TY - JOUR

T1 - Field Theory of Charge Sharpening in Symmetric Monitored Quantum Circuits

AU - Barratt, Fergus

AU - Agrawal, Utkarsh

AU - Gopalakrishnan, Sarang

AU - Huse, David A.

AU - Vasseur, Romain

AU - Potter, Andrew C.

N1 - Publisher Copyright:
© 2022 American Physical Society.

PY - 2022/9/16

Y1 - 2022/9/16

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevLett.129.120604

DO - 10.1103/PhysRevLett.129.120604

M3 - Article

C2 - 36179163

AN - SCOPUS:85138861339

SN - 0031-9007

VL - 129

JO - Physical review letters

JF - Physical review letters

IS - 12

M1 - 120604

ER -