Contributor info: Mr Oscar Bouverot-Dupuis

Oscar Bouverot-Dupuis, Silvia Pappalardi, Jorge Kurchan, Anatoli Polkovnikov, Laura Foini

SciPost Phys. 19, 050 (2025) · published 20 August 2025 | Toggle abstract · pdf

We study the behaviour of two-time correlation functions at late times for finite system sizes considering observables whose (one-point) average value does not depend on energy. In the long time limit, we show that such correlation functions display a ramp and a plateau determined by the correlations of energy levels, similar to what is already known for the spectral form factor. The plateau value is determined, in absence of degenerate energy levels, by the fluctuations of diagonal matrix elements, which highlights differences between different symmetry classes. We show this behaviour analytically by employing results from Random Matrix Theory and the Eigenstate Thermalisation Hypothesis, and numerically by exact diagonalization in the toy example of a Hamiltonian drawn from a Random Matrix ensemble and in a more realistic example of disordered spin glasses at high temperature. Importantly, correlation functions in the ramp regime do not show self-averaging behaviour, and, at difference with the spectral form factor the time average does not coincide with the ensemble average.

Oscar Bouverot-Dupuis

SciPost Phys. 17, 130 (2024) · published 11 November 2024 | Toggle abstract · pdf

An XXZ spin chain at zero magnetization is subject to spatially correlated baths acting as dissipation. We show that the low-energy excitations of this model are described by a dissipative sine-Gordon field theory, i.e. a sine-Gordon action with an additional long-range interaction emerging from dissipation. The field theory is then exactly mapped onto a generalized Coulomb gas which, in addition to the usual integer charges, displays half-integer charges that originate from the dissipative baths. These new charges come in pairs linked by a charge independent logarithmic interaction. In the Coulomb gas picture, we identify a Berezinsky–Kosterlitz–Thouless-like phase transition corresponding to the binding of charges and derive the associated perturbative renormalization group equations. For superohmic baths, the transition is due to the binding of the integer charges, while for subohmic baths, it is due to the binding of the half-integer charges, thereby signaling a dissipation-induced transition.