scholarly journals Matrix product state based algorithm for determining dispersion relations of quantum spin chains with periodic boundary conditions

2012 ◽  
Vol 85 (3) ◽  
Author(s):  
B. Pirvu ◽  
J. Haegeman ◽  
F. Verstraete
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Dispersion Relations ◽  
Quantum Spin ◽  
Spin Chains ◽  
Matrix Product ◽  
Product State ◽  
Quantum Spin Chains ◽  
Matrix Product State

scholarly journals BETHE ANSATZ SOLUTIONS FOR TEMPERLEY–LIEB QUANTUM SPIN CHAINS

2000 ◽  
Vol 15 (21) ◽  
pp. 3395-3425 ◽  
Author(s):  
R. C. T. GHIOTTO ◽  
A. L. MALVEZZI
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Quantum Group ◽  
Bethe Ansatz ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Free Boundary Conditions

We solve the spectrum of quantum spin chains based on representations of the Temperley–Lieb algebra associated with the quantum groups [Formula: see text] for Xn=A1, Bn, Cn and Dn. The tool is a modified version of the coordinate Bethe ansatz through a suitable choice of the Bethe states which give to all models the same status relative to their diagonalization. All these models have equivalent spectra up to degeneracies and the spectra of the lower-dimensional representations are contained in the higher-dimensional ones. Periodic boundary conditions, free boundary conditions and closed nonlocal boundary conditions are considered. Periodic boundary conditions, unlike free boundary conditions, break quantum group invariance. For closed nonlocal cases the models are quantum group invariant as well as periodic in a certain sense.

scholarly journals Perfect Integrability and Gaudin Models

2020 ◽  
Author(s):  
Kang Lu ◽  
Keyword(s):  
Boundary Conditions ◽  
Lie Algebras ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Simple Lie Algebras ◽  
Gaudin Models

We suggest the notion of perfect integrability for quantum spin chains and conjecture that quantum spin chains are perfectly integrable. We show the perfect integrability for Gaudin models associated to simple Lie algebras of all finite types, with periodic and regular quasi-periodic boundary conditions.

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.

scholarly journals Matrix product states forsu(2) invariant quantum spin chains

2016 ◽  
Vol 2016 (8) ◽  
pp. 083101 ◽  
Author(s):  
Rubina Zadourian ◽  
Andreas Fledderjohann ◽  
Andreas Klümper
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Matrix Product ◽  
Quantum Spin Chains ◽  
Matrix Product States ◽  
Invariant Quantum
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