# Theoretical Physics

**16 July 2014**

**Time:**14:00 to 15:00

**Location:**EC Stoner SR 8.60

Andrew Goldsborough (Warwick)

An Introduction to Tensor Networks

Tensor network methods provide elegant and powerful tools for the simulation of quantum many-body systems. Their original manifestation, the density-matrix renormalization group (DMRG) is now understood to be based on a variational update of a matrix product state (MPS), and has found applications in a wide range of fields such as quantum chemistry and quantum information as well as condensed matter physics. More recent developments have extended the methods to, e.g., critical systems (MERA), two-dimensional lattices (PEPS) and topologically

ordered states.

The aim of this talk is to provide a pedagogical introduction to tensor network methods. Beginning with a description of the standard notation used in the field and conceptual arguments that justify the use of tensor networks for various applications within quantum many-body simulation. The focus will then switch to matrix product states (MPS) as the simplest but most widely applied form of tensor network. The talk will end with an example of how the concepts of

tensor networks can be applied to the case of disordered systems.

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