PHY 771.02, Tensor network state methods, Fall 2017
Synopsis
Tensor network states are a recent and very successful (numerical) approach for the investigation of stronglycorrelated quantum manybody systems that is not bothered by the sign problem of quantum Monte Carlo. It is applied mostly for studies of condensed matter, ultracold atomic gases, and quantum chemistry.
We will discuss:
 The densitymatrix renormalization group (DMRG) in its traditional interpretation of Hilbert space decimation. This allows for the approximation of the manybody ground state, often to machine precision.
 The DMRG in the modern formulation of matrix product states (MPS).
 Generalizations for the study of nonequilibrium phenomena and the computation of response functions as, e.g., measured in ARPES and neutron scattering experiments.
 Generalizations for the study of finitetemperature states using purifications of density operators and socalled minimally entangled typical thermal states.
 Modifications for the study of open quantum systems (decoherence etc.)
 Scaling of entanglement entropies in quantum manybody systems. This allows us to bound the computational complexity of the MPS methods.
 Generalizations to higher dimensions and connections to realspace renormalization group: projected entangled pair states (PEPS) and the multiscale entanglement renormalization ansatz (MERA).
have a nice day!
