Quantum many-body conformal dynamics: Symmetries, geometry, conformal tower states, and entropy production

摘要

In this article we study the quench dynamics of Galilean and scale-invariant many-body systems which can be prepared using interacting atomic gases. The far-from-equilibrium dynamics is investigated by employing m-body density matrices, which are most conveniently defined in terms of a special basis, the conformal tower states. We explicitly illustrate that, although during the initial stage of the dynamics all symmetries can be broken and absent in the unitary evolution because of the initialization of the state, there is always an emergent conformal symmetry in the long-time limit. The emergence of this dynamic conformal symmetry is robust and always occurs, even when scale and other symmetries (such as rotational symmetry) are still fully broken in the many-body states; it uniquely defines the characteristics of the asymptotic dynamics near a scale-invariant strong-coupling fixed point. As an immediate application of the asymptotic dynamics of the microscopic density matrices, we focus on the effects of this emergent conformal symmetry on two observables: the moment of inertia tensor I_(ij) (t ), i, j = x, y, z, and the entropy density field S(r, t ) in the hydrodynamic flow of strongly interacting particles. We show that the long-time behavior of these observables is completely set by conformal symmetry, while the leading long-time corrections depend on interference effects between different conformal tower states. The emergent conformal symmetry naturally leads to entropy conservation and conformal cooling, an energy-conserving cooling of a strongly interacting gas during free expansion. When the interaction Hamiltonian breaks the scale symmetry, we further demonstrate that there is a direct cause-effect relation between conformal symmetry breaking in the long-time limit and a nonvanishing entropy production. This suggests that the entropy production rate is a natural parameter for categorizing the breaking of conformal symmetry.