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

Abstract

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 Möbius transformation on the complex coordinates. The non-equilibrium dynamics is then determined by the corresponding sequence of Möbius transformations, from which the Lyapunov exponent ${\lambda }_L$ is defined. We use Furstenberg's theorem to classify the dynamical phases and show that except for a few \emph{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 ${\lambda }_L$. On the contrary, the subsystem entanglement entropy at an exceptional point could grow as $\sqrt{n}$ 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.

66 pages, 1 table, many figures; This is part II on randomly driven CFTs

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Cited by in corpus (21)

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• Inhomogeneous quenches as state preparation in two-dimensional conformal field theories
• Thermal and dissipative effects on the heating transition in a driven critical system
• Local operator quench induced by two-dimensional inhomogeneous and homogeneous CFT Hamiltonians
• Universal out-of-equilibrium dynamics of 1D critical quantum systems perturbed by noise coupled to energy
• Exactly solvable non-unitary time evolution in quantum critical systems I: Effect of complex spacetime metrics
• Floquet engineered inhomogeneous quantum chaos in critical systems
• Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results
• Driven Non-Unitary Dynamics of Quantum Critical Systems
• Inhomogeneous Quantum Quenches of Conformal Field Theory with Boundaries
• Scattering Expansion for Localization in One Dimension: from Disordered Wires to Quantum Walks
• Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking
• Insights from the exact analytical solution of periodically driven transverse field Ising chain
• From time crystals to time quasicrystals: Exploring quasiperiodic phases in transverse field Ising chains
• Scattering Expansion for Localization in One Dimension
• Stable time rondeau crystals in dissipative many-body systems
• Spatially Structured Entanglement from Nonequilibrium Thermal Pure States
• Phase transitions from Heating to non-heating in SU(1, 1) quantum dynamics: applications to Bose-Einstein condensates and periodically driven coupled oscillators
• Emergence of prethermal time quasicrystalline order in a quasiperiodically driven non-interacting spin chain