Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems

By S. Gopalakrishnan, D. Huse, V. Khemani, Romain Vasseur. Physical review B, 2018

205 citations recorded by the source corpus.

We address the hydrodynamics of operator spreading in interacting integrable lattice models. In these models, operators spread through the ballistic propagation of quasiparticles, with an operator front whose velocity is locally set by the fastest quasiparticle velocity. In interacting integrable systems, this velocity depends on the density of the other quasiparticles, so equilibrium density fluctuations cause the front to follow a biased random walk, and therefore to broaden diffusively. Ballistic front propagation and diffusive front broadening are also generically present in nonintegrable systems in one dimension; thus, although the mechanisms for operator spreading are distinct in the two cases, these coarse-grained measures of the operator front do not distinguish between the two cases. We present an expression for the front-broadening rate; we explicitly derive this for a particular integrable model (the ``Floquet-Fredrickson-Andersen'' model), and argue on kinetic grounds that it should apply generally. Our results elucidate the microscopic mechanism for diffusive corrections to ballistic transport in interacting integrable models.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mathematics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b9589de462608b4409034376da5603596bb89db6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. Shenglong Xu
3. V. Khemani
4. Matthew Fisher
5. Brian Swingle
6. S. Vijay
7. B. Doyon
8. E. Altman

In Computational Mathematics

1. B. Doyon
2. Matthew Fisher

In Nuclear and High Energy Physics

1. A. Nahum
2. Matthew Fisher
3. B. Doyon
4. S. Vijay
5. E. Altman
6. D. Parker
7. Xiangyu Cao
8. Brian Swingle

Citations in the corpus

• Diffusion in generalized hydrodynamics and quasiparticle scattering (2018, methodology): “In a following publication [66], the diagonal part of the diffusion matrix was shown to be obtainable from quasiparticle spreading, and it was shown that diffusion has consequences for the dynamics of the out-of-time correlators (OTOC) [82] in interacting integrable systems, which displays the gener”
• Random Quantum Circuits (2022, background): “This model captures many features of more complicated integrable systems, but permits solutions of various quantities including non-equilibrium steady-states, operator and entanglement spreading, and generalized hydrodynamics (247, 254, 255, 248, 249).”
• Scrambling Dynamics and Out-of-Time-Ordered Correlators in Quantum Many-Body Systems (2022, background): “For a generic system with short-ranged interaction and no disorder, local operators spread ballistically, which has been shown in numerous systems including field theories [54, 55], free and integrable models [56, 57], interacting spin chains [58, 59] and circuit models [60–63].”
• A Universal Operator Growth Hypothesis (2018, background): “[10] Sarang Gopalakrishnan, David A Huse, Vedika Khemani, and Romain Vasseur, “Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems,” arXiv:1809.”
• Entanglement in a fermion chain under continuous monitoring (2018, unknown): “[77–85].”
• Lecture notes on Generalised Hydrodynamics (2019, background): “6 to the cases of integrable models, as done in [88, 103] and [41, 86, 130].”