51. Field Theory of Charge Sharpening in Symmetric Monitored Quantum Circuits
- Author
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Fergus Barratt, Utkarsh Agrawal, Sarang Gopalakrishnan, David A. Huse, Romain Vasseur, and Andrew C. Potter
- Subjects
Quantum Physics ,Condensed Matter - Strongly Correlated Electrons ,Statistical Mechanics (cond-mat.stat-mech) ,Strongly Correlated Electrons (cond-mat.str-el) ,General Physics and Astronomy ,FOS: Physical sciences ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,Quantum Physics (quant-ph) ,Condensed Matter - Statistical Mechanics - Abstract
Monitored quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the non-equilibrium dynamics and steady-state distribution of charge fluctuations. These include a charge-fuzzy phase in which charge information is rapidly scrambled leading to slowly decaying spatial fluctuations of charge in the steady state, and a charge-sharp phase in which measurements collapse quantum fluctuations of charge without destroying the volume-law entanglement of neutral degrees of freedom. By taking a continuous-time, weak-measurement limit, we construct a controlled replica field theory description of these phases and their intervening charge-sharpening transition in one spatial dimension. We find that the charge fuzzy phase is a critical phase with continuously evolving critical exponents that terminates in a modified Kosterlitz-Thouless transition to the short-range correlated charge-sharp phase. We numerically corroborate these scaling predictions also hold for discrete-time projective-measurement circuit models using large-scale matrix-product state simulations, and discuss generalizations to higher dimensions., Comment: 5+8 pages, 3 figures
- Published
- 2021