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We translate effectively our earlier quantum constructions to the classical language and using Yang-Baxterisation of the Faddeev-Reshetikhin-Takhtajan algebra are able to construct Lax operators and associated $r$-matrices of classical…
In this contribution we review the theory of integrability of quantum systems in one spatial dimension. We introduce the basic concepts such as the Yang-Baxter equation, commuting currents, and the algebraic Bethe ansatz. Quite extensively…
The relation between the Seiberg-Witten prepotentials, Nekrasov functions and matrix models is discussed. We derive quasiclassically the matrix models of Eguchi-Yang type, describing the instantonic contribution to the deformed partition…
We introduce lattice models with explicit N=2 supersymmetry. In these interacting models, the supersymmetry generators Q^+ and Q^- yield the Hamiltonian H={Q^+,Q^-} on any graph. The degrees of freedom can be described as either fermions…
Using the density matrix renormalization group technique, we study spin superlattices composed of a repeated pattern of two spin-1/2 XXZ chains with different anisotropy parameters. The magnetization curve can exhibit two plateaus, a non…
Using the Jordan-Wigner fermionization in two dimensions we obtain the zz wave vector- and frequency-dependent structure factor for the spin-1/2 isotropic XY model on a spatially anisotropic square lattice. We use the obtained results to…
Here we consider a class of energy eigenstates of the spin-1/2 XXZ chain that exist both for anisotropies 1 and larger than 1. We show that at the isotropic point their contributions are behind the diffusion constant being infinite, spin…
We study the topological properties of a spin-orbit coupled Hofstadter model on the Kagome lattice. The model is time-reversal invariant and realizes a $\mathbb{Z}_2$ topological insulator as a result of artificial gauge fields. We develop…
The spin-1/2 XXZ Heisenberg chain with two types of boundary terms is considered. For the first type, the Hamiltonian is hermitian but not for the second type which includes the U_{q}[SU(2)] symmetric case. It is shown that for a certain…
The magnetization process of the $S=1/2$ anisotropic spin ladder with the ferromagnetic rung interaction is investigated using the numerical diagonalization of finite-size clusters. It is found that the translational symmetry broken…
We study the spin-1/2 Ising-XXZ model on a decorated honeycomb lattice composed of five spins per unit cell, one Ising spin, and four Heisenberg spins. This model involving the Heisenberg exchange interaction is one of the few models that…
We introduce novel polynomial deformations of the Lie algebra $sl(2)$. We construct their finite-dimensional irreducible representations and the corresponding differential operator realizations. We apply our results to a class of spin…
We show that the honeycomb tight-binding model hosts an exact microscopic avatar of its low-energy SU(2) valley symmetry and parity anomaly. Specifically, the SU(2) valley symmetry arises from a collection of conserved, integer quantized…
We consider spin chain models with exotic symmetries that change the length of the spin chain. It is known that the XXZ Heisenberg spin chain at the supersymmetric point $\Delta=-1/2$ possesses such a symmetry: it is given by the…
Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter, and quantum information science. Their local symmetries enforce the charge conservation observed in the laws of physics. Impressive…
A class of kinetically constrained models with reflection symmetry is proposed as an extension of the Fredrickson-Andersen model. It is proved that the proposed model on the square lattice exhibits a freezing transition at a non-trivial…
We study the higher spin anologs of the six vertex model on the basis of its symmetry under the quantum affine algebra $U_q(\slth)$. Using the method developed recently for the XXZ spin chain, we formulate the space of states, transfer…
The bootstrap programme for finding exact S-matrices of integrable quantum field theories with N=1 supersymmetry is investigated. New solutions are found which have the same fusing data as bosonic theories related to the classical affine…
This paper is part of an effort to gain further understanding of 2D Logarithmic Conformal Field Theories (LCFTs) by exploring their lattice regularizations. While all work so far has dealt with the Virasoro algebra (or the product of left…
The characterization of quantum spin liquid phases in Kitaev materials has been a subject of intensive studies over the recent years, both theoretically and experimentally. Most theoretical studies have focused on an isotropically…