Quenched coupling, entangled equilibria, and correlated composite operators: a tale of two O(N) models

Abstract

A macroscopic version of Einstein-Podolsky-Rosen entanglement is obtained by quenching a quadratic coupling between two O(N ) vector models. A quench of the mixed vacuum produces an excited entangled state, reminiscent of purified thermal equilibrium, whose properties can be studied analytically in the free limit of the individual field theories.The decoupling of different wavelength modes in free field theory prevents true thermalisation but a more subtle difference is that the density operator obtained by a partial trace does not commute with the post-quench Hamiltonian. Generalized thermal behaviour is obtained at late times, in the limit of weak initial mixing or a smooth but rapid quench. More surprisingly, late-time correlation functions of composite operators in the post-quench free field theory share interesting properties with correlators in strongly coupled systems. We propose a holographic interpretation of our result.

Tidal excitation as mixing in thermal CFT

“…The identification of the proper thermal operators is essential for our calculation of the mixing of composite operators. The importance of compositeness is a familiar theme in investigations of fundamental holography [28,29], but we encountered a new twist. The operators of the singlet models have to be singlets under the gauge group, and this condition necessitates replacing partial derivatives with gauge covariant derivatives, as usual.…”

Dynamical Symmetry and the Thermofield State at Large N

“…In what follows, we will be demonstrating the existence and explicit construction of Ĝ[ f ] in perturbation theory. This will be performed through solving the condition (15) .…”

“…We build on the initial work of [13] where the collective Hamiltonian representation of the real time SK contour was used to study emergent [14] space-time. A number of interesting recent works concern the O(N) model [15,16] and its holographic role. The dynamical symmetry and the large N collective TFD state wavefunction(al) described in the present work clearly hold more general relevance.…”

Operator thermalisation in d > 2: Huygens or resurgence

“…A motivation behind the operator thermalisation hypothesis, and one of its strengths, is that it can be used to study surprising similarities between ordinary interacting systems and free or integrable systems [6,10,11,13]. While pure exponential decay occurs in free systems in contrast to naive expectations, it is generally masked by leading power law decay for d > 2, as well as multiplied by inverse powers of time.…”

“…Nonetheless, it is known that nontrivial interference effects can effectively mimic equilibration. For example, after quantum quenches [3][4][5][6], correlation functions in free QFTs approach those of a generalised Gibbs ensemble [4,[7][8][9], characterised by chemical potentials for all conserved charges which in free QFTs is equivalent to a momentum-dependent temperature. Similarly, nontrivial time dependence arises when considering composite operators.…”