Simulations with matrix product states
Abstract
Matrix product states (MPS) are considered to be the most efficient parametrization of quantum states that emerge as ground states or lowlying excitations of shortranged Hamiltonians in one spatial dimension. The most powerful simulation algorithms for strongly correlated quantum systems in one dimension, the family of densitymatrix renormalizationgroup(DMRG) algorithms, can be understood as acting in this very particular state class and find a particularly transparent formulation if expressed in terms of matrix product states. In this set of lectures, I will introduce matrix product states, discuss their properties, the typical quantum mechanical operations expressed in their language, matrix product operators, and present both static and dynamic simulation algorithms. I will also make a connection to elements of entanglement theory.
 Publication:

Lectures on the Physics of Strongly Correlated Systems XVI: Sixteenth Training Course in the Physics of Strongly Correlated Systems
 Pub Date:
 September 2012
 DOI:
 10.1063/1.4755823
 Bibcode:
 2012AIPC.1485..135S