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A<sc>bstract</sc> We establish an equivalence between two different quantum quench problems, the joining local quantum quench and the Möbius quench, in the context of (1 + 1)-dimensional conformal field theory (CFT). Here, in the former, two initially decoupled systems (CFTs) on finite intervals are joined att= 0. In the latter, we consider the system that is initially prepared in the ground state of the regular homogeneous Hamiltonian on a finite interval and, aftert= 0, let it time-evolve by the so-called Möbius Hamiltonian that is spatially inhomogeneous. The equivalence allows us to relate the time-dependent physical observables in one of these problems to those in the other. As an application of the equivalence, we construct a holographic dual of the Möbius quench from that of the local quantum quench. The holographic geometry involves an end-of-the-world brane whose profile exhibits non-trivial dynamics.
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Exactly solvable floquet dynamics for conformal field theories in dimensions greater than two
A<sc>bstract</sc> We find classes of driven conformal field theories (CFT) ind+ 1 dimensions withd> 1, whose quench and floquet dynamics can be computed exactly. The setup is suitable for studying periodic drives, consisting of square pulse protocols for which Hamiltonian evolution takes place with different deformations of the original CFT Hamiltonian in successive time intervals. These deformations are realized by specific combinations of conformal generators with a deformation parameterβ; theβ< 1 (β> 1) Hamiltonians can be unitarily related to the standard (Lüscher-Mack) CFT Hamiltonians. The resulting time evolution can be then calculated by performing appropriate conformal transformations. Ford≤ 3 we show that the transformations can be easily obtained in a quaternion formalism. Evolution with such a single Hamiltonian yields qualitatively different time dependences of observables depending on the value ofβ, with exponential decays characteristic of heating forβ> 1, oscillations forβ< 1 and power law decays forβ= 1. This manifests itself in the behavior of the fidelity, unequal-time correlator, and the energy density at the end of a single cycle of a square pulse protocol with different hamiltonians in successive time intervals. When the Hamiltonians in a cycle involve generators of a single SU(1, 1) subalgebra we calculate the Floquet Hamiltonian. We show that one can get dynamical phase transitions for anyβby varying the time period of a cycle, where the system can go from a non-heating phase which is oscillatory as a function of the time period to a heating phase with an exponentially damped behavior. Our methods can be generalized to other discrete and continuous protocols. We also point out that our results are expected to hold for a broader class of QFTs that possesses an SL(2,C) symmetry with fields that transform as quasi-primaries under this. As an example, we briefly comment on celestial CFTs in this context.
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- Award ID(s):
- 2111673
- PAR ID:
- 10651942
- Publisher / Repository:
- Springer Nature
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2024
- Issue:
- 9
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1007/JHEP09(2024)095
