scholarly journals Non-local Correlations in the Haldane Phase for an XXZ Spin-1 Chain: A Perspective from Infinite Matrix Product State Representation

2012 ◽  
Vol 81 (7) ◽  
pp. 074003 ◽  
Author(s):  
Yao Heng Su ◽  
Sam Young Cho ◽  
Bo Li ◽  
Hong-Lei Wang ◽  
Huan-Qiang Zhou
Keyword(s):  
Infinite Matrix ◽  
Matrix Product ◽  
Product State ◽  
State Representation ◽  
Matrix Product State ◽  
Local Correlations ◽  
Non Local

scholarly journals Matrix product state representation of quasielectron wave functions

2018 ◽  
Vol 2018 (5) ◽  
pp. 053101 ◽  
Author(s):  
J Kjäll ◽  
E Ardonne ◽  
V Dwivedi ◽  
M Hermanns ◽  
T H Hansson
Keyword(s):  
Wave Functions ◽  
Matrix Product ◽  
Product State ◽  
State Representation ◽  
Matrix Product State

scholarly journals Matrix product state representation of non-Abelian quasiholes

2015 ◽  
Vol 92 (4) ◽  
Author(s):  
Yang-Le Wu ◽  
B. Estienne ◽  
N. Regnault ◽  
B. Andrei Bernevig
Keyword(s):  
Matrix Product ◽  
Product State ◽  
State Representation ◽  
Matrix Product State

scholarly journals Tangent-space methods for truncating uniform MPS

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Bram Vanhecke ◽  
Maarten Van Damme ◽  
Jutho Haegeman ◽  
Laurens Vanderstraeten ◽  
Frank Verstraete
Keyword(s):  
Tangent Space ◽  
Computational Cost ◽  
Infinite Matrix ◽  
Matrix Product ◽  
Product State ◽  
Matrix Product State ◽  
Product Operator ◽  
Tensor Network ◽  
Network Simulations ◽  
Central Bottleneck

An essential primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a smaller bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for contracting projected entangled pair states. We formulate a tangent-space based variational algorithm to achieve this goal for uniform (infinite) matrix product states. The algorithm exhibits a favourable scaling of the computational cost, and we demonstrate its usefulness by several examples involving the multiplication of a matrix product state with a matrix product operator.

scholarly journals MATRIX PRODUCT STATE REPRESENTATION FOR SLATER DETERMINANTS AND CONFIGURATION INTERACTION STATES

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345029 ◽  
Author(s):  
PIETRO SILVI ◽  
DAVIDE ROSSINI ◽  
ROSARIO FAZIO ◽  
GIUSEPPE E. SANTORO ◽  
VITTORIO GIOVANNETTI
Keyword(s):  
Configuration Interaction ◽  
A Priori ◽  
Slater Determinant ◽  
Matrix Product ◽  
Product State ◽  
Exact Representation ◽  
State Representation ◽  
Product Representation ◽  
Matrix Product State ◽  
Exact Matrix

Slater determinants are product states of filled quantum fermionic orbitals. When they are expressed in a configuration space basis chosen a priori, their entanglement is bound and controlled. This suggests that an exact representation of Slater determinants as finitely-correlated states is possible. In this paper we analyze this issue and provide an exact Matrix Product representation for Slater determinant states. We also argue possible meaningful extensions that embed more complex configuration interaction states into the description.

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