The goal of project NTopQuant is to elucidate the role of exceptional nodal phases in open and correlated quantum systems. To motivate this endeavor, we take a few steps back and start at the mathematical notion of Hermiticity. This is a property that matrices can have, and is seen as one of the fundamental tenets in physics as such Hermitian matrices can be used to describe isolated quantum systems. At the same time, dissipation is ubiquitous in nature, and generally leads to qualitatively new and exciting phenomena outside the realm of isolated materials. In this context, we arrive at the notion of non-Hermitian matrices, which play a central role in both classical and quantum systems. Non-Hermiticity can be encountered in many fields in physics, and even beyond, such as nonconservative biological systems. In recent years, non-Hermiticity has been studied in the context of topology revealing a dramatic enrichment of the phenomenology of topological phases resulting in a cross-disciplinary domain that is rapidly expanding. It is in this context that we study open and correlated quantum systems.
In particular, we are interested in understanding the impact of so-called exceptional nodal phases. When studying the properties of matrices, one naturally looks at their so-called eigenvalues. When two or more eigenvalues are equivalent, this is called a degeneracy and such degeneracies can be viewed as topological objects. Non-Hermitian matrices generally feature degeneracies that are known as exceptional points. These are truly non-Hermitian degeneracies at which not only the eigenvalues but also the eigenvectors coalesce. While exceptional points of the simplest form have been studied extensively, little is known about more complicated so-called higher-order exceptional nodal structures, where more eigenvalues and eigenvectors coalesce. Moreover, historically non-Hermitian systems have been predominantly studied in optics, and only recently the gaze has turned to open and correlated quantum systems.
With NTopQuant, we aim to expand our knowledge and understanding of such systems by studying through the lens of non-Hermitian topology. In doing so, we focus on the study of higher-order exceptional points, investigate the topological properties of open quantum systems through the lens of non-Hermiticity, address what role exceptional nodal phases play in Moiré materials, and look at nonlinear optical systems.
