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.
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.
In this study, we investigate the many-body non-Hermitian skin effect at finite temperatures in the thermodynamic limit. Our findings indicate an interesting correspondence between the non-Hermitian skin effect and a linear electric potential effect in this case. This correspondence leads to a unique distribution in non-Hermitian systems; particles in these many-body non-Hermitian systems do not inhabit the energy eigenstates of their single-body counterparts. As a result, the many-body non-Hermitian skin effect is significantly different from the single-body non-Hermitian skin effect. Specifically, for fermionic systems the non-Hermitian skin effect disrupts the original phase, leading to a real-space Fermi surface. For bosonic systems, it can direct bosons to condense in corners at a decay rate that surpasses exponential, even at high temperatures. It also triggers a remarkable phase transition, resulting in spontaneous U(1) symmetry breaking. Uniquely, this does not generate a Goldstone mode, presenting a deviation from traditional expectations as per the Goldstone theorem.
Non-Hermitian many-body physics reveals a rich interplay between topology, localization, and boundary effects, yet their collective behavior in interacting disordered systems remains largely unexplored. In this work, we study an interacting non-Hermitian spin chain subject to a quasi-periodic longitudinal field, providing a unified and controlled setting, where non-Hermitian dynamics, interactions, and localization mechanisms intertwine. Remarkably, we discover a "D-shaped" many-body mobility edge that separates extended and localized eigenstates, while simultaneously delineating regimes of many-body localization and the many-body skin effect (where many-body eigenstates acquire an anomalous drift towards a boundary under open boundaries) emerging from the combined action of interactions, non-Hermiticity, and driving amplitude. We demonstrate that the skin effect induces multifractal scaling in the non-Hermitian eigenstates, providing a clear signature of the many-body skin effect. Employing diagnostics such as the fractal dimension, complex eigenvalue fractions, and many-body inverse participation ratios, we map out a unified phase diagram in which all measures consistently identify the "D-shaped" mobility edge. Finally, we probe this interplay using both complex level-spacing statistics and dynamical observables such as density imbalance, entanglement growth, and wave-packet evolution, culminating in a rich many-body mobility phase diagram that captures both the many-body skin effect and localization transitions. Our results identify a clear, defining signature of the "D-shaped" many-body mobility edge, and underscore its pivotal role in shaping the physics of open quantum many-body systems.
The non-Hermitian skin effect describes the phenomenon of exponential localization of single-particle eigenstates near the boundary of the system. We consider its generalization to the many-body regime by investigating a general class of interacting fermion lattice models in Markovian open quantum systems. Therein, the elementary excitations from the "vacuum" (steady state) are given by two types of dissipative fermionic modes composed of single-fermion operators, which govern the long-time nonequilibrium dynamics. We perturbatively calculate the self-energy matrix of these bare modes in the presence of interactions, and utilize the non-Bloch band theory to derive an exact integral representation. By imposing complex momentum conservation, we obtain a simplified expression for corrections to Liouvillian spectrum that agrees well with numerical calculations to high precision. We further perform perturbative analysis of Liouvillian eigenstates and identify signatures of interaction-enhanced NHSE at the quasiparticle level, manifested as renormalization of the generalized Brillouin zone. Our results establish a diagrammatic framework for dissipative interacting fermions with non-Hermitian skin effect in a description of full-fledged Lindblad master equations, which resembles Fermi liquid theory in terms of interaction-dressed quasiparticles.
The non-Hermitian skin effect (NHSE), characterized by a macroscopic accumulation of eigenstates at the edge of a system with open boundaries, is often ascribed to a non-trivial point-gap topology of the Bloch Hamiltonian. We revisit this connection and separate the question of the NHSE as a spectral reconstruction effect in clean systems from the question of stable topological protection. For a Hatano-Nelson ladder, where point-gap winding and non-normality can be varied independently, we demonstrate that, in a clean translationally invariant multiband setting, the NHSE can occur without point-gap winding and, conversely, that point-gap winding can persist without the NHSE. These results establish that in the clean case the connection between point-gap winding and the NHSE only holds in the scalar one-band case but, in general, not in the multiband case. Even more importantly, the eigenspectrum of non-normal operators is generically highly sensitive to boundary conditions and perturbations, and therefore does not constitute a stable object encoding topological information. Instead, topological properties are reflected in the splitting of the singular-value spectrum for finite systems and, in the semi-infinite limit, correspond to boundary-localized kernel modes implied by the index of the corresponding Toeplitz operator.
Abstract We analytically study zero-energy eigenstates for two non-Hermitian models based on the Su–Schrieffer–Heeger (SSH) chain. The first model is an infinite non-Hermitian SSH chain with nonreciprocal hoppings to a neighboring site and two barriers. We find analytical expressions for the eigenfunctions, including those that describe resonant states. For resonant states, an analogue of the non-Hermitian skin effect is observed. For the second model, a finite non-Hermitian SSH chain with nonreciprocal hoppings with an even or odd number of sites, we also find the eigenfunctions and observe the non-Hermitian skin effect. All results are obtained using the derived Green’s function of the infinite non-Hermitian SSH chain.
The non-Hermitian skin effect, namely, that the eigenvalues and eigenstates of a non-Hermitian tight-binding Hamiltonian have significant differences under open or periodic boundary conditions, is a remarkable phenomenon of non-Hermitian systems. Inspired by the presence of the non-Hermitian skin effect, we study the evolution of wave packets in non-Hermitian systems, which can be determined using the single-particle Green's function. Surprisingly, we find that in the thermodynamic limit, the Green's function does not depend on boundary conditions, despite the presence of skin effect. We provide a general proof for this statement in arbitrary dimension with finite hopping range, with an explicit illustration in the non-Hermitian Su-Schrieffer-Heeger model. We also explore its applications in noninteracting open quantum systems described by the master equation. We demonstrate that the evolution of the density matrix is independent of the boundary condition.