Non-Hermitian Many-Body Localization Through Singular Value Decomposition

A hallmark of disordered many-body interacting quantum systems are many-body localized (MBL) regimes. A strong quenched disorder can suppress the resonant processes responsible for the transport of particles or energy. Thus, MBL is considered a consequence of unitary evolution, and it is expected to be washed away when coupling the system to an environment. The study of the interplay of dissipation and MBL has been a topic of recent interest, in particular thanks to the advancements in non-Hermitian (NH) physics [1-4]. NH Hamiltonians are used as an effective tool to describe dissipation in open quantum systems, and are derived from a GKSL master equation for null-measurement conditioning (no-jump trajectories). However, most studies up to date focused on standard MBL Hamiltonians, subjected to a uniform dissipation. In this work, we take a different perspective and investigate whether random dissipation can induce NH localization in an otherwise clean many-body system. We propose the use of the singular value decomposition, motivated by recent works in non-Hermitian physics [5-6], as the right tool to diagnose MBL in a non-Hermitian setting. Within this context, we find that an inhomogeneous non-Hermiticity induces a form of many-body localization [7], with the same confidence with which localization is seen in similar Hermitian systems.

[1] R. Hamazaki et al., Phys. Rev. Lett. 123, 090603 (2019)

[2] R. Hamazaki et al., arXiv:2206.02984

[3] G. De Tomasi and I. M. Khaymovich. Phys. Rev. B 106, 094204 (2022)

[4] G. De Tomasi and I. M. Khaymovich. arXiv:2302.00015

[5] D. Porras and S. Fernández-Lorenzo. Phys. Rev. Lett. 122, 143901 (2019)

[6] M. Brunelli et al., SciPost Phys. 15, 173 (2023)

[7] F. Roccati, F. Balducci, R. Shir, A. Chenu. in preparation