Eigenstate entanglement scaling for critical interacting spin chains

Journal Article · 01 February 2022 · Quantum

DOI: https://doi.org/10.22331/q-2022-02-02-642 · OSTI ID:1981315

Miao, Qiang ^[1]; Barthel, Thomas ^[2]

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1. Duke Univ., Durham, NC (United States); Duke Univ., Durham, NC (United States)
2. Duke Univ., Durham, NC (United States)

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.

• Research Organization: Duke Univ., Durham, NC (United States)
• Sponsoring Organization: USDOE Office of Science (SC); USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0019449
• OSTI ID: 1981315
• Journal Information: Quantum, Journal Name: Quantum Vol. 6; ISSN 2521-327X
• Publisher: Quantum Science Open CommunityCopyright Statement
• Country of Publication: United States
• Language: English