We revisit the fate of the skin modes in many-body non-Hermitian fermionic systems. Contrary to the single-particle case, the many-body ground state cannot exhibit an exponential localization of all eigenstates due to the Pauli exclusion principle. However, asymmetry can still exist in the density profile, which can be quantified using the imbalance between the two halves of the system. Using the non-Hermitian Su-Schrieffer-Heeger (SSH) chain as an illustration, we show the existence of two distinct scaling regimes for the imbalance. In the first one, the imbalance grows linearly with the system size, as generically expected. In the second one, the imbalance saturates to a finite value. By combining high-precision exact diagonalization calculations and analytical arguments, we observe that the imbalance does not scale when the occupied bands can be deformed to their Hermitian limit. This suggests a direct connection between the corresponding bulk topological invariants and the skin effect in many-body systems. Importantly, this relation also holds for interacting systems.
Bibliographical noteKAUST Repository Item: Exported on 2022-09-09
Acknowledgements: The authors thank Jens Bardarson, Jérémy Bensadon, Tomáš Bzdušek, Frédéric Mila, Titus Neupert, Nicolas Regnault, Casey Wojcik, and Songbo Zhang for the useful discussions. Exact diagonalization studies were performed with QuSpin and DMRG calculations were done using TeNPy Library (version 0.8.4) . To achieve an arbitrary precision, we employed mpmath library . This work was supported by a grant from the Swiss National Supercomputing Centre (CSCS) under Project No. s1008 and by the Swiss NSF (Grant No. 172543). F.A. acknowledges support from the KAUST Gifted Student Program and the EPFL Research Internship Program.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.