Operator Spreading and the Emergence of Dissipative Hydrodynamics under Unitary Evolution with Conservation Laws
By V. Khemani, Ashvin Vishwanath, D. Huse. Physical Review X, 2017
413 citations recorded by the source corpus.
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 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) non-conserved operators. This emission leads to dissipation in the operator hydrodynamics, with the dissipative process being the 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 non-observable, 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 (OTOC) 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.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/664b4472f008605c0776996b09eb1dd5243ea76d
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Citations in the corpus
- Random Quantum Circuits (2022, methodology): “This process can be described via coupled hydrodynamic equations (92).”
- Unitary circuits of finite depth and infinite width from quantum channels (2019, methodology): “[32] Vedika Khemani, Ashvin Vishwanath, and David A.”
- Engineered dissipation for quantum information science (2022, background): “Finally, at the intersection of quantum dynamical systems and quantum thermodynamics are questions about equilibration, when quantum systems can be described thermodynamically 273–276 , and quantifying the information complexity of such systems 277,278 .”
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement (2018, neutral): “[9, 13, 18, 22, 28–39].”
- Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos (2018, background): “In the presence of additional conserved densities (like energy or charge), the late time saturation of the OTOC is a power-law in time instead of exponential [45, 46].”
- Entanglement and Charge-Sharpening Transitions in U(1) Symmetric Monitored Quantum Circuits (2021, background): “[12] Vedika Khemani, Ashvin Vishwanath, and David A.”
- Locality, Quantum Fluctuations, and Scrambling (2018, methodology): “This has already been studied in the random brickwork circuit [38, 39], but we anticipate new interesting physics associated with the interplay with the large N effects.”
- Disentangling Scrambling and Decoherence via Quantum Teleportation (2018, methodology): “The fact that the projector ΠDD0 can halt the chaotic dynamics of U is consistent with the traversable wormhole interpretation of the Hayden-Preskill thought experiment [5,11,29].”
- Localization from Hilbert space shattering: From theory to physical realizations (2020, background): “[49] Vedika Khemani, Ashvin Vishwanath, and David A.”
- Localization in Fractonic Random Circuits (2018, methodology): “Since the initial condition involves a dipole operator, which acts as a conserved U(1) charge without any conservation laws on its higher moments, this is a situation that should map onto the analysis of [18], and serves as a sanity check on our results.”
- A Universal Operator Growth Hypothesis (2018, background): “Recent work has shifted focus from states to operator growth in many-body systems [6–11].”
- Onset of random matrix behavior in scrambling systems (2018, methodology): “,37,38,39,40]. These techniques were used to give the rst logarithmic estimate of scrambling [18]. More recently they have been used to calculate OTOC for k-local [22] and geometrically local systems [41,42,43]. These models are currently being used as testbeds to establish \quantum supremacy" ”
- Entanglement in a fermion chain under continuous monitoring (2018, neutral): “[77–85].”
- Fracton phases of matter (2020, methodology): “For example, it has been shown that the presence of charge conservation leads to certain operators having a slow diffusively spreading piece, in addition to a ballistic piece [106, 107].”
- Scrambling Dynamics and Out-of-Time-Ordered Correlators in Quantum Many-Body Systems (2022, background): “There are also generalizations of the random unitary circuit to respect charge conservation [74, 75], dipolar conservation [76] or other kinetic constraints, which are important for studying the interplay between transport phenomena and scrambling.”