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Entanglement and purification transitions in non-Hermitian quantum mechanics



Michael Gullans, Sarang Gopalakrishnan


A quantum system subject to continuous measurement and post-selection evolves according to a non- Hermitian Hamiltonian. We show that, as one increases the rate of post-selection, this non- Hermitian Hamiltonian can undergo a spectral phase transition. On one side of this phase transition (for weak post-selection) an initially mixed density matrix remains mixed at all times, and an initially unentangled state develops volume-law entanglement; on the other side, an arbitrary initial state approaches a unique pure state with low entanglement. We identify this transition with an exceptional point in the spectrum of the non-Hermitian Hamiltonian, at which PT symmetry is spontaneously broken. We characterize the transition as well as the nontrivial steady state that emerges at late times in the mixed phase using exact diagonalization and an approximate, analyti- cally tractable mean-field theory; these methods yield consistent conclusions.
Physical Review Letters


Gullans, M. and Gopalakrishnan, S. (2021), Entanglement and purification transitions in non-Hermitian quantum mechanics, Physical Review Letters, [online],, (Accessed May 26, 2024)


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Created April 30, 2021, Updated June 16, 2021