TY - JOUR
T1 - Entanglement and Purification Transitions in Non-Hermitian Quantum Mechanics
AU - Gopalakrishnan, Sarang
AU - Gullans, Michael J.
N1 - Publisher Copyright:
© 2021 American Physical Society.
PY - 2021/4/30
Y1 - 2021/4/30
N2 - A quantum system subject to continuous measurement and postselection evolves according to a non-Hermitian Hamiltonian. We show that, as one increases the strength of postselection, this non-Hermitian Hamiltonian can undergo a spectral phase transition. On one side of this phase transition (for weak postselection), 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, analytically tractable mean-field theory; these methods yield consistent conclusions.
AB - A quantum system subject to continuous measurement and postselection evolves according to a non-Hermitian Hamiltonian. We show that, as one increases the strength of postselection, this non-Hermitian Hamiltonian can undergo a spectral phase transition. On one side of this phase transition (for weak postselection), 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, analytically tractable mean-field theory; these methods yield consistent conclusions.
UR - http://www.scopus.com/inward/record.url?scp=85105456834&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85105456834&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.126.170503
DO - 10.1103/PhysRevLett.126.170503
M3 - Article
C2 - 33988446
AN - SCOPUS:85105456834
SN - 0031-9007
VL - 126
JO - Physical review letters
JF - Physical review letters
IS - 17
M1 - 170503
ER -