On thermality of CFT eigenstates

Abstract

The Eigenstate Thermalization Hypothesis (ETH) provides a way to understand how an isolated quantum mechanical system can be approximated by a thermal density matrix. We find a class of operators in (1+1)-$d$ conformal field theories, consisting of quasi-primaries of the identity module, which satisfy the hypothesis only at the leading order in large central charge. In the context of subsystem ETH, this plays a role in the deviation of the reduced density matrices, corresponding to a finite energy density eigenstate from its hypothesized thermal approximation. The universal deviation in terms of the square of the trace-square distance goes as the 8th power of the subsystem fraction and is suppressed by powers of inverse central charge ($c$). Furthermore, the non-universal deviations from subsystem ETH are found to be proportional to the heavy-light-heavy structure constants which are typically exponentially suppressed in $\sqrt{h/c}$, where $h$ is the conformal scaling dimension of the finite energy density state. We also examine the effects of the leading finite size corrections.

25 pages, 2 figures; published version with a few references added

References in corpus (10)

• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT
• Thermalization and Revivals after a Quantum Quench in Conformal Field Theory
• Quantum Entanglement of Localized Excited States at Finite Temperature
• Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT

Cited by in corpus (47)

• Universal Dynamics of Heavy Operators in CFT${}_2$
• Probing thermality beyond the diagonal
• ETH and Modular Invariance of 2D CFTs
• Heavy Operators and Hydrodynamic Tails
• A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled
• Typicality and thermality in 2d CFT
• Charged structure constants from modularity
• Generalized Eigenstate Thermalization in 2d CFTs
• Universality of Quantum Information in Chaotic CFTs
• Phases of scrambling in eigenstates
• Bounds on the density of states and the spectral gap in CFT${}_2$
• Generalized Gibbs Ensemble of 2d CFTs at large central charge in the thermodynamic limit
• Thermalization in Large-N CFTs
• Generalized Spectral Form Factors and the Statistics of Heavy Operators
• Thermal Stress Tensor Correlators, OPE and Holography
• Holographic Quantum Scars
• Multiboundary wormholes and OPE statistics
• Holographic Renyi Entropy at High Energy Density
• Quantum thermalization and Virasoro symmetry
• Entanglement versus entwinement in symmetric product orbifolds
• Note on ETH of descendant states in 2D CFT
• Eigenstate Thermalisation in the conformal Sachdev-Ye-Kitaev model: an analytic approach
• Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory -- I. Single-particle states
• Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part II. Multi-particle states
• Subsystem distances between quasiparticle excited states
• Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry
• Trace distance between fermionic Gaussian states from a truncation method
• Zero modes of local operators in 2d CFT on a cylinder
• Lightcone Modular Bootstrap and Tauberian Theory: A Cardy-like Formula for Near-extremal Black Holes
• Spectrum of quantum KdV hierarchy in the semiclassical limit
• Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains
• Unveiling Eigenstate Thermalization for Non-Hermitian systems
• Subsystem entropy in 2d CFT and KdV ETH
• Rényi entropy at large energy density in 2D CFT
• Subsystem eigenstate thermalization hypothesis for translation invariant systems
• Ergodicity breaking and deviation from Eigenstate Thermalisation in relativistic QFT
• Entanglement Properties of Boundary State and Thermalization
• Remarks on effects of projective phase on eigenstate thermalization hypothesis
• A Strategy for Proving the Strong Eigenstate Thermalization Hypothesis : Chaotic Systems and Holography
• Generalized Gibbs Ensemble of 2D CFTs with U(1) Charge from the AGT Correspondence
• Quantum many-body physics from a gravitational lens
• Taking the temperature of quantum many-body scars
• Universal thermalization dynamics in (1+1)d QFTs
• Perturbative distinguishability of black hole microstates from AdS/CFT correspondence
• Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions
• Subsystem fidelity in two-dimensional conformal field theories
• Subsystem Thermalization Hypothesis in Quantum Spin Chains with Conserved Charges