Related papers: Integrable quantum spin chains and their classical…
We examine certain classical continuum long wave-length limits of prototype integrable quantum spin chains. We define the corresponding construction of classical continuum Lax operators. Our discussion starts with the XXX chain, the…
We study the integrable boundaries and crosscaps of classical sigma models. We show that there exists a classical analog of the integrability condition and KT-relation of the boundary and crosscap states of quantum spin chains. We also…
Exploiting the quantum integrability condition we construct an ancestor model associated with a new underlying quadratic algebra. This ancestor model represents an exactly integrable quantum lattice inhomogeneous anisotropic model and at…
We describe random loop models and their relations to a family of quantum spin systems on finite graphs. The family includes spin 1/2 Heisenberg models with possibly anisotropic spin interactions and certain spin 1 models with…
This note is a review of the recently revealed intriguing connection between integrable quantum spin chains and integrable many-body systems of classical mechanics. The essence of this connection lies in the fact that the spectral problem…
Heisenberg-type higher order symmetries are studied for both classical and quantum mechanical systems separable in cartesian coordinates. A few particular cases of this type of superintegrable systems were already considered in the…
Type-I quantum impurities are investigated in the context of the integrable Heisenberg model. This type of defects is associated to the (q)-harmonic oscillator algebra. The transmission matrices associated to this particular type of defects…
A large (infinitely-dimensional) class of completely integrable (possibly non-autonomous) spin chains is discovered associated to an infinite-dimensional Lie Algebra of infinite rank. The complete set of integrals of motion is constructed…
An explicit expression for all the quantum integrals of motion for the isotropic Heisenberg $s=1/2$ spin chain is presented. The conserved quantities are expressed in terms of a sum over simple polynomials in spin variables. This…
Quantum spin chains are prototype quantum many-body systems. They are employed in the description of various complex physical phenomena. The goal of this paper is to provide an introduction to the subject by focusing on the time evolution…
In this letter we present a general classification of integrable models of identical classical spins coupled via the isotropic Heisenberg Hamiltonian. Our constructive proof of integrability provides a solution scheme for the equations…
A quantum computing circuit is presented that approximates a single spin wave quantum on a linear chain of spin 1/2 particles described by a Heisenberg Hamiltonian. The circuit is a product state where each qubit represents a spin. The spin…
In this letter, I develop a new topologically invariant coherent state path integral for spin systems, and apply it to the quantum Heisenberg model on a square lattice. As a result, the quantum nonlinear $\sigma$ model for arbitrary values…
We study the structure of the spectrum of the infinite XXZ quantum spin chain, an anisotropic version of the Heisenberg model. The XXZ chain Hamiltonian preserves the number of down spins (or particle number), allowing to represent it as a…
We present a general method of folding an integrable spin chain, defined on a line, to obtain an integrable open spin chain, defined on a half-line. We illustrate our method through two fundamental models with sl(2) Lie algebra symmetry:…
It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also…
We derive an explicit mapping between the spectra of conserved local operators of integrable quantum lattice models and the density distributions of their thermodynamic particle content. This is presented explicitly for the Heisenberg XXZ…
We investigate classes of quantum Heisenberg spin systems which have different coupling constants but the same energy spectrum and hence the same thermodynamical properties. To this end we define various types of isospectrality and…
In this paper, we develop the framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show that they occur naturally in the…
We investigate certain classes of integrable classical or quantum spin systems. The first class is characterized by the recursively defined property $P$ saying that the spin system consists of a single spin or can be decomposed into two…