Real-time false-vacuum decay in the quantum Ising chain reproduces the Fonseca–Zamolodchikov rate

Recent real-time simulations of false-vacuum decay in the quantum Ising chain report decay-rate prefactors that disagree with each other and with field theory by factors up to three. We prepare the metastable state by a real-time ramp of the longitudinal field, measure the survival rate per site of an infinite matrix-product state, and compare it with the decay rate that Fonseca and Zamolodchikov obtained from the free energy of the Ising field theory continued to negative field. At two lattice spacings and scaling variables y = 2.2–2.8 the ratio is 1.008 with a standard deviation of 0.015 over 6 runs, with no adjustable parameter, once the first correction to the thin-wall formula is kept. The two-kink coefficient π∆E/18 used in recent comparisons is too large by π2/9, as anticipated by Fonseca and Zamolodchikov, and exponential fits to the order parameter return rates 147–390 times larger than the nucleation rate. The survival rate, or equivalently the growth rate of the bubble density, is the observable that quantum simulators should compare with theory.