Non-Hermitian Many-Body Localization in Coupled Hatano-Nelson Interacting Chains

Kuldeep Suthar^1*, Yi-Cheng Wang^1,2, Yi-Ping Huang³, Jhih-Shih You⁴, Hsiang-Hua Jen¹

¹Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan
²Department of Physics, National Taiwan University, Taipei, Taiwan
³Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
⁴Department of Physics, National Taiwan Normal University, Taipei, Taiwan

* Presenter:Kuldeep Suthar, email:kuldeep@gate.sinica.edu.tw

The physics of non-Hermitian systems has attracted significant interests in recent years. The phenomena of
non-Hermiticity originate from an exchange of energy or particles with environment and leads to several rich
properties such as parity-time symmetry breaking, exceptional points unique to non-Hermitian topology etc.
Recently, it has been shown that a non-Hermitian system with random disorder or quasi-periodic potential
possessing time-reversal symmetry exhibit complex-real transition. In this work, we study the many-body
localization in coupled Hatano-Nelson interacting chains. In contrast to the previous studies of the spinless
fermionic system, the two-chain system shows a complex-real transition which does not coincide to the
localization transition. Moreover, the critical coupling strength of the transition decreases as the ratio of
respective non-reciprocal hopping varied. We further investigate the two-chain model with gain-loss terms,
and study the localization and eigen-spectrum properties of the system. Our study opens up a direction
towards an exploration of the critical effects of disordered non-Hermitian many-body systems in cold-atom
experiments.

Keywords: Many-body localization, Non-Hermitian Systems, Disordered Systems, Optical lattices, Ultracold atoms