We consider the physical combinatorics of critical lattice models and their associated conformal field theories arising in the continuum scaling limit. As examples, we consider A-type unitary minimal models and the level-1 sl(2) Wess-Zumino-Witten (WZW) model. The Hamiltonian of the WZW model is the Uq(sl(2)) invariant XXX spin chain. For simplicity, we consider these theories only in their vac...

A simple Mathematica code based on the differential realization of hard-core boson operators for finding exact solutions of the periodic-N spin-1/2 systems with or beyond nearest neighbor interactions is proposed, which can easily be used to study general spin-1/2 interaction systems. As an example, The code is applied to study XXX spin-1/2 chain with nearest neighbor interaction in a uniform t...

Renormalization of twist-three operators and integrable lattice models. Abstract We address the problem of solution of the QCD three-particle evolution equations which govern the Q 2-dependence of the chiral-even quark-gluon-quark and three-gluon correlators contributing to a number of asymmetries at leading order and the transversely polarized structure function g 2 (x Bj). The quark-gluon-qua...

We investigate the exact overlaps between eigenstates of integrable spin chains and a special class states called “integrable initial/final states”. These satisfy integrability constraint, they are closely related to boundary conditions. derive new algebraic relations for states, which lead set recursion overlaps. solve these thus we overlap formulas, valid in XXX Heisenberg chain its higher ge...

Renormalization of twist-three operators and integrable lattice models. Abstract We address the problem of solution of the QCD three-particle evolution equations which govern the Q 2-dependence of the chiral-even quark-gluon-quark and three-gluon correlators contributing to a number of asymmetries at leading order and the transversely polarized structure function g 2 (x Bj). The quark-gluon-qua...

This article explores the concurrence, including entanglement, in a two-qubit Heisenberg XXX chain with Dzyaloshinskii-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions. The concurrence expression was developed using physical variables connected chosen system. Our results indicate that temperature, spin coupling constant $J$, x-components $D_x$, $\Gamma_x$ may all play role determi...

Renormalization of twist-three operators and integrable lattice models. Abstract We address the problem of solution of the QCD three-particle evolution equations which govern the Q 2-dependence of the chiral-even quark-gluon-quark and three-gluon correlators contributing to a number of asymmetries at leading order and the transversely polarized structure function g 2 (x Bj). The quark-gluon-qua...

Generative neural samplers offer a complementary approach to Monte Carlo methods for problems in statistical physics and quantum field theory. This work tests the ability of generative estimate observables real-world low-dimensional spin systems. It maps out how autoregressive models can sample configurations Heisenberg chain via classical approximation based on Suzuki-Trotter transformation. W...

We present a detailed analysis of the structure of the conservation laws in quantum integrable chains of the XYZ-type and in the Hubbard model. The essential tool for the former class of models is the boost operator, which provides a recursive way of calculation of the integrals of motion. With its help, we establish the general form of the XYZ conserved charges in terms of simple polynomials i...

A new recursion formula is presented for the correlation functions of the integrable spin 1/2 XXX chain with inhomogeneity. It relates the correlators involving n consecutive lattice sites to those with n− 1 and n− 2 sites. In a series of papers by V. Korepin and two of the present authors, it was discovered that the correlators have a certain specific structure as functions of the inhomogeneit...