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Eigenstate entanglement scaling for critical interacting spin chains

Publication ,  Journal Article
Miao, Q; Barthel, T
Published in: Quantum
January 1, 2022

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.

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Published In

Quantum

DOI

EISSN

2521-327X

Publication Date

January 1, 2022

Volume

6

Start / End Page

642
 

Citation

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Chicago
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MLA
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Miao, Q., & Barthel, T. (2022). Eigenstate entanglement scaling for critical interacting spin chains. Quantum, 6, 642. https://doi.org/10.22331/Q-2022-02-02-642
Miao, Q., and T. Barthel. “Eigenstate entanglement scaling for critical interacting spin chains.” Quantum 6 (January 1, 2022): 642. https://doi.org/10.22331/Q-2022-02-02-642.
Miao Q, Barthel T. Eigenstate entanglement scaling for critical interacting spin chains. Quantum. 2022 Jan 1;6:642.
Miao, Q., and T. Barthel. “Eigenstate entanglement scaling for critical interacting spin chains.” Quantum, vol. 6, Jan. 2022, p. 642. Scopus, doi:10.22331/Q-2022-02-02-642.
Miao Q, Barthel T. Eigenstate entanglement scaling for critical interacting spin chains. Quantum. 2022 Jan 1;6:642.

Published In

Quantum

DOI

EISSN

2521-327X

Publication Date

January 1, 2022

Volume

6

Start / End Page

642