Subsystem entropy in 2d CFT and KdV ETH
arXiv:2409.19046 · doi:10.1103/PhysRevResearch.7.023121
Abstract
We study subsystem entropy in 2d CFTs, for subsystems constituting a finite fraction of the full system. We focus on the extensive contribution, which scales linearly with the subsystem size in the thermodynamic limit. We employ the so-called diagonal approximation to evaluate subsystem entropy for the chaotic CFTs in thermal state (canonical ensemble), microcanonical ensemble, and in a primary state, matching previously known results. We then proceed to find analytic expressions for the subsystem entropy at leading order in , when the global CFT state is the KdV generalized Gibbs ensemble or the KdV microcanonical ensemble. Previous studies of primary eigenstates have shown that, akin to fixed-area states in AdS/CFT, corresponding subsystem entanglement spectrum is flat. This behavior is seemingly in sharp contradiction with the one for the thermal (microcanonical) state, and thus in apparent contradiction with the subsystem Eigenstate Thermalization Hypothesis (ETH). In this work, we resolve this issue by comparing the primary state with the KdV (micro)canonical ensemble. We show that the results are consistent with the KdV-generalized version of the subsystem ETH, in which local properties of quantum eigenstates are governed by their values of conserved KdV charges. Our work solidifies evidence for the KdV-generalized ETH in 2d CFTs and emphasizes Renyi entropy as a sensitive probe of the reduced-density matrix.
54 pages, 6 figures
References in corpus (109)
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Entanglement Entropy and Quantum Field Theory
- Thermalization and its mechanism for generic isolated quantum systems
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Aspects of Holographic Entanglement Entropy
- A Covariant Holographic Entanglement Entropy Proposal
- Entanglement entropy and conformal field theory
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- Towards a derivation of holographic entanglement entropy
- Evolution of Entanglement Entropy in One-Dimensional Systems
- Generalized gravitational entropy
- Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
- Quantum corrections to holographic entanglement entropy
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
- Holographic Entanglement Entropy: An Overview
- The Page curve of Hawking radiation from semiclassical geometry
- Solving the 3D Ising Model with the Conformal Bootstrap
- Generalized Gibbs ensemble in integrable lattice models
- Entanglement entropy in free quantum field theory
- Entanglement Renyi entropies in holographic theories
- Complete Generalized Gibbs Ensemble in an interacting Theory
- Holographic duality from random tensor networks
- Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
- Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
- Entanglement and correlation functions following a local quench: a conformal field theory approach
- Entanglement entropy of two disjoint intervals in conformal field theory
- Generalized Thermalization in an Integrable Lattice System
- The Gravity Dual of Renyi Entropy
- Holographic Entanglement Entropy
- Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
- Entanglement entropy of two disjoint intervals in conformal field theory II
- Deriving covariant holographic entanglement
- Does a single eigenstate encode the full Hamiltonian?
- Holographic Calculations of Renyi Entropy
- Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
- Proof of the Holographic Formula for Entanglement Entropy
- Remarks on the entanglement entropy for disconnected regions
- Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
- Holographic entanglement beyond classical gravity
- Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
- Subsystem ETH
- Entanglement entropy of excited states
- Flat entanglement spectra in fixed-area states of quantum gravity
- Entanglement and matrix elements of observables in interacting integrable systems
- A c-theorem for the entanglement entropy
- Holographic Renyi Entropy from Quantum Error Correction
- Semiclassical 3D gravity as an average of large-c CFTs
- A Cardy Formula for Three-Point Coefficients: How the Black Hole Got its Spots
- On short interval expansion of Rényi entropy
- Relative Entropies in Conformal Field Theory
- Eigenstate Thermalization Hypothesis and Free Probability
- Renyi Entropy of Chaotic Eigenstates
- Some Calculable Contributions to Holographic Entanglement Entropy
- Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians
- Modular Hamiltonian of Excited States in Conformal Field Theory
- Structure of chaotic eigenstates and their entanglement entropy
- Universal Thermal Corrections to Single Interval Entanglement Entropy for Conformal Field Theories
- Holographic Rényi entropy for CFT with symmetry
- Holographic Phases of Renyi Entropies
- Probing thermality beyond the diagonal
- Analytical results for the entanglement Hamiltonian of a free-fermion chain
- Relative entropy of excited states in two dimensional conformal field theories
- Entanglement Entropy of a Massive Fermion on a Torus
- Universal eigenstate entanglement of chaotic local Hamiltonians
- Analytic Euclidean Bootstrap
- On thermality of CFT eigenstates
- Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models
- Shape Dependence of Holographic Rényi Entropy in General Dimensions
- A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled
- Comments on Renyi entropy in AdS/CFT
- Shape Dependence of Holographic Renyi Entropy in Conformal Field Theories
- Single Interval Rényi Entropy At Low Temperature
- Generalized Eigenstate Thermalization in 2d CFTs
- Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
- Renyi entropies of free bosons on the torus and holography
- Universality of Quantum Information in Chaotic CFTs
- Beurling-Selberg Extremization and Modular Bootstrap at High Energies
- Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT
- Enhanced corrections near holographic entanglement transitions: a chaotic case study
- One-loop universality of holographic codes
- Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis
- Probing beyond ETH at large
- Thermal Correlation Functions of KdV Charges in 2D CFT
- Eigenstate thermalization and rotational invariance in ergodic quantum systems
- Eigenstate entanglement: Crossover from the ground state to volume laws
- Thermality and excited state Rényi entropy in two-dimensional CFT
- Generalized Gibbs Ensemble of 2d CFTs at large central charge in the thermodynamic limit
- Coupled minimal models revisited
- Holographic Calculation for Large Interval Rényi Entropy at High Temperature
- Exact generalized partition function of 2D CFTs at large central charge
- Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians
- Holographic Renyi Entropy at High Energy Density
- Large Interval Limit of Rényi Entropy At High Temperature
- Note on ETH of descendant states in 2D CFT
- Eigenstate entanglement scaling for critical interacting spin chains
- Rényi Entropy of Free Compact Boson on Torus
- Quantifying quantum chaos through microcanonical distributions of entanglement
- KdV-charged black holes
- A Modified Cosmic Brane Proposal for Holographic Renyi Entropy
- Average pure-state entanglement entropy in spin systems with SU(2) symmetry
- Generalized Free Cumulants for Quantum Chaotic Systems
- Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems
- Corrections to holographic entanglement plateau
- Zero modes of local operators in 2d CFT on a cylinder
- Spectrum of quantum KdV hierarchy in the semiclassical limit
- Correlation functions and quantum measures of descendant states
- Typical entanglement entropy in systems with particle-number conservation
- Scaling functions for eigenstate entanglement crossovers in harmonic lattices