Operator growth in 2d CFT

@article{Caputa2021OperatorGI,
  title={Operator growth in 2d CFT},
  author={Pawel Caputa and Shouvik Datta},
  journal={Journal of High Energy Physics},
  year={2021}
}
Abstract We investigate and characterize the dynamics of operator growth in irrational two-dimensional conformal field theories. By employing the oscillator realization of the Virasoro algebra and CFT states, we systematically implement the Lanczos algorithm and evaluate the Krylov complexity of simple operators (primaries and the stress tensor) under a unitary evolution protocol. Evolution of primary operators proceeds as a flow into the ‘bath of descendants’ of the Verma module. These… 

Figures from this paper

Growth of a renormalized operator as a probe of chaos
We propose that the size of an operator evolved under holographic renormalization group flow shall grow linearly with the scale and interpret this behavior as a manifestation of the saturation of the
Virasoro Entanglement Berry Phases
We study the parallel transport of modular Hamiltonians encoding entanglement properties of a state. In the case of 2d CFT, we consider a change of state through action with a suitable diffeomorphism
Probing the entanglement of operator growth
In this work we probe the operator growth for systems with Lie symmetry using tools from quantum information. Namely, we investigate the Krylov complexity, entanglement negativity, von Neumann
Krylov Localization and suppression of complexity
A notion of quantum complexity can be effectively captured by quantifying the spread of an operator in Krylov space as a consequence of time evolution. Complexity is expected to behave differently in

References

SHOWING 1-10 OF 60 REFERENCES
Symmetries near the horizon
Abstract We consider a nearly-AdS2 gravity theory on the two-sided wormhole geometry. We construct three gauge-invariant operators in NAdS2 which move bulk matter relative to the dynamical
Quantum thermalization and Virasoro symmetry
We initiate a systematic study of high energy matrix elements of local operators in 2d CFT. Knowledge of these is required in order to determine whether the eigenstate thermalization hypothesis (ETH)
Unveiling Operator Growth Using Spin Correlation Functions
TLDR
It is argued that it is possible to distinguish between operator-hopping and operator growth dynamics; the latter being a hallmark of quantum chaos in many-body quantum systems.
Typicality and thermality in 2d CFT
Abstract We identify typical high energy eigenstates in two-dimensional conformal field theories at finite c and establish that correlation functions of the stress tensor in such states are
Exact Correlators of Giant Gravitons from dual N=4 SYM
A class of correlation functions of half-BPS composite operators are computed exactly (at finite $N$) in the zero coupling limit of N=4 SYM theory. These have a simple dependence on the
Operator growth in the SYK model
A bstractWe discuss the probability distribution for the “size” of a time-evolving operator in the SYK model. Scrambling is related to the fact that as time passes, the distribution shifts towards
Generalized Eigenstate Thermalization Hypothesis in 2D Conformal Field Theories.
TLDR
It is proposed that in the thermodynamic limit large central charge 2D CFTs satisfy generalized eigenstate thermalization, with the values of qKdV charges forming a complete set of thermodynamically relevant quantities, which unambiguously determine expectation values of all local observables from the vacuum family.
Semi-classical Virasoro blocks: proof of exponentiation
Virasoro conformal blocks are expected to exponentiate in the limit of large central charge c and large operator dimensions h i , with the ratios h i /c held fixed. We prove this by employing the
A Universal Operator Growth Hypothesis
We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued
Bounding the space of holographic CFTs with chaos
A bstractThermal states of quantum systems with many degrees of freedom are subject to a bound on the rate of onset of chaos, including a bound on the Lyapunov exponent, λL ≤ 2π/β. We harness this
...
1
2
3
4
5
...