[Paper Review] Non-Hermitian skin clusters from strong interactions

R. Shen, Ching Hua Lee|arXiv (Cornell University)|Jul 7, 2021

Quantum Mechanics and Non-Hermitian Physics4 citations

TL;DR

This paper introduces non-Hermitian skin clusters—translation-invariant many-body particle configurations arising from strong, asymmetric correlated hoppings in lattice models with quenched single-particle dynamics. Unlike conventional non-Hermitian skin effects, these clusters emerge from Hilbert space fragmentation and are not bound to physical boundaries, exhibiting unique features like loop gaps and robustness under dynamics, with their structure independent of generalized Brillouin zone analysis.

ABSTRACT

Strong, non-perturbative interactions often lead to new exciting physics, as epitomized by emergent anyons from the Fractional Quantum Hall effect. Within the actively investigated domain of non-Hermitian physics, we discover a new family of states known as non-Hermitian skin clusters. Taking distinct forms as Vertex, Topological, Interface, Extended, and Localized skin clusters, they generically originate from asymmetric correlated hoppings on a lattice, in the strongly interacting limit with quenched single-body energetics. Distinct from non-Hermitian skin modes which accumulate at boundaries, our skin clusters are predominantly translation-invariant particle clusters. As purely interacting phenomena, they fall outside the purview of generalized Brillouin zone analysis, although our effective lattice formulation provides alternative analytic and topological characterization. Non-Hermitian skin clusters fundamentally originate from the fragmentation structure of the Hilbert space and may thus be of significant interest in modern many-body contexts like the ETH and quantum scars.

Motivation & Objective

• To identify and characterize new non-Hermitian many-body phenomena beyond single-particle mechanisms.
• To explore how strong, non-perturbative interactions in non-Hermitian systems can lead to emergent, translation-invariant particle clusters.
• To demonstrate that these skin clusters are not describable by generalized Brillouin zone theory, despite their topological and analytic features.
• To investigate the role of Hilbert space fragmentation in generating non-local, interacting skin states independent of physical boundaries.

Proposed method

• Formulates a minimal 1D bosonic model with unbalanced two-body correlated hoppings, where single-particle hoppings are quenched.
• Defines a Hamiltonian with asymmetric hopping amplitudes controlled by a parameter γ, ensuring no single-particle states are involved.
• Analyzes the model using exact diagonalization and dynamical evolution to identify stable, translation-invariant eigenstates.
• Characterizes the Hilbert space structure by identifying non-trivial states via local occupation conditions: ⟨ψ|n̂_i n̂_{i+3}|ψ⟩ > 0 and ⟨ψ|n̂_i|ψ⟩ > 1.
• Computes the dimension of the N-boson sector relative to the full Hilbert space to assess sector filling and fractal dimension scaling.
• Uses effective lattice mapping for 3-boson sectors to analyze embedding and scaling behavior in large systems.

Experimental results

Research questions

• RQ1 Can strong, non-perturbative interactions in non-Hermitian systems give rise to new types of many-body localization beyond boundary-accumulated skin modes?
• RQ2 How do Hilbert space fragmentation and correlated hopping lead to translation-invariant particle clusters in non-Hermitian systems?
• RQ3 To what extent are these skin clusters robust under dynamical evolution, even without physical boundaries?
• RQ4 Why are these clusters outside the scope of generalized Brillouin zone analysis, and what alternative characterization applies?
• RQ5 How does the fractal dimension of the N-boson sector scale with system size and filling factor, and what does this imply for many-body localization?

Key findings

• Non-Hermitian skin clusters are translation-invariant many-body states that emerge exclusively from strong, asymmetric correlated hoppings, not from single-particle dynamics.
• These clusters are robust under dynamical evolution and do not require physical boundaries, distinguishing them from conventional non-Hermitian skin modes.
• The 4- and 5-boson sectors in the model nearly fill the full Hilbert space, with fractal dimension D ≈ 1 under filling ν > 1/3.
• For the 3-boson sector, the ratio of sector dimension to full Hilbert space dimension scales as R ∝ 1/L, remaining finite in the large-L limit.
• The system exhibits a critical length L = 12 for the 4-boson case, beyond which the sector dimension closely matches the full Hilbert space dimension.
• The skin clusters are characterized by a loop gap rather than line or point gaps, indicating a distinct topological and spectral structure.