Non-Hermitian systems arise naturally as effective descriptions of open quantum systems and display properties with no Hermitian analogue, such as degeneracies in both eigenstates and eigenvalues—the so-called exceptional points. Although non-Hermitian physics has appeared across many areas for decades, in recent years it has attracted tremendous interest in condensed matter due to its rich topological structure. Non-Hermiticity not only extends the Altland–Zirnbauer classification of topological phases, but also introduces intrinsically new types of topology associated with the complex energy spectrum [1,2].

Exceptional points further exhibit an enhanced sensitivity to perturbations. This feature has led to proposals for highly responsive sensors [3], the engineering of stronger topological superconductors [4], and several other intriguing phenomena. The presence of exceptional points also drastically modifies the critical behavior of topological systems.

In this seminar, I will discuss a series of works [5–8] in which we explore criticality in non-Hermitian systems, with particular emphasis on non-Hermitian topological models. We show that, in addition to exhibiting phase transitions with behavior distinct from their Hermitian counterparts, their finite-temperature critical properties display surprising features. Most strikingly, they host phases with oscillations in temperature reminiscent of imaginary-time crystals, and their critical theories are described by non-unitary conformal field theories.

References:
[1] Emil J. Bergholtz, Jan Carl Budich, & Flore K. Kunst, Rev. Mod. Phys. 93, 015005 (2021)
[2] Kang Yang et al Rep. Prog. Phys. 87 078002 (2024)
[3] Jan Carl Budich & Emil J. Bergholtz, Phys. Rev. Lett. 125, 180403 (2020)
[4] Rodrigo Arouca, J Cayao, AM Black-Schaffer, Phys. Rev. B 108, L060506 (2023)
[5] Rodrigo Arouca, Ching Hua Lee, & Cristiane Morais Smith, Phys. Rev.B 102, 245145 (2020)
[6] Rodrigo Arouca, Eduardo C. Marino, & Cristiane Morais Smith, npj Quantum Frontiers 1, 2 (2022)
[7] Diego F. Munoz-Arboleda, Rodrigo Arouca, & Cristiane Morais Smith, Phys. Rev. B 110, 115135 (2024)
[8] Emiel Slootman, Lumen Eek, Cristiane Morais Smith, Rodrigo Arouca Physical Review B 112, 085149 (2025)

Talks