Field Theory of Charge Sharpening in Symmetric Monitored Quantum Circuits

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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 nonequilibrium 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.
Funding Information
  • National Science Foundation (DMR-1653271, DMR-1653007, OMA-2120757)
  • Air Force Office of Scientific Research (FA9550-21-1-0123)
  • Alfred P. Sloan Foundation
  • National Science Foundation (DMR-1653271, DMR-1653007, OMA-2120757)
  • Air Force Office of Scientific Research (FA9550-21-1-0123)
  • Alfred P. Sloan Foundation

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