Beyond-Hermitian Quantum Physics

The fundamental premise of quantum theory is two-fold: unitary dynamics and nonunitary measurement. The former is generated by a hermitian operator, whereas the latter entails non-hermitian operation. Beyond-hermitian quantum physics has attracted much attention due to experimental and theoretical advances in AMO, condensed matter and nonequilibrium statistical physics [1]. These developments give us fresh insights into how to control strongly correlated dissipative systems with novel functionalities operating far from equilibrium. A full knowledge of types and occurrence times of quantum jumps allows a complete description of quantum trajectories. A subclass thereof without quantum jumps can be described by a non-hermitian Hamiltonian. Here many important properties such as symmetries, topological properties with many-body effects fundamentally altered. Transposition and complex comjugation, which are equivalent in hermitian physics, become inequivalent in the non-hermitian framework, leading to nontrivial topological phases [2] through unification and ramification of topological phases [3] and resulting in 38 symmetry classes instead of 10 in the Altland-Zirnbauer classification [4]. In random matrices, transposition symmetry leads to two new universality classes of level-spacing statistics other than the Ginibre ensemble. In many-body physics, non-hermiticity leads to the dynamical sign reversal of magnetic correlations in dissipative Hubbard models [6] and anomalous g-theorem-violating reversion of renormalization-group flows in the Kondo problem [7].
[1] Ashida, et al., arXiv:2006.01837. [2] Gong, et al., PRX 8, 031079. [3] Kawabata, et al., Nat. Commun. 10, 297 (2019). [4] Kawabata, et al., PRX 9, 041015 (2019). [5] Hamazaki, et al., Phys. Rev. Research 3, 023286 (2020). [6] Nakawaga, et al., PRL 124, 147203 (2020). [7] Nakawaga, et al., PRL 121, 203001 (2018).