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 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.

Entanglement in a spin ring with anisotropic interactions

2015 ◽  
Vol 13 (07) ◽  
pp. 1550057 ◽  
Author(s):  
Marcos Gaudiano ◽  
Omar Osenda
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Nearest Neighbor ◽  
Slight Modification ◽  
Periodic Boundary Conditions ◽  
Spin Chains ◽  
Anisotropic Interactions ◽  
Spin Pairs ◽  
The Relationship ◽  
General Conditions

The relationship between entanglement and anisotropy is studied in small spin chains with periodic boundary conditions. The Hamiltonian of the spin chains is given by a slight modification of the dipolar Hamiltonian. The effect of the anisotropy is analyzed using the concurrence shared by spin pairs, but the study is not restricted to nearest-neighbor (NN) entanglement. It is shown that, under rather general conditions, the inclusion of anisotropic terms diminishes the entanglement shared between the spins of the chain irrespective of its range or its magnetic character.

ENTANGLEMENT DYNAMICS IN QUANTUM SPIN CHAINS

2008 ◽  
Vol 06 (supp01) ◽  
pp. 727-732 ◽  
Author(s):  
MŁOSZ MICHALSKI
Keyword(s):  
Temporal Evolution ◽  
Periodic Boundary Conditions ◽  
Analytic Form ◽  
Quantum Spin ◽  
Spin Chains ◽  
Heisenberg Chain ◽  
Entanglement Dynamics ◽  
Quantum Spin Chains ◽  
Entanglement Measures

We study patterns of temporal evolution, creation and transport, of entanglement in quantum spin chains. The model used is an isotropic Heisenberg chain with periodic boundary conditions, and we obtain in analytic form the time dependence of concurrence and negativity of various pairs of spins in the system. The objective of the present study is to assess the usefulness of various averaged entanglement measures in the characterization of entangling properties of quantum evolutions.

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