#### Alladi Ramakrishnan Hall

#### Anatomy of Some Unconventional Phases

#### Ipsita Mandal

##### Shiv Nadar Institute of Eminence

*I will discuss the theoretical explorations of some unconventional phases of matter, encompassing both non-interacting and interacting systems.*

First, I will focus on critical Fermi surface states, where there is a well-defined Fermi surface, but no quasiparticles, as a result of strong interactions between the Fermi surface and some emergent massless boson(s). I will outline a framework to extract the low-energy physics of such systems (dubbed as non-Fermi liquids) in a controlled approximation, using the tool of dimensional regularization. I will demonstrate how I have applied these techniques to extract the low-energy properties of the non-Fermi liquid phases in various strongly correlated systems.

Second, I will discuss some of my work involving triangular moiré superlattices. I will also outline the possibility of the emergence of non-Fermi liquid behaviour in such systems.

In the non-interacting category, I will focus on non-Hermitian (NH) “Hamiltonians”, which appear in the effective description of various physical settings, ranging from classical photonics to dissipative quantum materials. Using simple examples, I will discuss some topological aspects of such systems, related to the concept of Exceptional Points (EPs). EPs showcase degeneracies at which two or more eigenvalues and eigenvectors coalesce. Second-order EPs are by far the most studied due to their abundance, requiring only the tuning of two real parameters. Higher-order EPs generically require more fine-tuning, and are thus assumed to play a much less prominent role. However, I will show that physically relevant symmetries make higher-order EPs dramatically more abundant and conceptually richer. In the presence of sublattice symmetries, I will discuss the emergence of unexpected odd-order EPs, which exhibit enhanced sensitivity in the behaviour of the eigenvector collapse in their neighbourhood, depending on the path chosen to approach the singular point.

Done