Fate of the non-Hermitian skin effect in many-body fermionic systems

Abstract

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.

8+3 pages, 9 figures, comments are welcome

References in corpus (20)

• Topological Origin of Non-Hermitian Skin Effects
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Topological Transition in a Non-Hermitian Quantum Walk
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits
• Higher-order non-Hermitian skin effect
• Acoustic non-Hermitian skin effect from twisted winding topology
• Observation of higher-order non-Hermitian skin effect
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Second-order topological non-Hermitian skin effects
• Realization of active metamaterials with odd micropolar elasticity
• Anderson transition in three-dimensional systems with non-Hermitian disorder
• Non-Hermitian second-order skin and topological modes
• Guided accumulation of active particles by topological design of a second-order skin effect
• Finite-size effects in non-Hermitian topological systems
• Localization in open quantum systems
• R-DMFT study of a non-Hermitian skin effect for correlated systems: analysis based on a pseudo-spectrum
• Scaling rule in critical non-Hermitian skin effect

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