Eigenstate entanglement scaling for critical interacting spin chains

Abstract

With increasing subsystem size and energy, bipartite entanglement entropies of energy eigenstates cross over from the groundstate scaling to a volume law. In previous work, we pointed out that, when strong or weak eigenstate thermalization (ETH) applies, the entanglement entropies of all or, respectively, almost all eigenstates follow a single crossover function. The crossover functions are determined by the subsystem entropy of thermal states and assume universal scaling forms in quantum-critical regimes. This was demonstrated by field-theoretical arguments and the analysis of large systems of non-interacting fermions and bosons. Here, we substantiate such scaling properties for integrable and non-integrable interacting spin-1/2 chains at criticality using exact diagonalization. In particular, we analyze XXZ and transverse-field Ising models with and without next-nearest-neighbor interactions. Indeed, the crossover of thermal subsystem entropies can be described by a universal scaling function following from conformal field theory. Furthermore, we analyze the validity of ETH for entanglement in these models. Even for the relatively small system sizes that can be simulated, the distributions of eigenstate entanglement entropies are sharply peaked around the subsystem entropies of the corresponding thermal ensembles.

8 pages, 7 figures. Data for larger systems, added discussion of substructures due to approximately conserved quantities, minor improvements. Published version. This complements arXiv:1905.07760 and arXiv:1912.10045

References in corpus (12)

• Thermalization and its mechanism for generic isolated quantum systems
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• Entropy and Entanglement in Quantum Ground States
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems
• Bound states and entanglement in the excited states of quantum spin chains
• Evidence for a floating phase of the transverse ANNNI model at high frustration
• Weak eigenstate thermalization with large deviation bound
• Study of the phase diagram of the Kitaev-Hubbard chain

Cited by in corpus (10)

• Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians
• Holographic reconstruction of black hole spacetime: machine learning and entanglement entropy
• Exponential shortcut to measurement-induced entanglement phase transitions
• Tight-binding billiards
• Subsystem distances between quasiparticle excited states
• Subsystem entropy in 2d CFT and KdV ETH
• Entanglement transition through Hilbert-space localization
• No eigenstate of the critical transverse-field Ising chain satisfies the area law
• Energy Spectra of Compressed Quantum States
• Volume-law entanglement entropy of typical pure quantum states