RQC Seminar

76th RQC Seminar

• Speaker

  Dr. Vanja Maric
  ( Université Paris-Saclay )

• Date

  13:00-14:00, August 14, 2023 (Monday)

• Venue

  Hybrid(ZOOM・ Wako Main Research 3F 335 Seminar Room C01）

• Title

  Universality in the tripartite information after global quenches

• Inquiries

  rqc_info[at]ml.riken.jp

Abstract
We consider the (Rényi-α) tripartite information of three, macroscopically large, adjacent subsystems A, B,C in infinite quantum spin chains. At equilibrium in clean 1D systems with local Hamiltonians, it generally vanishes. A notable exception is the ground state of conformal critical systems, in which it is known to be a universal function of the cross ratio x = |A||C|/[(|A| + |B|)(|C| + |B|)], where |A| denotes A’s length. We identify different classes of states that, under time evolution with translationally invariant Hamiltonians, locally relax to states with a nonzero tripartite information, which furthermore exhibits a universal dependency on x. In particular, we investigate stationary states emerging after global quenches in noninteracting spin chains: we report a numerical study, develop a field theory description, map the calculation into a Riemann-Hilbert problem and derive analytic formulae for the tripartite information. This allows us to infer the value of the tripartite information in the scaling limit x→ 1^-, which we call ``residual tripartite information''. If nonzero, our analysis points to a universal residual value -log 2 independently of the Rényi index α, and hence applies also to the genuine (von Neumann) tripartite information.

References: V. Maric, M. Fagotti. Universality in the tripartite information after global quenches. arXiv:2209.14253

V. Maric, M. Fagotti. Universality in the tripartite information after global quenches: (generalized) quantum XY models. JHEP 2023, 140 (arXiv:2302.01322).

V. Maric. Universality in the tripartite information after global quenches: spin flip and semilocal charges. arXiv:2307.01842