Leinweber Seminar: Non-perturbative constraints on phase diagrams of non-equilibrium systems. - Tarun Grover, UCSD
1:30 pm
MCP 201
Non-perturbative constraints on phase diagrams of non-equilibrium systems.
In this talk I will discuss constraints on renormalization group (RG) flows and the stability of phases in nonequilibrium systems using information-theoretic inequalities, with examples drawn from both quantum and classical settings. The central quantity underlying these constraints is the conditional mutual information (CMI), which quantifies correlations between spatially separated regions that are not mediated by their surroundings. I will present two results. The first relies on the assumption that the CMI is UV-finite (i.e. independent of the short-distance cutoff) and implies that a fixed point with smaller CMI cannot be destabilized toward one with larger CMI. One consequence is that a system described by a Gibbs state of a local Hamiltonian cannot be directly destabilized into a phase with long-range CMI, such as those occurring at the directed-percolation critical point, or in two-dimensional flocking phases, or in recently proposed strong-to-weak symmetry-breaking systems.
The second result bounds the CMI of a convex mixture of states in terms of the CMI of individual components. I will use this inequality to infer perturbative stability of spontaneous symmetry breaking states against arbitrary quantum channels that explicitly break symmetry ("spontaneous symmetry breaking without symmetry").