Exact volume-law entangled zero-energy eigenstates in a large class of spin models
arXiv:2410.22773 · doi:10.1103/PhysRevLett.134.210403
Abstract
Exact solutions for excited states in non-integrable quantum Hamiltonians have revealed novel dynamical phenomena that can occur in quantum many-body systems. This work proposes a method to analytically construct a specific set of volume-law-entangled zero-energy exact excited eigenstates in a large class of spin Hamiltonians. In particular, we show that all spin chains that satisfy a simple set of conditions host exact volume-law zero-energy eigenstates in the middle of their spectra. Examples of physically relevant spin chains of this type include the transverse-field Ising model, PXP model, spin- model, and spin- Kitaev chain. Although these eigenstates are highly atypical in their structure, they are thermal with respect to local observables. Our framework also unifies many recent constructions of volume-law entangled eigenstates in the literature. Finally, we show that a similar construction also generalizes to spin models on graphs in arbitrary dimensions.
References in corpus (58)
- Anyons in an exactly solved model and beyond
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Nonequilibrium dynamics of closed interacting quantum systems
- Probing many-body dynamics on a 51-atom quantum simulator
- Quantum many-body scars
- Quantum Quench in the Transverse Field Ising Chain
- Generalized Gibbs ensemble in integrable lattice models
- Eigenstate Thermalization Hypothesis
- Quantum Many-Body Scars and Weak Breaking of Ergodicity
- Complete Generalized Gibbs Ensemble in an interacting Theory
- Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
- Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
- Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
- Generalized Thermalization in an Integrable Lattice System
- Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
- Alternatives to Eigenstate Thermalization
- Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain
- Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 XY Magnets
- Exact Excited States of Non-Integrable Models
- Quantum Many-Body Scars: A Quasiparticle Perspective
- An introduction to integrable techniques for one-dimensional quantum systems
- Unified structure for exact towers of scar states in the AKLT and other models
- Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
- Observation of many-body scarring in a Bose--Hubbard quantum simulator
- Many Body Scars as a Group Invariant Sector of Hilbert Space
- Eta-pairing states as true scars in an extended Hubbard Model
- Quantum scars from zero modes in an Abelian lattice gauge theory on ladders
- Disorder-Free Localization and Many-Body Quantum Scars from Magnetic Frustration
- Large Classes of Quantum Scarred Hamiltonians from Matrix Product States
- Exact three-colored quantum scars from geometric frustration
- From tunnels to towers: quantum scars from Lie Algebras and q-deformed Lie Algebras
- Quantum Many-Body Scar States in Two-Dimensional Rydberg Atom Arrays
- Quantum many-body scars from virtual entangled pairs
- Entanglement of Exact Excited Eigenstates of the Hubbard Model in Arbitrary Dimension
- Exact localized and ballistic eigenstates in disordered chaotic spin ladders and the Fermi-Hubbard model
- Quasi-symmetry groups and many-body scar dynamics
- Group theoretic approach to many-body scar states in fermionic lattice models
- Hilbert Space Fragmentation and Exact Scars of Generalized Fredkin Spin Chains
- Exact Floquet quantum many-body scars under Rydberg blockade
- Exact many-body scars and their stability in constrained quantum chains
- Short distance correlators in the XXZ spin chain for arbitrary string distributions
- Scars from protected zero modes and beyond in quantum link and quantum dimer models
- Excited state correlations of the finite Heisenberg chain
- Exact Quantum Scars in the Chiral Non-Linear Luttinger Liquid
- Deformed Symmetry Structures and Quantum Many-body Scar Subspaces
- New exact eigenstates in the Lesanovsky model, proximity to integrability and the PXP model, and approximate scar states
- Quantum Many-Body Scars from Einstein-Podolsky-Rosen States in Bilayer Systems
- Multi-magnon quantum many-body scars from tensor operators
- Exhaustive Characterization of Quantum Many-Body Scars using Commutant Algebras
- Spin-1 Kitaev model in one dimension
- Exact eigenstates of extended SU() Hubbard models: Generalizations of -pairing states with -particle off-diagonal long-range order
- Weak universality, quantum many-body scars and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality
- Exact Thermal Eigenstates of Nonintegrable Spin Chains at Infinite Temperature
- Volume-entangled exact scar states in the PXP and related models in any dimension
- Robust quantum many-body scars in the one-dimensional spin-1 Kitaev model
- Tower of two-dimensional scar states in a localized system
- Escaping many-body localization in an exact eigenstate