Bera, S and Haldar, A and Banerjee, S (2024) Dynamical mean-field theory for Rényi entanglement entropy and mutual information in the Hubbard model. In: Physical Review B, 109 (3).
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Abstract
Quantum entanglement, lacking any classical counterpart, provides a fundamental new route to characterize the quantum nature of many-body states. In this work, we discuss an implementation of a new path integral method Phys. Rev. Res. 2, 033505 (2020)10.1103/PhysRevResearch.2.033505 for fermions to compute entanglement for extended subsystems in the Hubbard model within dynamical mean-field theory (DMFT) in one and two dimensions. The new path integral formulation measures entanglement by applying a "kick"to the underlying interacting fermions. We show that the Rényi entanglement entropy can be extracted efficiently within the DMFT framework by integrating over the strength of the kick term. Using this method, we compute the second Rényi entropy as a function of subsystem size for metallic and Mott insulating phases of the Hubbard model. We explore the thermal entropy to entanglement crossover in the subsystem Rényi entropy in the correlated metallic phase. We show that the subsystem-size scaling of the second Rényi entropy is well described by the crossover formula which interpolates between the volume-law thermal Rényi entropy and the universal boundary-law Rényi entanglement entropy with logarithmic violation, as predicted by conformal field theory. We also study the mutual information across the Mott metal-insulator transition. © 2024 American Physical Society.
| Item Type: | Journal Article |
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| Publication: | Physical Review B |
| Publisher: | American Physical Society |
| Additional Information: | The copyright for this article belongs to author. |
| Keywords: | Entropy; Mean field theory; Metal insulator boundaries; Metal insulator transition; Mott insulators; Quantum entanglement; Semiconductor insulator boundaries, Classical counterpart; Dynamical mean-field theory; Entanglement entropy; Many-body state; Mutual informations; One dimension; Path integral method; Quantum nature; Renyi's entropy; Thermal, Hubbard model |
| Department/Centre: | Division of Physical & Mathematical Sciences > Centre for High Energy Physics Division of Physical & Mathematical Sciences > Instrumentation Appiled Physics Division of Physical & Mathematical Sciences > Physics |
| Date Deposited: | 04 Mar 2024 07:02 |
| Last Modified: | 04 Mar 2024 07:02 |
| URI: | https://eprints.iisc.ac.in/id/eprint/84171 |
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