Strong-coupling-expansion analysis of the false-vacuum decay rate of the lattice ϕ4model in 1 + 1 dimensions

Abstract

Strong-coupling expansion is performed for the lattice phi^4 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 eleventh order. We carried out 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 tunnelling phenomenon lies out of perturbative treatments, our series expansion reproduces the instanton-theory behaviour for high potential barrier. For shallow barrier, on the contrary, our result tells that the relaxation is no more described by instanton, but the decay rate acquires notable enhancement.