Constructing Non-Hermitian Theories with Tunable Exceptional Points and Controlled State Purification

• URL: http://arxiv.org/abs/2608.05052v1
• Date: Wed, 05 Aug 2026 17:00:23 GMT
• Title: Constructing Non-Hermitian Theories with Tunable Exceptional Points and Controlled State Purification
• Abstract summary: We show momentum-space deformation provides a general design principle for creating and controlling exceptional points (EP's) in non-Hermitian quantum systems.<n>EP's are a hallmark of many-body non-Hermitian quantum systems.<n>We also establish EP's as a universal mechanism for purifying arbitrary mixed quantum states.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Exceptional points (EP's) are a hallmark of non-Hermitian quantum systems. We show that momentum-space deformation provides a general design principle for creating and controlling EP's in quadratic many-body Hamiltonians. We identify universal criteria for the momentum sectors to host EP's and the corresponding critical deformation strengths, while revealing that a single momentum-sector EP induces quite remarkably an exponential proliferation of many-body eigenvector coalescences. We further establish EP's as a universal mechanism for purifying arbitrary mixed quantum states, uncovering distinct purification regimes and a fundamental odd-even system-size dichotomy in the thermodynamic limit. Our framework also provides a systematic reverse-engineering protocol for generating short- and long-range, reciprocal and nonreciprocal non-Hermitian quantum matter, together with an explicit Lindblad embedding. These results thus establish momentum-space deformation as a unified route to exceptional-point engineering and controlled design of many-body non-Hermitian quantum systems.

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