Solvable non-Hermitian skin effect in many-body unitary dynamics

• URL: http://arxiv.org/abs/2205.01321v3
• Date: Mon, 18 Jul 2022 06:57:07 GMT
• Title: Solvable non-Hermitian skin effect in many-body unitary dynamics
• Authors: Marko Znidaric
• Abstract summary: We study unitary evolution of bipartite entanglement in a circuit with nearest-neighbor random gates. We find a sudden transition in the purity relaxation rate the origin of which is in the underlying boundary localized eigenmodes -- the skin effect.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We study unitary evolution of bipartite entanglement in a circuit with nearest-neighbor random gates. Deriving a compact non-unitary description of purity dynamics on qudits we find a sudden transition in the purity relaxation rate the origin of which is in the underlying boundary localized eigenmodes -- the skin effect. We provide the full solution of the problem, being one of the simplest iterations of two-site matrices, namely, that each is a sum of only two projectors. This leads to rich dynamics influenced by the Jordan normal form of the kernel and, most importantly, a spectrum that is completely discontinuous in the thermodynamic limit. It provides a simple example of how a seemingly innocuous many-body unitary evolution can harbor interesting mathematical effects: an effective non-symmetric Toeplitz transfer matrix description causes a phantom relaxation, such that the correct relaxation rate is not given by the matrix spectrum, but rather by its pseudospectrum.

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