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This thesis expands the available techniques at weak coupling by investigating the linear space of Feynman integrals and the role that (super)symmetry plays in reducing the number of integrals necessary to calculate correlators in the…
We extend the previous study of extracting crystalline symmetry-protected topological invariants to the correlated regime. We construct the interacting Hofstadter model defined on square lattice with the rotation and translation symmetry…
We study a model of densely packed self-avoiding loops on the annulus, related to the Temperley Lieb algebra with an extra idempotent boundary generator. Four different weights are given to the loops, depending on their homotopy class and…
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…
Using transfer-matrix extended phenomenological renormalization-group methods [M.A.Yurishchev, Nucl. Phys. B (Proc. Suppl.) 83-84, 727 (2000); hep-lat/9908019; J. Exp. Theor. Phys. 91, 332 (2000); cond-mat/0108002] the improved estimates…
The six-vertex F model on the square lattice constitutes the unique example of an exactly solved model exhibiting an infinite-order phase transition of the Kosterlitz-Thouless type. As one of the few non-trivial exactly solved models, it…
This work analyzes a percolation model on the diamond hierarchical lattice (DHL), where the percolation transition is retarded by the inclusion of a probability of erasing specific connected structures. It has been inspired by the recent…
We solve the classical square-lattice dimer model with periodic boundaries and in the presence of a field $\boldsymbol{t}$ that couples to the (vector) flux, by diagonalizing a modified version of Lieb's transfer matrix. After deriving the…
We construct perturbation series for the q-th moment of eigenfunctions of various critical random matrix ensembles in the strong multifractality regime close to localization. Contrary to previous investigations, our results are valid in the…
We build the trigonometric solutions of the Yang-Baxter equation that can not be obtained from quantum groups in any direct way. The solution is obtained using the construction suggested recently from the rational conformal field theory…
We study the null dipole deformation of N=4 super Yang-Mills theory, which is an example of a potentially solvable "dipole CFT": a theory that is non-local along a null direction, has non-relativistic conformal invariance along the…
In this article, we introduce endocabling as a technique to deform involutive, non-degenerate set-theoretic solutions to the Yang-Baxter equation (``solutions'', for short) by means of $\lambda$-endomorphisms of their associated permutation…
We use the formalism of strange correlators to construct a critical classical lattice model in two dimensions with the \emph{Haagerup fusion category} $\mathcal{H}_3$ as input data. We present compelling numerical evidence in the form of…
We consider a unitary circuit where the underlying gates are chosen to be R-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer…
In this work, we study the transmission properties of one dimensional finite periodic systems with $\mathcal{PT}$-symmetry. A simple closed form expression is obtained for the total transmittance from a lattice of N cells, that allows us to…
This thesis describes the development of the density matrix embedding theory (DMET) and its applications to lattice strongly correlated electron problems, including a review of DMET theory and algorithms (Ch 2), investigation of finite size…
This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…
Jamming and percolation transitions in the standard random sequential adsorption of particles on regular lattices are characterized by a universal set of critical exponents. The universality class is preserved even in the presence of…
We consider (a) the partition functions of the anisotropic dimer model on the rectangular (2M-1) x (2N-1) lattice with free and cylindrical boundary conditions with a single monomer residing on the boundary and (b) the partition function of…
An infinite number of spin chains are solved and it is derived that the ground-state phase transitions belong to the universality classes with central charge c=m/2, where m is an integer. The models are diagonalized by automatically…