Exact Thermal Eigenstates of Nonintegrable Spin Chains at Infinite Temperature

Abstract

The eigenstate thermalization hypothesis (ETH) plays a major role in explaining thermalization of isolated quantum many-body systems. However, there has been no proof of the ETH in realistic systems due to the difficulty in the theoretical treatment of thermal energy eigenstates of nonintegrable systems. Here, we write down analytically thermal eigenstates of nonintegrable spin chains. We consider a class of theoretically tractable volume-law states, which we call entangled antipodal pair (EAP) states. These states are thermal, in the most fundamental sense that they are indistinguishable from the Gibbs state with respect to all local observables, with infinite temperature. We then identify Hamiltonians having the EAP state as an eigenstate and rigorously show that some of these Hamiltonians are nonintegrable. Furthermore, a thermal pure state at an arbitrary temperature is obtained by the imaginary time evolution of an EAP state. Our results offer a potential avenue for providing a provable example of the ETH.

6 pages, 2 figures and Supplemental Material

References in corpus (37)

• The density-matrix renormalization group in the age of matrix product states
• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Probing many-body dynamics on a 51-atom quantum simulator
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Quantum many-body scars
• Breakdown of thermalization in finite one-dimensional systems
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• 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
• Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
• Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
• Finite Temperature Density Matrix Renormalization using an enlarged Hilbert space
• Exact Excited States of Non-Integrable Models
• Finite-size scaling of eigenstate thermalization
• Quantum quenches and thermalization in one-dimensional fermionic systems
• Canonical Thermal Pure Quantum State
• Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems
• Violation of area-law scaling for the entanglement entropy in spin 1/2 chains
• Large Classes of Quantum Scarred Hamiltonians from Matrix Product States
• Dynamical purification and the emergence of quantum state designs from the projected ensemble
• Improved thermal area law and quasi-linear time algorithm for quantum Gibbs states
• Entanglement over the rainbow
• From conformal to volume-law for the entanglement entropy in exponentially deformed critical spin 1/2 chains
• Thermal equilibrium of a macroscopic quantum system in a pure state
• Thermalization without eigenstate thermalization hypothesis after a quantum quench
• Macroscopic and Microscopic Thermal Equilibrium
• Proof of the absence of local conserved quantities in the XYZ chain with a magnetic field
• Crosscap States in Integrable Field Theories and Spin Chains
• Proof of absence of local conserved quantities in the mixed-field Ising chain
• Weak universality, quantum many-body scars and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality
• NoRA: A Tensor Network Ansatz for Volume-Law Entangled Equilibrium States of Highly Connected Hamiltonians
• Counting atypical black hole microstates from entanglement wedges

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• Proof of absence of local conserved quantities in two- and higher-dimensional quantum Ising models
• Numerical extraction of crosscap coefficients in microscopic models for (2+1)D conformal field theory
• Dichotomy theorem separating complete integrability and non-integrability of isotropic spin chains
• Symmetric tensor scars with tunable entanglement from volume to area law
• Spatially Structured Entanglement from Nonequilibrium Thermal Pure States
• Stable infinite-temperature eigenstates in SU(2)-symmetric nonintegrable models
• No boundary density matrix in elliptic de Sitter dS/${\mathbb{Z}}_2$
• Exact Quench Dynamics from Thermal Pure Quantum States
• Additional quantum many-body scars of the spin-$1$ $XY$ model with Fock-space cages and commutant algebras