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Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases

Wen, Xueda and Gu, Yingfei and Vishwanath, Ashvin and Fan, Ruihua (2022) Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases. SciPost Physics, 13 (4). ISSN 2542-4653. doi:10.21468/scipostphys.13.4.082.

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In this sequel (to [Phys. Rev. Res. 3, 023044(2021)], arXiv:2006.10072), we study randomly driven (1 + 1) dimensional conformal field theories (CFTs), a family of quantum many-body systems with soluble non-equilibrium quantum dynamics. The sequence of driving Hamiltonians is drawn from an independent and identically distributed random ensemble. At each driving step, the deformed Hamiltonian only involves the energy-momentum density spatially modulated at a single wavelength and therefore induces a M\"obius transformation on the complex coordinates. The non-equilibrium dynamics is then determined by the corresponding sequence of M\"obius transformations, from which the Lyapunov exponent λ_L is defined. We use Furstenberg's theorem to classify the dynamical phases and show that except for a few exceptional points that do not satisfy Furstenberg's criteria, the random drivings always lead to a heating phase with the total energy growing exponentially in the number of driving steps n and the subsystem entanglement entropy growing linearly in n with a slope proportional to central charge c and the Lyapunov exponent λ_L. On the contrary, the subsystem entanglement entropy at an exceptional point could grow as √n while the total energy remains to grow exponentially. In addition, we show that the distributions of the operator evolution and the energy density peaks are also useful characterizations to distinguish the heating phase from the exceptional points: the heating phase has both distributions to be continuous, while the exceptional points could support finite convex combinations of Dirac measures depending on their specific type. In the end, we compare the field theory results with the lattice model calculations for both the entanglement and energy evolution and find remarkably good agreement.

Item Type:Article
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URLURL TypeDescription
Wen, Xueda0000-0002-3285-5033
Gu, Yingfei0000-0001-8645-879X
Additional Information:We thank for helpful discussions with Dan Borgnia, Daniel Jafferis, Bo Han, Eslam Khalaf, Ching Hua Lee, Ivar Martin, Shinsei Ryu, Hassan Shapourian, Tsukasa Tada, Michael Widom, Jie-Qiang Wu, and Yahui Zhang. XW, RF and AV are supported by a Simons Investigator award (AV) and by the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (651440, AV). AV and RF are supported by the DARPA DRINQS program (award D18AC00033). YG is supported by the the Simons Foundation through the “It from Qubit” program.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)D18AC00033
Simons Foundation651440
Issue or Number:4
Record Number:CaltechAUTHORS:20221104-610921700.12
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117716
Deposited By: Research Services Depository
Deposited On:17 Nov 2022 20:03
Last Modified:17 Nov 2022 20:03

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