This course is no longer offered.
The course will provide an overview of the field of matrix product and tensor network approaches to many body systems.
Many-body systems are hindered by an exponential complexity in the number of their constituents and thus are hard to solve. Large many body systems however present exotic emerging behaviour ( such as spin liquid, superconducting and super-fluid phases) that we want to understand from first principles. Tensor networks provide a novel theoretical and computational framework to analyse collective emergence in many body systems. We will use Tensor Networks to study classical and quantum many body systems at and out-of equilibrium. The syllabus includes an introduction to the tensor network formalism and graphical notation, the recipe for describing the partition function of a classical model as the norm of a matrix product state (1D),or tensor product state (higher D).
The characterization of the properties of these states like expectation values, correlation functions, and entropies. The renormalization group in the language of tensor networks. The correspondence between statistical mechanics and quantum mechanics and some aspects of outof- equilibrium dynamics in 1 and higher dimensions. We will describe powerful numerical algorithms based on tensor networks like DMRG in 1D and its generalizations in higher D. Students are expected to have a solid background in quantum mechanics and statistical mechanics.
Assessment: Continuous Assessment