CPM Seminar

Numerical approach to the dynamics of integrable models

Alexandre Faribault

Ludwig-Maximillians-Universität

In this talk I intend to show how one can use integrability to study the static properties, equilibrium dynamics and even non-equilibrium dynamics of a class of integrable systems which is used to describe phenomenons ranging from superconductivity to various aspects of quantum computation.

The Bethe Ansatz gives us a numerically tractable access to the exact eigenenergies and eigenstates of these Hamiltonians. These can then be used to compute the various needed quantities, be they form factors, norms of states or overlaps of different eigenstates. Additionally, this specific approach can provide an efficient truncation scheme which allows one to treat relatively large system sizes while keeping numerical errors under perfect control.

Numerical results will focus on the reduced BCS fermionic pairing model, but we will discuss a wide variety of systems for which the general techniques can be used.