Abstract
In this paper and its sequel, we study non-equilibrium dynamics in driven 1+1D conformal field theories (CFTs) with periodic, quasi-periodic, and random driving. We study a soluble family of drives in which the Hamiltonian only involves the energy-momentum density spatially modulated at a single wavelength. The resulting time evolution is then captured by a M\"obius coordinate transformation. In this Part I, we establish the general framework and focus on the first two classes. In periodically driven CFTs, we generalize earlier work and study the generic features of entanglement/energy evolution in different phases, i.e. the heating, non-heating phases and the phase transition between them. In quasi-periodically driven CFTs, we mainly focus on the case of driving with a Fibonacci sequence. We find that (i) the non-heating phases form a Cantor set of measure zero; (ii) in the heating phase, the Lyapunov exponents (which characterize the growth rate of the entanglement entropy and energy) exhibit self-similarity, and can be arbitrarily small; (iii) the heating phase exhibits periodicity in the location of spatial structures at the Fibonacci times; (iv) one can find exactly the non-heating fixed point, where the entanglement entropy/energy oscillate at the Fibonacci numbers, but grow logarithmically/polynomially at the non-Fibonacci numbers; (v) for certain choices of driving Hamiltonians, the non-heating phases of the Fibonacci driving CFT can be mapped to the energy spectrum of electrons propagating in a Fibonacci quasi-crystal. In addition, another quasi-periodically driven CFT with an Aubry-Andr\'e like sequence is also studied. We compare the CFT results to lattice calculations and find remarkable agreement.
Highlights
Nonequilibrium dynamics in time-dependent driven quantum many-body systems has received extensive recent attention
We are interested in a quantum (1 + 1)-dimensional [(1 + 1)D] conformal field theory (CFT), which may be viewed as the low-energy effective field theory of a many-body system at the critical point
We extend the previous study on periodic driving to quasiperiodic2 and random drivings, and make a connection to the familiar concepts of crystal, quasicrystal, and disordered systems
Summary
Nonequilibrium dynamics in time-dependent driven quantum many-body systems has received extensive recent attention. In this work and its upcoming sequel, we introduce and study a general class of soluble models of driven CFTs with a variety of driving protocols We determine their dynamical phase diagrams of heating versus nonheating behavior, when the periodicity of the drive is absent. ΛL > 0 represents a heating phase, and we show that total energy of the system grows exponentially as E (n) ∝ e2λL·n and the entanglement entropy of the subsystem that includes the energy-momentum density peaks grows linearly in time as S(n) ∝ λLn. One interesting universal phenomenon here is that the total energy and the entanglement are not distributed evenly in the system, instead the driven state will develop an array of peaks of energy-momentum density in the real space. The nonheating phase in the parameter space of a Fibonacci driving CFT corresponds to the energy spectrum of a Fibonacci quasicrystal Both form a Cantor set of measure zero. We provide several appendices with details of calculations and examples
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
