Effective non-unitarity in many-body systems

Objetivo

In many-body quantum systems, say one-dimensional spin chains, eigenstates are exponentially close in energy and can therefore be resolved only on timescales exponentially large in system size. As such they can not be in general directly probed in experiments. Despite that one typically uses spectral properties, like eigenenergies and eigenstates, historically used in single-particle systems, as quantifiers of quantum chaos even in many-body systems. For that reason such methods can sometimes fail, mathematically, because the infinite size and the infinite time limits do not commute. In the project we will alleviate that by building a framework that will focus only on the dynamics of relevant degrees of freedom, resulting in a non-unitary description, which will help us to address a number of important old problems as well as analyse properties of more recent phases of matter.

We will construct suitable non-unitary propagators, for instance on the space of local operators, and study their properties. This will allow to elegantly express correlation functions and thus directly study observable quantities. The method is versatile, providing a uniform tool to study dynamical properties from integrability to chaos. Because it can work directly in the thermodynamic limit we expect it to outperform existing techniques, and is ideally suited to study the ergodicity transition. We will use it to find new integrable systems, including circuits that could be used in validating quantum computers. We will also study cases of slow ergodicity breaking, like prethermalization, and identify instances of discrete time crystals. Due to non-unitarity pseudospectra could be relevant, and we plan to explore physical situations where one has to rely on pseudospectra rather than spectra of matrices.