar field living on the half line with interactions introduced via a periodic potential at the boundary. An SU(2) current algebra underlies this system and the interacting boundary…
We employ the density matrix renormalization group to construct the exact time-dependent exchange correlation potential for an impurity model with an applied transport voltage. Even for short-ranged interaction we find an infinitely…
The free energy of the Penner model is shown to be closely related to the integral over the two diagonalizing unitary matrices of a complex rectangular matrix.
We present a brief review on integrability of multispecies zero range process in one dimension introduced recently. The topics range over stochastic $R$ matrices of quantum affine algebra $U_q (A^{(1)}_n)$, matrix product construction of…
We obtain general solutions for some flat Friedmann universes filled with a scalar field in induced gravity models and models including the Hilbert-Einstein curvature term plus a scalar field conformally coupled to gravity. As is well…
We introduce and solvev a special family of integrable interacting vertex models that generalizes the well known six-vertex model. In addition to the usual nearest-neighbor interactions among the vertices, there exist extra hard-core…
Critical systems are described by conformal field theories, whose dynamics can be exactly solved in two dimensions. In the presence of a boundary, with the so-called method of images it is possible to study the surface critical behaviour of…
An original boundary integral formulation is proposed for the problem of a semi-infinite crack at the interface between two dissimilar elastic materials in the presence of heat flows and mass diffusion. Symmetric and skew-symmetric weight…