Charge fluctuation and charge-resolved entanglement in monitored quantum circuit with $U(1)$ symmetry

• URL: http://arxiv.org/abs/2210.16009v2
• Date: Wed, 23 Nov 2022 04:55:10 GMT
• Title: Charge fluctuation and charge-resolved entanglement in monitored quantum circuit with $U(1)$ symmetry
• Authors: Hisanori Oshima and Yohei Fuji
• Abstract summary: We study a (1+1)-dimensional quantum circuit consisting of Haar-random unitary gates and projective measurements. We find a phase transition between two phases characterized by bipartite charge fluctuation growing with the subsystem size or staying constant.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study a (1+1)-dimensional quantum circuit consisting of Haar-random unitary gates and projective measurements that conserve a total $U(1)$ charge and thus have $U(1)$ symmetry. In addition to a measurement-induced entanglement transition between a volume-law and an area-law entangled phase, we find a phase transition between two phases characterized by bipartite charge fluctuation growing with the subsystem size or staying constant. At this charge-fluctuation transition, steady-state quantities obtained by evolving an initial state with a definitive total charge exhibit critical scaling behaviors akin to Tomonaga-Luttinger-liquid theory for equilibrium critical quantum systems with $U(1)$ symmetry, such as logarithmic scaling of bipartite charge fluctuation, power-law decay of charge correlation functions, and logarithmic scaling of charge-resolved entanglement whose coefficient becomes a universal quadratic function in a flux parameter. These critical features, however, do not persist below the transition in contrast to a recent prediction based on replica field theory and mapping to a classical statistical mechanical model.

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