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

• DOI: 10.48550/arxiv.2312.11635
• Publication Date: 2023-01-01
• Authors: Aranya Bhattacharya; Rathindra Nath Das; Bidyut Dey; Johanna Erdmenger
• Keywords: Quantum Zeno effect; Hamiltonian (control theory); Time evolution; Quantum system

Using spread complexity and entropy, we study non-unitary quantum dynamics. For non-hermitian Hamiltonians, extend the bi-Lanczos construction for Krylov basis to Schr\"odinger picture. Moreover, implement an algorithm adapted complex symmetric Hamiltonians. This reduces computational memory requirements by half compared construction. We apply this one-dimensional tight-binding Hamiltonian subject repeated measurements at fixed small time intervals, resulting in effective find that initially grows with time, followed extended decay period saturation. The choice of initial state determines saturation value entropy. In analogy measurement-induced phase transitions, consider a quench between hermitian evolution induced turning on regular different frequencies. as function measurement frequency, which starts growing increases. asymptotes infinity when gap is taken zero, indicating onset Zeno effect, according impede evolution.