Simulating a Catalyst induced Quantum Dynamical Phase Transition of a Heyrovsky reaction with different models for the environment

TL;DR

This paper analytically demonstrates that a catalyst can induce a quantum dynamical phase transition in a Heyrovsky reaction, affecting molecular dissociation through environment-induced spectral discontinuities, modeled with different environmental approximations.

Contribution

It introduces an analytical framework linking catalyst-induced dissociation to quantum phase transitions, incorporating environment effects via Lorentzian and Gaussian models.

Findings

Critical dissociation condition when bonding is √2 times molecular bonding

Environment broadening causes spectral discontinuities indicative of phase transition

Resonance features in tunneling current reflect critical spectral properties

Abstract

Through an appropriate election of the molecular orbital basis, we show analytically that the molecular dissociation occurring in a Heyrovsky reaction can be interpreted as a Quantum Dynamical Phase Transition, i.e., an analytical discontinuity in the molecular energy spectrum induced by the catalyst. The metallic substrate plays the role of an environment that produces an energy uncertainty on the adatom. This broadening induces a critical behavior not possible in a quantum closed system. We use suitable approximations on symmetry, together with both Lanczos and canonical transformations, to give analytical estimates for the critical parameters of molecular dissociation. This occurs when the bonding to the surface is (\sqrt{2}) times the molecular bonding. This value is slightly weakened for less symmetric situations. However simple, this conclusion involves a high order perturbative solution of the molecule-catalyst system. This model is further simplified to discuss how an environment-induced critical phenomenon can be evaluated through an idealized perturbative tunneling microscopy set-up. In this case, the energy uncertainties in one or both atoms are either Lorentzian or Gaussian. The former results from the Fermi Golden Rule, i.e., a Markovian approximation. The Gaussian uncertainty, associated with non-Markovian decoherent processes, requires the introduction of a particular model of a spin bath. The partially coherent tunneling current is obtained from the Generalized Landauer-B\"uttiker Equations. The resonances observed in these transport parameters reflect, in many cases, the critical properties of the resonances in the molecular spectrum.