Quantum dynamics of multiparty competition

Competition among multiple orders is a defining feature of strongly correlated matter, from frustrated magnets to high-T_c superconductors. Here, I will present two examples where quantum dynamics is governed by such multiparty competition.
In the first part, we briefly discuss the dynamics of a Kondo impurity coupled to an attractive Fermi–Hubbard bath. Examining transport between two one-dimensional leads connected by the impurity, we find long-time competition among charge, magnetic, and superconducting orders: a dynamical crossover from superconducting to charge-density-wave order precedes a DC current peak driven by Kondo correlations.
In the second part, we study one-dimensional fermions evolving under a BCS Hamiltonian with gap Δ, subject to on-site, spin-selective number measurements at rate p. Defying the common expectation that LOCC measurements cannot increase steady-state entanglement, we show that for Δ>0 the steady-state entropy S_s grows with p over a finite interval 0<p<p_th. The mechanism is a multiparty competition among unitary entanglement generation, measurement, and fermion pairing: pairing suppresses entanglement, measurement suppresses pairing, and together these effects yield a net increase in entanglement S_s as the measurement rate p rises.
Taken together, these results showcase the rich nonequilibrium phenomena that arise from multiparty competition under both unitary and monitored dynamics.