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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 3: Quantum Dynamics
MP 3.4: Talk
Monday, March 18, 2024, 16:10–16:30, HL 001
Spread complexity for measurement-induced non-unitary dynamics and quantum Zeno effect — •Aranya Bhattacharya1, Rathindra Nath Das2, Bidyut Dey3, and Johanna Erdmenger2 — 1Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland — 2Institute for Theoretical Physics and Astrophysics and Würzburg-Dresden Cluster of Excellence ct.qmat Julius-Maximilians-Universität Würzburg
Am Hubland, 97074 Würzburg, Germany — 3Indian Institute of Technology Kanpur, Kanpur 208016, Uttar Pradesh, India
We study the behaviour of spread complexity and spread entropy in quantum systems evolving under non-unitary dynamics. For non-hermitian Hamiltonians, we extend the bi-Lanczos construction of the Krylov basis to the Schrödinger picture. Also, a specialized algorithm is implemented for complex symmetric Hamiltonians, effectively reducing the computational memory requirements by half. We apply this construction to the one-dimensional tight-binding Hamiltonian subject to repeated measurements at fixed small time intervals. These result in effective non-unitary dynamics. In analogy to measurement-induced phase transitions, we consider a quench between hermitian and non-hermitian Hamiltonian evolution induced by turning on regular measurements at different frequencies. As a function of the measurement frequency, we find a transition that shifts the time at which the spread complexity starts growing, indicating the onset of the quantum Zeno effect.
Keywords: Krylov complexity; Quantum Zeno Effect; Projective Measurements; Non-unitary evolution