  The phase diagram of the one-dimensional Su-Schrieffer-Heeger model of
spinless fermions coupled to quantum phonons is determined by quantum Monte
Carlo simulations. It differs significantly from previous work. In addition to
Luttinger liquid and bond-order-wave (BOW) phases, we find an extended
charge-density-wave (CDW) phase. Because of different broken symmetries, BOW
and CDW phases are connected by a retardation-driven phase transition. Our
results are consistent with the theory of the frustrated $XXZ$ chain, including
unconventional power-law exponents at criticality, and an interpretation in
terms of deconfined quantum criticality via proliferation of solitons.
