Details

Autor(en) / Beteiligte

• Khemani, Vedika
• Vishwanath, Ashvin
• Huse, David A.

Titel

Operator Spreading and the Emergence of Dissipative Hydrodynamics under Unitary Evolution with Conservation Laws

Ist Teil von

• Physical review. X, 2018-09, Vol.8 (3), p.031057, Article 031057

Ort / Verlag

College Park: American Physical Society

Erscheinungsjahr

2018

Link zum Volltext

Quelle

Free E-Journal (出版社公開部分のみ）

Beschreibungen/Notizen

• We study the scrambling of local quantum information in chaotic many-body systems in the presence of a locally conserved quantity like charge or energy that moves diffusively. The interplay between conservation laws and scrambling sheds light on the mechanism by which unitary quantum dynamics, which is reversible, gives rise to diffusive hydrodynamics, which is a slow dissipative process. We obtain our results in a random quantum circuit model that is constrained to have a conservation law. We find that a generic spreading operator consists of two parts: (i) a conserved part which comprises the weight of the spreading operator on the local conserved densities, whose dynamics is described by diffusive charge spreading; this conserved part also acts as a source that steadily emits a flux of (ii) nonconserved operators. This emission leads to dissipation in the operator hydrodynamics, with the dissipative process being the slow conversion of operator weight from local conserved operators to nonconserved, at a rate set by the local diffusion current. The emitted nonconserved parts then spread ballistically at a butterfly speed, thus becoming highly nonlocal and, hence, essentially nonobservable, thereby acting as the “reservoir” that facilitates the dissipation. In addition, we find that the nonconserved component develops a power-law tail behind its leading ballistic front due to the slow dynamics of the conserved components. This implies that the out-of-time-order commutator between two initially separated operators grows sharply upon the arrival of the ballistic front, but, in contrast to systems with no conservation laws, it develops a diffusive tail and approaches its asymptotic late-time value only as a power of time instead of exponentially. We also derive these results within an effective hydrodynamic description which contains multiple coupled diffusion equations.