Non-perturbative False Vacuum Decay Using Lattice Monte Carlo in Imaginary Time

We present a new method for calculating quantum tunneling rates using lattice Monte Carlo simulations in imaginary time. This method is designed with the goal of studying false vacuum decay non-perturbatively on the lattice. We derive a new formula, which is similar in form to Fermi’s Golden Rule, which gives the decay rate in terms of an implicit decay amplitude. We then show how to calculate this implicit decay amplitude on the lattice. To deal with the suppression of the false vacuum state in the Euclidean path integral, we develop a new sampling method which combines results from multiple Monte Carlo simulations. For a simple family of one-dimensional quantum systems, we reproduce the tunneling rates calculated from the Schrodinger equation.

💡 Research Summary

The paper introduces a novel, fully non‑perturbative technique for computing false‑vacuum decay rates using lattice Monte Carlo simulations performed in imaginary (Euclidean) time. The authors begin by reviewing the importance of metastable false‑vacuum states in a variety of contexts—cosmological phase transitions, electroweak baryogenesis, gravitational‑wave production, and even QCD at finite density—highlighting the limitations of the traditional semiclassical Callan‑Coleman approach when couplings become strong.

To overcome the intrinsic difficulty that false‑vacuum configurations are exponentially suppressed in the Euclidean path integral, the authors construct two auxiliary Hamiltonians. The “false‑vacuum Hamiltonian” (H_{\text{FV}} = H + \bar V_{\text{FV}}(x)) adds a repulsive potential that lifts the true‑vacuum region, thereby isolating the false‑vacuum sector. Conversely, the “true‑vacuum Hamiltonian” (H_{\text{TV}} = H + \bar V_{\text{TV}}(x)) adds a barrier that prevents the system from entering the false‑vacuum basin. Both modifications are designed to coincide with the original Hamiltonian in the region of interest, ensuring that low‑energy dynamics are unchanged while the sampling problem is alleviated.

The core theoretical development is the “Implicit Decay Amplitude Method.” Starting from the transition amplitude
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