Nonequilibrium Broken-Symmetry States from Retained Observables

Abstract

In equilibrium, broken-symmetry states are selected by the competition between energy and entropy. Out of equilibrium, slowly relaxing observables retain information about the preparation and may reshape this competition, allowing orders that are not thermally favored. Identifying such states ordinarily requires following slow, protocol-dependent dynamics. Here we recast this dynamical selection as a static constrained variational problem. A small set of experimentally measurable or numerically accessible quantities-particle number, energy, and slow observables-defines a constraint space. The underlying dynamics determines where the system lies in this space, while entropy maximization over both quasiparticle occupations and a prescribed class of candidate orders determines which order is selected. Restricting the variational states to the Gaussian manifold yields a computationally inexpensive constrained Hartree-Fock implementation. For photoexcited Hubbard models, the approach reproduces the long-time TDHF suppression of square-lattice antiferromagnetism and identifies incommensurate spiral order in place of the equilibrium $120^\circ$ state on the triangular lattice. For a continuously driven ferromagnetic double-exchange model, evaluating the constrained order map at the stationary NESS energy reveals a restricted region in which Neel order is favored. The framework therefore turns the search for nonequilibrium broken-symmetry states into a practical static screening problem, without requiring simulations of every preparation protocol.