LAUSR

Fundamental open questions about the two-dimensional Holstein model of electrons coupled to quantum phonons are addressed by continuous-time quantum Monte Carlo simulations. The critical temperature of the charge-density-wave transition is determined by a finite-size scaling of a renormalization-group-invariant correlation ratio. $T_c$ is finite for any nonzero coupling for classical phonons, and suppressed by quantum lattice fluctuations. The phase transition---also detectable via the fidelity susceptibility and machine learning---is demonstrated to be in the universality class of the two-dimensional quantum Ising model. We discuss the possibility of $T_c=0$ at weak coupling and present evidence for a spin-gapped, bipolaronic metal above $T_c$.