No eigenstate of the critical transverse-field Ising chain satisfies the area law
arXiv:2303.09525 · doi:10.1103/PhysRevB.109.L201116
Abstract
We argue that, in a basis common to all one-site shift invariant conserved charges, there is no eigenstate of a noninteracting local spin-1/2 chain Hamiltonian that satisfies the area law if the ground state has half-integer central charge. That is to say, in those models all (quasi)local one-site shift invariant conserved operators are gapless. From the standpoint of bipartite entanglement properties, we show indeed that there are three distinct one-site shift invariant noninteracting models, two of which are equivalent to the XX model (for one of them the transformation breaks one-site shift invariance) and the other to the critical Ising model. The former class has two locally distinct one-site shift invariant excited states satisfying the area law; the latter two classes have none.
arXiv comment5+6 pages, 7 figures. Typos corrected, figures updated
References in corpus (51)
- Concentrating Partial Entanglement by Local Operations
- Area laws for the entanglement entropy - a review
- Entanglement in quantum critical phenomena
- Entanglement entropy and conformal field theory
- An Area Law for One Dimensional Quantum Systems
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Entanglement entropy in free quantum field theory
- Quantum Many-Body Scars and Weak Breaking of Ergodicity
- Aspects of generic entanglement
- Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
- Thermodynamical Property of Entanglement Entropy for Excited States
- Entanglement Temperature and Entanglement Entropy of Excited States
- Entanglement of low-energy excitations in Conformal Field Theory
- Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
- Entanglement entropy of two disjoint blocks in XY chains
- Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
- Entanglement entropy of excited states
- Entanglement and matrix elements of observables in interacting integrable systems
- Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians
- On Conservation Laws, Relaxation and Pre-relaxation after a Quantum Quench
- Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
- Volume Law and Quantum Criticality in the Entanglement Entropy of Excited Eigenstates of the Quantum Ising Model
- Renyi Entropy of Chaotic Eigenstates
- Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians
- The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties
- Spectra and eigenstates of spin chain Hamiltonians
- Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems
- Structure of chaotic eigenstates and their entanglement entropy
- Entanglement of excited states in critical spin chians
- Excited state entanglement in homogeneous fermionic chains
- Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models
- Entanglement in ground and excited states of gapped fermion systems and their relationship with fermi surface and thermodynamic equilibrium properties
- Bound states and entanglement in the excited states of quantum spin chains
- Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
- Statistical properties of eigenstate amplitudes in complex quantum systems
- Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents
- Explicit Hamiltonians Inducing Volume Law for Entanglement Entropy in Fermionic Lattices
- Excited state entanglement in one dimensional quantum critical systems: Extensivity and the role of microscopic details
- Bipartite entanglement entropy of the excited states of the free fermions and the harmonic oscillators
- Rényi entropies of generic thermodynamic macrostates in integrable systems
- Eigenstate entanglement: Crossover from the ground state to volume laws
- Entanglement and relative entropies for low-lying excited states in inhomogeneous one-dimensional quantum systems
- Corrections to universal Rényi entropy in quasiparticle excited states of quantum chains
- Eigenstate entanglement scaling for critical interacting spin chains
- Excited States in Spin Chains from Conformal Blocks
- Entanglement Entropy of Fermions from Wigner Functions: Excited States and Open Quantum Systems
- Universality in the tripartite information after global quenches
- Free-fermion Page Curve: Canonical Typicality and Dynamical Emergence
- Entanglement Entropy of Excited States in the Quantum Lifshitz Model
- Universality in the tripartite information after global quenches: (generalised) quantum XY models
- Nonlocal fermions and the entropy volume law