Strong-coupling-expansion analysis of the false-vacuum decay rate of the lattice φ⁴ model in 1 + 1 dimensions

Strong-coupling expansion is performed for the lattice φ⁴ model in 1 + 1 dimensions. Because the strong-coupling limit itself is not solvable, we employed numerical calculations so as to set up unperturbed eigensystems. Restricting the number of Hilbert-space bases, we performed linked-cluster expansion up to 11th order. We carried out an alternative simulation by means of the density-matrix renormalization group. Thereby, we confirmed that our series-expansion data with a convergence-acceleration trick are in good agreement with the simulation result. Through the analytic continuation to the domain of negative biquadratic interaction, we obtain the false-vacuum decay rate. Contrary to common belief that the tunnelling phenomenon lies out of perturbative treatments, our series expansion reproduces the instanton-theory behaviour for a high potential barrier. For a shallow barrier, in contrast, our result tells us that the relaxation is no longer described by an instanton, but the decay rate acquires notable enhancement.