Theory Seminar: Maximizing Rényi Entropy to approximate thermal states

 

Giacomo Giudice (MPQ Theory Department)
Tensor networks have been incredibly efficient at describing many-body physics at low-energy, particularly in one dimension.

Giacomo Giudice (MPQ Theory Department)
Herbert-Walther Lecture Hall G0.25
Wed 10. April 2019, 11: 30 am (MEZ)

Abstract:

Tensor networks have been incredibly efficient at describing many-body physics at low-energy, particularly in one dimension.

    A key ingredient of this success, from a numerical perspective, is the stability and accuracy of variational approximations of pure states. However, success for mixed states has been more moderate. In particular, there are currently no variational methods to approximate thermal states. Yet describing thermal states of many-body system is of interest, not only from a fundamental standpoint, but also to describe experiments. In the first part of this talk, I will introduce an alternative family of mixed states, namely those that maximize the Rényi entropy under certain constraints. Under the hypothesis of local Hamiltonians, I hope to convince you that local observables become indistinguishable from their thermal counterparts. Therefore, this class of states introduces novel perspectives for numerical methods. The second part of the talk will be dedicated to introducing algorithms to approximate such states with tensor networks.