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.

Using Elasticity to Correct for Boundary Effects in Calculations of Stress-Diffusion Coupling Parameters

2006 ◽  
Vol 978 ◽  
Author(s):  
Brian Puchala ◽  
Michael Falk ◽  
Krishna Garikipati
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Defect Formation ◽  
Correction Term ◽  
Periodic Boundary Conditions ◽  
Formal Proof ◽  
Free Boundaries ◽  
Slow Convergence ◽  
Free Boundary Conditions

AbstractThe effect of stress on diffusion during semiconductor processing becomes important as device dimensions shrink from microns to nanometers. Simulating these effects requires accurate parameterization of the formation and migration volume tensors of the defects that mediate diffusion on the atomistic scale. We investigate the effect of boundary conditions on the accuracy of atomistic calculations of defect formation energies and formation volume tensors. Linear elasticity provides a correction to the effect of the boundaries on the resulting relaxation volume tensor. By a formal proof we show that the correction term is zero for free boundaries and for periodic boundary conditions with zero mean boundary stress. This is demonstrated in the far field for periodic and free boundary conditions for an isotropic (vacancy) and an anisotropic (<110> intersitial) defect in Stillinger-Weber silicon. For periodic boundary conditions, formation volume tensor components converge to within 5% in a 216 atom simulation cell. For free boundary conditions, slow convergence of elastic constants results in slow convergence of formation volumes. Most significantly, this provides a new method to calculate the formation volume from constant volume calculations. This removes the need for relaxing boundaries, allowing for simpler and more efficient algorithms. We apply this method to both the vacancy and the <110> interstitial in Stillinger-Weber silicon.

scholarly journals Quantum spin chains with quantum group symmetry

1996 ◽  
Vol 174 (3) ◽  
pp. 477-507 ◽  
Author(s):  
M. Fannes ◽  
B. Nachtergaele ◽  
R. F. Werner
Keyword(s):  
Quantum Group ◽  
Quantum Spin ◽  
Spin Chains ◽  
Group Symmetry ◽  
Quantum Spin Chains

scholarly journals Yang-Baxter integrable Lindblad equations

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Aleksandra A. Ziolkowska ◽  
Fabian Essler
Keyword(s):  
Bethe Ansatz ◽  
Quantum Spin ◽  
Spin Chains ◽  
Integrable Models ◽  
Late Time ◽  
Quantum Spin Chains ◽  
Operator Formalism ◽  
One Dimensional ◽  
Time Dynamics

We consider Lindblad equations for one dimensional fermionic models and quantum spin chains. By employing a (graded) super-operator formalism we identify a number of Lindblad equations than can be mapped onto non-Hermitian interacting Yang-Baxter integrable models. Employing Bethe Ansatz techniques we show that the late-time dynamics of some of these models is diffusive.

Sign in / Sign up

Export Citation Format

Share Document