Universality of Quantum Information in Chaotic CFTs

Abstract

We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite volume limit when the full system is an energy eigenstate. This reduced density matrix is close in trace distance to a density matrix, to which we refer as the ETH density matrix, that is independent of all the details of an eigenstate except its energy and charges under global symmetries. In two dimensions, the ETH density matrix is universal for all theories with the same value of central charge. We argue that the ETH density matrix is close in trace distance to the reduced density matrix of the (micro)canonical ensemble. We support the argument in higher dimensions by comparing the Von Neumann entropy of the ETH density matrix with the entropy of a black hole in holographic systems in the low temperature limit. Finally, we generalize our analysis to the coherent states with energy density that varies slowly in space, and show that locally such states are well described by the ETH density matrix.

43 pages

References in corpus (5)

• Thermalization and its mechanism for generic isolated quantum systems
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Bulk Emergence and the RG Flow of Entanglement Entropy
• Relative entropy of excited states in conformal field theories of arbitrary dimensions
• Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis

Cited by in corpus (36)

• Universal Dynamics of Heavy Operators in CFT${}_2$
• Entanglement Wedge Cross Section from CFT: Dynamics of Local Operator Quench
• Probing thermality beyond the diagonal
• ETH and Modular Invariance of 2D CFTs
• A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled
• Generalized Eigenstate Thermalization in 2d CFTs
• Thermal Correlation Functions of KdV Charges in 2D CFT
• Probing beyond ETH at large $c$
• Thermal Conformal Blocks
• Subsystem trace distance in low-lying states of $(1+1)$-dimensional conformal field theories
• Generalized Gibbs Ensemble of 2d CFTs at large central charge in the thermodynamic limit
• Thermalization in Large-N CFTs
• Thermal Stress Tensor Correlators, OPE and Holography
• Exact generalized partition function of 2D CFTs at large central charge
• Entanglement entropy in (1+1)D CFTs with multiple local excitations
• Universality in asymptotic bounds and its saturation in $2$D CFT
• Holographic Renyi Entropy at High Energy Density
• Near Lightcone Thermal Conformal Correlators and Holography
• Quantum thermalization and Virasoro symmetry
• Note on ETH of descendant states in 2D CFT
• Universal Dynamics of Heavy Operators in Boundary CFT${}_2$
• Extended Eigenstate Thermalization and the role of FZZT branes in the Schwarzian theory
• Eigenstate Thermalisation in the conformal Sachdev-Ye-Kitaev model: an analytic approach
• The Bulk-to-Boundary Propagator in Black Hole Microstate Backgrounds
• Interactions resolve state-dependence in a toy-model of AdS black holes
• Eigenstate Thermalization Hypothesis and Approximate Quantum Error Correction
• Zero modes of local operators in 2d CFT on a cylinder
• Spectrum of quantum KdV hierarchy in the semiclassical limit
• Subsystem entropy in 2d CFT and KdV ETH
• Microstate Distinguishability, Quantum Complexity, and the Eigenstate Thermalization Hypothesis
• Rényi entropy at large energy density in 2D CFT
• Subsystem eigenstate thermalization hypothesis for translation invariant systems
• Generalized Gibbs Ensemble of 2D CFTs with U(1) Charge from the AGT Correspondence
• Quantum many-body physics from a gravitational lens
• Universal thermalization dynamics in (1+1)d QFTs
• A polynomial time algorithm for studying physical observables in chaotic eigenstates