Many-body chaos in the antiferromagnetic quantum critical metal
Abstract
Here, we compute the scrambling rate at the antiferromagnetic (AFM) quantum critical point, using the fixed point theory found by Schlief, Lunts, and Lee. At this strongly coupled fixed point, there is an emergent control parameter $$w \ll 1$$ that is a ratio of natural parameters of the theory. The strong coupling is unequally felt by the two degrees of freedom: the bosonic AFM collective mode is heavily dressed by interactions with the electrons, while the electron is only marginally renormalized. We find that the scrambling rates act as a measure of the “degree of integrability” of each sector of the theory: the Lyapunov exponent for the boson $$λ^{(B)}_L \sim \mathcal{O} (\sqrt{w})k_BT/ℏ$$ is significantly larger than the fermion one $$λ^{(F)}_L \sim \mathcal{O}(w^2)k_BT/ℏ$$, where $$\textit{T}$$ is the temperature. Although the interaction strength in the theory is of order unity, the larger Lyapunov exponent is still parametrically smaller than the universal upper bound of $$λ_L = 2πk_BT/ℏ$$. We also compute the spatial spread of chaos by the boson operator, whose low-energy propagator is highly nonlocal. We find that this nonlocality leads to a scrambled region that grows exponentially fast at intermediate distances, giving an infinite “butterfly velocity” of the chaos front, a result that has also been found in lattice models with long-range interactions.
- Authors:
-
- Flatiron Institute, New York, NY (United States)
- Harvard Univ., Cambridge, MA (United States)
- Publication Date:
- Research Org.:
- Harvard Univ., Cambridge, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1803504
- Grant/Contract Number:
- SC0019030
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 23; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics
Citation Formats
Lunts, Peter, and Patel, Aavishkar A. Many-body chaos in the antiferromagnetic quantum critical metal. United States: N. p., 2019.
Web. doi:10.1103/physrevb.100.235104.
Lunts, Peter, & Patel, Aavishkar A. Many-body chaos in the antiferromagnetic quantum critical metal. United States. https://doi.org/10.1103/physrevb.100.235104
Lunts, Peter, and Patel, Aavishkar A. Mon .
"Many-body chaos in the antiferromagnetic quantum critical metal". United States. https://doi.org/10.1103/physrevb.100.235104. https://www.osti.gov/servlets/purl/1803504.
@article{osti_1803504,
title = {Many-body chaos in the antiferromagnetic quantum critical metal},
author = {Lunts, Peter and Patel, Aavishkar A.},
abstractNote = {Here, we compute the scrambling rate at the antiferromagnetic (AFM) quantum critical point, using the fixed point theory found by Schlief, Lunts, and Lee. At this strongly coupled fixed point, there is an emergent control parameter $w \ll 1$ that is a ratio of natural parameters of the theory. The strong coupling is unequally felt by the two degrees of freedom: the bosonic AFM collective mode is heavily dressed by interactions with the electrons, while the electron is only marginally renormalized. We find that the scrambling rates act as a measure of the “degree of integrability” of each sector of the theory: the Lyapunov exponent for the boson $λ^{(B)}_L \sim \mathcal{O} (\sqrt{w})k_BT/ℏ$ is significantly larger than the fermion one $λ^{(F)}_L \sim \mathcal{O}(w^2)k_BT/ℏ$, where $\textit{T}$ is the temperature. Although the interaction strength in the theory is of order unity, the larger Lyapunov exponent is still parametrically smaller than the universal upper bound of $λ_L = 2πk_BT/ℏ$. We also compute the spatial spread of chaos by the boson operator, whose low-energy propagator is highly nonlocal. We find that this nonlocality leads to a scrambled region that grows exponentially fast at intermediate distances, giving an infinite “butterfly velocity” of the chaos front, a result that has also been found in lattice models with long-range interactions.},
doi = {10.1103/physrevb.100.235104},
journal = {Physical Review B},
number = 23,
volume = 100,
place = {United States},
year = {Mon Dec 02 00:00:00 EST 2019},
month = {Mon Dec 02 00:00:00 EST 2019}
}
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