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

Abstract

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-away from equilibrium dynamics are 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 have focused on the effects of this emergent conformal symmetry on two observables: the moment of inertia tensor, Iij(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 behaviour 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 non-vanishing entropy production. This suggests that the entropy production rate is a natural parameter for categorizing the breaking of conformal symmetry. arXiv:1904.11549v1 [cond-mat.quant-gas]

Bulk Viscosity and Contact Correlations in Attractive Fermi Gases

“…1. The logarithmic singularity for small frequencies corresponds via Fourier transform to the logarithmic singularity of the bulk viscosity at long times, ζ(t) ∼ ln(t)/(a 2 t) [46]. Precisely at unitarity, the bulk viscosity vanishes for all frequencies due to the v 2 ∝ a −2 factor.…”

Nonrelativistic Conformal Invariance in Mesoscopic Two-Dimensional Fermi Gases

“…The hyperradial distribution should be observable experimentally by sampling the many-body wavefunction using recently developed single-atom imaging techniques [55,56], thus verifying the conformal symmetry on a microscopy level, with deviations from our predictions (for example, at stronger interactions or for deformed or rotating traps) a signature of anomalous or explicit symmetry breaking. More broadly, the mesoscopic 2D Fermi gas constitutes an experimentally relevant toy model in which the conformal symmetry can be studied exactly using elementary techniques, which provides a new way to address current problems such as conformal non-equilibrium dynamics [26,[66][67][68][69][70][71].…”

Dynamics of strongly interacting Fermi gases with time-dependent interactions: Consequence of conformal symmetry

“…Introduction. -Conformal symmetry [1][2][3] imposes severe constraints on the dynamics of non-relativistic scale invariant quantum systems, thanks to an overarching SO(2,1) symmetry that generally occurs for quantum systems with dynamical critical exponent z = 2 [4][5][6][7][8][9]. The most prominent example of such systems are atomic gases, where the quantum critical point can be accessed using a Feshbach resonance [10].…”

“…When an atomic gas deviates from its critical point, the scale invariance of the Hamiltonian is broken, and the interactions can be described by a finite length scale, a, that parametrizes the strength of the interactions. Previously studies have focused on the dynamical effects caused by time-independent interactions [9,11]. However, since conformal symmetry is dynamical, one can further consider the dynamics of driven quantum critical systems.…”

“…For specificity, we will focus on the dynamics near the strongly interacting SIFP, and present general results later. Close to the strongly interacting SIFP, the total Hamiltonian can be expanded as [9,11]:…”