Many-Body Non-Hermitian Skin Effect for Multipoles

• URL: http://arxiv.org/abs/2401.04162v2
• Date: Sat, 28 Sep 2024 08:04:10 GMT
• Title: Many-Body Non-Hermitian Skin Effect for Multipoles
• Authors: Jacopo Gliozzi, Giuseppe De Tomasi, Taylor L. Hughes,
• Abstract summary: We investigate the fate of the non-Hermitian skin effect in one-dimensional $textU(1)$ systems. Key feature of the non-Hermitian skin effect for $m$-pole conserving systems is the generation of an $(m+1)$th multipole moment. In addition, we explore the dynamical consequences of the $m$-pole skin effect, focusing on charge and entanglement propagation.
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• Abstract: In this work, we investigate the fate of the non-Hermitian skin effect in one-dimensional systems that conserve the dipole moment and higher moments of an associated global $\text{U}(1)$ charge. Motivated by field theoretical arguments and lattice model calculations, we demonstrate that the key feature of the non-Hermitian skin effect for $m$-pole conserving systems is the generation of an $(m+1)$th multipole moment. For example, in contrast to the conventional skin effect where charges are anomalously localized at one boundary, the dipole-conserving skin effect results in charges localized at both boundaries, in a configuration that generates an extremal quadrupole moment. In addition, we explore the dynamical consequences of the $m$-pole skin effect, focusing on charge and entanglement propagation. Both numerically and analytically, we provide evidence that long-time steady-states have Fock-space localization and an area-law scaling of entanglement entropy, which serve as quantum indicators of the skin effect.

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