Going beyond Hermitian Physics

Remarkable advances in experimental techniques and theoretical methods in AMO physics have made beyond-Hermitian physics a new research frontier. Complete knowledge about quantum jumps allows a description of quantum dynamics at the single-trajectory level [1]. A subclass thereof without quantum jumps can be described by non-hermitian Hamiltonians [2]. Here, symmetry, topology and many-body effects are fundamentally altered [3]. Importantly, transposition and complex conjugation, which are equivalent in hermitian physics, become inequivalent, leading to proliferation of new topological phases and symmetry classes [4]. In many-body physics, dissipation leads to violation of the g-theorem in the Kondo problem [5], and the complex eigenspectrum allows intermediate-state engineering, esp. the dynamical sign reversal of magnetism in dissipative Hubbard models [6]. Nonorthogonality of eigenstates permits continuous a quantum phase transition between gapped phases without gap closing [7]. Nonunitary dynamics and PT-symmetry can be utilized to surpass the Lieb-Robinson bound [8]. Beyond-hermiticity has also important implications in statistical physics, esp. Yang-Lee zeros [9] which can directly be observed in photonic experiments [10]. Yang-Lee zeros have recently been found to play a key role in BCS superconductivity [11]. I will present these latest developments of beyond-Hermitian physics.

References

[1] M. Ueda, Quantum Opt. 1, 131 (1989); Phys. Rev. A 41, 3875 (1990).

[2] Y. Ashida, Z. Gong and M. Ueda, Adv. Phys. 69, 249 (2020).

[3] Z. Gong, et al., Phys. Rev. X 8, 031078 (2018).

[4] K. Kawabata, et al., Phys. Rev. X 9, 041015 (2020).

[5] M. Nakagawa, et al., Phys. Rev. Lett. 121, 203001 (2018).

[6] M. Nakagawa, et al., Phys. Rev. Lett. 124, 147203 (2020).

[7] N. Matsumoto, et al., Phys. Rev. Lett. 126, 260601 (2020).

[8] Y. Ashida and M. Ueda, Phys. Rev. Lett. 120, 185301 (2018).

[9] N. Matsumoto, M. Nakagawa and M. Ueda, Phys. Rev. Res. 4, 033250 (2022).

[10] H. Gao, et al., Phys. Rev. Lett. 132, 176601 (2024).

[11] H. Li, et al., Phys. Rev. Lett. 131, 216001 (2023).