scholarly journals Quantum Spin Chains and Integrable Many-Body Systems of Classical Mechanics

2015 ◽  
pp. 29-48 ◽  
Author(s):  
A. Zabrodin
Keyword(s):  
Classical Mechanics ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Many Body ◽  
Many Body Systems

Quantum spin chains and classical integrable systems

2018 ◽  
Author(s):  
Anton Zabrodin
Keyword(s):  
Integrable Systems ◽  
Quantum Spin ◽  
Spin Chains ◽  
Algebraic Equations ◽  
Quantum Spin Chains ◽  
Many Body ◽  
Finite Dimensional ◽  
The Family ◽  
Classical Correspondence ◽  
Remarkable Relation

This chapter is a review of the recently established quantum-classical correspondence for integrable systems based on the construction of the master T-operator. For integrable inhomogeneous quantum spin chains with gl(N)-invariant R-matrices in finite-dimensional representations, the master T-operator is a sort of generating function for the family of commuting quantum transfer matrices depending on an infinite number of parameters. Any eigenvalue of the master T-operator is the tau-function of the classical modified KP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0th time of the hierarchy. This implies a remarkable relation between the quantum spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, a system of algebraic equations can be obtained for the spectrum of the spin chain Hamiltonians.

scholarly journals On Many-Body Localization for Quantum Spin Chains

2016 ◽  
Vol 163 (5) ◽  
pp. 998-1048 ◽  
Author(s):  
John Z. Imbrie
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Many Body

scholarly journals A sufficient criterion for integrability of stochastic many-body dynamics and quantum spin chains

2002 ◽  
Vol 35 (33) ◽  
pp. 7187-7204 ◽  
Author(s):  
Vladislav Popkov ◽  
M Ebrahim Fouladvand ◽  
Gunter M Sch$uuml$tz
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Many Body ◽  
Sufficient Criterion ◽  
Body Dynamics

scholarly journals Ballistic transport and boundary resistances in inhomogeneous quantum spin chains

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Alberto Biella ◽  
Mario Collura ◽  
Davide Rossini ◽  
Andrea De Luca ◽  
Leonardo Mazza
Keyword(s):  
Ballistic Transport ◽  
Quantum Spin ◽  
Spin Chains ◽  
Matrix Product ◽  
Relaxation Dynamics ◽  
Quantum Spin Chains ◽  
Many Body ◽  
Matrix Product State ◽  
The Many ◽  
Local Defects

Abstract Transport phenomena are central to physics, and transport in the many-body and fully-quantum regime is attracting an increasing amount of attention. It has been recently revealed that some quantum spin chains support ballistic transport of excitations at all energies. However, when joining two semi-infinite ballistic parts, such as the XX and XXZ spin-1/2 models, our understanding suddenly becomes less established. Employing a matrix-product-state ansatz of the wavefunction, we study the relaxation dynamics in this latter case. Here we show that it takes place inside a light cone, within which two qualitatively different regions coexist: an inner one with a strong tendency towards thermalization, and an outer one supporting ballistic transport. We comment on the possibility that even at infinite time the system supports stationary currents and displays a non-zero Kapitza boundary resistance. Our study paves the way to the analysis of the interplay between transport, integrability, and local defects.

Introduction to Integrable Many-Body Systems II

2010 ◽  
Vol 60 (2) ◽  
Author(s):  
Ladislav Šamaj
Keyword(s):  
Bethe Ansatz ◽  
Ground State ◽  
Quantum Spin ◽  
Spin Chains ◽  
Scattering Method ◽  
Heisenberg Chain ◽  
Many Body ◽  
Xxz Model ◽  
The Subject ◽  
Many Body Systems

Introduction to Integrable Many-Body Systems IIThis is the second part of a three-volume introductory course about integrable systems of interacting bodies. The models of interest are quantum spin chains with nearest-neighbor interactions between spin operators, in particular Heisenberg spin-1/2 models. The Ising model in a transverse field, expressible as a quadratic fermion form by using the Jordan-Wigner transformation, is the subject of Sect. 12. The derivation of the coordinate Bethe ansatz for the XXZ Heisenberg chain and the determination of its absolute ground state in various regions of the anisotropy parameter are presented in Sect. 13. The magnetic properties of the ground state are explained in Sect. 14. Sect. 15 concerns excited states and the zero-temperature thermodynamics of the XXZ model. The thermodynamics of the XXZ Heisenberg chain is derived on the basis of the string hypothesis in Sect. 16; the thermodynamic Bethe ansatz equations are analyzed in high-temperature and low-temperature limits. An alternative derivation of the thermodynamics without using strings, leading to a non-linear integral equation determining the free energy, is the subject of Sect. 17. A nontrivial application of the Quantum Inverse Scattering method to the fully anisotropic XYZ Heisenberg chain is described in Sect. 18. Sect. 19 deals with integrable cases of isotropic spin chains with an arbitrary spin.

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