Spread complexity for measurement-induced non-unitary dynamics and Zeno effect

A bstract Using spread complexity and spread entropy, we study non-unitary quantum dynamics. For non-hermitian Hamiltonians, we extend the bi-Lanczos construction for the Krylov basis to the Schrödinger picture. Moreover, we implement an algorithm adapted to complex symmetric Hamiltonians. This redu...

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Published in:The journal of high energy physics Vol. 2024; no. 3; pp. 179 - 43
Main Authors: Bhattacharya, Aranya, Das, Rathindra Nath, Dey, Bidyut, Erdmenger, Johanna
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 29.03.2024
Springer Nature B.V
SpringerOpen
Subjects:
Algorithms
Asymptotes
Classical and Quantum Gravitation
Complexity
Elementary Particles
Entropy
Evolution
Hamiltonian functions
Integrable Hierarchies
Lattice Integrable Models
Phase Transitions
Physics
Physics and Astronomy
Quantum Dissipative Systems
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Time measurement
Lattice Integrable Models
Quantum Dissipative Systems
Integrable Hierarchies
Phase Transitions
ISSN:1029-8479, 1029-8479
Online Access:Get full text
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Summary:A bstract Using spread complexity and spread entropy, we study non-unitary quantum dynamics. For non-hermitian Hamiltonians, we extend the bi-Lanczos construction for the Krylov basis to the Schrödinger picture. Moreover, we implement an algorithm adapted to complex symmetric Hamiltonians. This reduces the computational memory requirements by half compared to the bi-Lanczos construction. We apply this construction to the one-dimensional tight-binding Hamiltonian subject to repeated measurements at fixed small time intervals, resulting in effective non-unitary dynamics. We find that the spread complexity initially grows with time, followed by an extended decay period and saturation. The choice of initial state determines the saturation value of complexity and entropy. 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. We find that as a function of the measurement frequency, the time at which the spread complexity starts growing increases. This time asymptotes to infinity when the time gap between measurements is taken to zero, indicating the onset of the quantum Zeno effect, according to which measurements impede time evolution.
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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP03(2024)179