Charge fluctuation and charge-resolved entanglement in a monitored quantum circuit with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>U</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> symmetry

We study a ($1+1$)-dimensional quantum circuit consisting of Haar-random unitary gates and projective measurements, both which conserve total $U(1)$ charge thus have symmetry. In addition to measurement-induced entanglement transition between volume-law an area-law entangled phase, we find phase two phases characterized by bipartite fluctuation growing with the subsystem size or staying constant. At this charge-fluctuation transition, steady-state quantities obtained evolving initial state definitive exhibit critical scaling behaviors akin Tomonaga-Luttinger-liquid theory for equilibrium systems symmetry, such as logarithmic fluctuation, power-law decay correlation functions, charge-resolved whose coefficient becomes universal quadratic function in flux parameter. These features, however, do not persist below contrast recent prediction based on replica field mapping classical statistical mechanical model.