scholarly journals Exploiting translational invariance in matrix product state simulations of spin chains with periodic boundary conditions

2011 ◽  
Vol 83 (12) ◽  
Author(s):  
B. Pirvu ◽  
F. Verstraete ◽  
G. Vidal
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Spin Chains ◽  
Matrix Product ◽  
Product State ◽  
Translational Invariance ◽  
Matrix Product State

scholarly journals Periodic Boundary Conditions for Dislocation Dynamics Simulations in Three Dimensions

2000 ◽  
Vol 653 ◽  
Author(s):  
Vasily V. Bulatov ◽  
Moon Rhee ◽  
Wei Cai
Keyword(s):  
Boundary Conditions ◽  
Large Scale ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Dislocation Dynamics ◽  
Three Dimensions ◽  
Translational Invariance ◽  
Timing Data ◽  
Dynamics Simulations ◽  
Consistent Treatment

AbstractThis article presents an implementation of periodic boundary conditions (PBC) for Dislocation Dynamics (DD) simulations in three dimensions (3D). We discuss fundamental aspects of PBC development, including preservation of translational invariance and line connectivity, the choice of initial configurations compatible with PBC and a consistent treatment of image stress. On the practical side, our approach reduces to manageable proportions the computational burden of updating the long-range elastic interactions among dislocation segments. The timing data confirms feasibility and practicality of PBC for large-scale DD simulations in 3D.

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 Efficient MPS Algorithm for Periodic Boundary Conditions and Applications Section: Solid matter Original Author's Text: English Abstract: We present the implementation of an efficient algorithm for the calculation of the spectrum of one-dimensional quantum systems with periodic boundary conditions. This algorithm is based on a matrix product representation for quantum states (MPS) and a similar representation for Hamiltonians and other operators (MPO). It is significantly more efficient for systems of about 100 sites and more than for small quantum systems. We apply the formalism to calculate the ground state and the first excited state of a spin-1 Heisenberg ring and deduce the size of a Haldane gap. The results are compared to previous high-precision DMRG calculations. Furthermore, we study the spin-1 systems with a biquadratic nearest-neighbor interaction and show the first results of an application to a mesoscopic Hubbard ring of spinless fermions, which carries a persistent current. Key words: matrix product representation for quantum states (MPS) and Hamiltonians (MPO), spin-1 Heisenberg ring, density matrix renormalization group (DMRG). List Issues Configure

2013 ◽  
Vol 58 (7) ◽  
pp. 657-665 ◽  
Author(s):  
M. Weyrauch ◽  
◽  
M.V. Rakov ◽  
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Nearest Neighbor ◽  
Periodic Boundary Conditions ◽  
Quantum Systems ◽  
Quantum States ◽  
Matrix Product ◽  
Product Representation ◽  
Density Matrix Renormalization ◽  
Small Quantum

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 Infinite boundary conditions for matrix product state calculations

2012 ◽  
Vol 86 (24) ◽  
Author(s):  
Ho N. Phien ◽  
Guifré Vidal ◽  
Ian P. McCulloch
Keyword(s):  
Boundary Conditions ◽  
Matrix Product ◽  
Product State ◽  
Matrix Product State
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