Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                

Classification of SL2 deformed Floquet conformal field theories

Bo Han and Xueda Wen
Phys. Rev. B 102, 205125 – Published 20 November 2020
PDFHTMLExport Citation
Abstract
Authors
Article Text
  • INTRODUCTION
  • SL2 DEFORMED FLOQUET CFT
  • CLASSIFYING THE SL2 DEFORMED FLOQUET CFT
  • CONCLUSION AND DISCUSSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Classification of the nonequilibrium quantum many-body dynamics is a challenging problem in condensed matter physics and statistical mechanics. In this work, we study the basic question that whether a (1+1) dimensional conformal field theory (CFT) is stable or not under a periodic driving with N noncommuting Hamiltonians. Previous works showed that a Floquet (or periodically driven) CFT driven by certain SL2 deformed Hamiltonians exhibit both nonheating (stable) and heating (unstable) phases. In this work, we show that the phase diagram depends on the types of driving Hamiltonians. In general, the heating phase is generic, but the nonheating phase may be absent in the phase diagram. For the existence of the nonheating phases, we give sufficient and necessary conditions for N=2 and sufficient conditions for N>2. These conditions are composed of N layers of data, with each layer determined by the types of driving Hamiltonians. Our results also apply to the single quantum quench problem with N=1.

    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    1 More
    • Received 19 August 2020
    • Accepted 22 October 2020

    DOI:https://doi.org/10.1103/PhysRevB.102.205125

    ©2020 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Conformal field theoryEntanglement entropy
    1. Physical Systems
    Floquet systems
    Condensed Matter, Materials & Applied PhysicsStatistical Physics & ThermodynamicsParticles & Fields

    Authors & Affiliations

    Bo Han1 and Xueda Wen2

    • 1Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
    • 2Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    Article Text (Subscription Required)

    Click to Expand

    References (Subscription Required)

    Click to Expand
    Issue

    Vol. 102, Iss. 20 — 15 November 2020

    Reuse & Permissions
    Access Options
    Author publication services for translation and copyediting assistance advertisement

    Authorization Required

    Log In
    Other Options
    ×

    Images

    • Figure 1
      Figure 1

      Different types of manifolds determined by Eq. (5) with different quadratic Casimir c(2). Each single point on the manifold specifies a deformed Hamiltonian through (2) and (3). Any point on the manifold is SL(2,R) equivalent to arbitrary points on the same manifold.

      Reuse & Permissions
    • Figure 2
      Figure 2

      Path integral representation of the correlation function 〈G|O(x,τ)|G〉 in a CFT with periodical boundary conditions. Here, x=0 and x=L are identified.

      Reuse & Permissions
    • Figure 3
      Figure 3

      Phase diagrams of a Floquet CFT with the both nonheating (in blue) and heating (in red) phases for the six kinds of pairings with N=2 in Table 1. The parameters are (from left to right and then top to bottom): elliptic-elliptic with C1=(1,0,0) and C2=(1,0.5,0); elliptic-parabolic with C1=(1,0,0) and C2=(1,1,0); elliptic-hyperbolic with C1=(1,0,0) and C2=(0,0.4,0); parabolic-parabolic with C1=(1,1,0) and C2=(1,0,1); parabolic-hyperbolic with C1=(1,1,0) and C2=(1,0.6,1); hyperbolic-hyperbolic with C1=(1,1.4,0) and C2=(1,0,1.4).

      Reuse & Permissions
    • Figure 4
      Figure 4

      C1C1=(σ10,σ1+,σ1−)=(0,1,0) is fixed (the vector in black). The normalized vectors C2C2 that satisfy the condition in Eq. (40) are in the region in green.

      Reuse & Permissions
    • Figure 5
      Figure 5

      Phase diagram in a Floquet CFT with N=2 driving Hamiltonians, both of which are of hyperbolic types. The corresponding Casimir vectors are C1=(1,a,0) and C2=(1,0,a), where we choose a=1.4 (left), 1.41421 (middle), and 1.41421356 (right). The location of the nonheating phase in blue will move to infinity as we approach a=2 from a<2. For a>2, the condition in (40) is violated, and the nonheating phase does not exist.

      Reuse & Permissions
    • Figure 6
      Figure 6

      Nonheating phases in a Floquet CFT with N=3 driving Hamiltonians, all of which are of hyperbolic types. We choose λ=1.1 (left) in (50) such that only the condition ηn=2<0 is satisfied, and λ=3 (right) such that only the condition ηN=3<0 is satisfied. The complemented regions are in the heating phase.

      Reuse & Permissions
    • Figure 7
      Figure 7

      Two vectors C1C1 and C2C2 corresponding to two noncommuting reflection matrices M1 and M2 in (B16).

      Reuse & Permissions
    • Figure 8
      Figure 8

      Heating line (in green) determined by Eqs. (B18) and (B19) in the unit cell with 0<Tj≤l/Cj (j=1,2) in the cases of C1=(1,0,0) and C2=(1,0.5,0) (left) and C1=(1,0,0) and C2=(−1,0.5,0) (right). Here we choose l=1. The blue dots represent the heating point as defined in Eq. (B15). The regions in red (blue) corresponds to a heating (nonheating) phase.

      Reuse & Permissions
    ×

    Sign up to receive regular email alerts from Physical Review B

    Log In

    Cancel
    ×

    Search

    Article Lookup

    Paste a citation or DOI
    Enter a citation
    ×