Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Status Confirmed
Seminar Series LPTMS
Subjects cond-mat.stat-mech
Date Tuesday 5 July 2022
Time 11:00
Institute LPTMS
Seminar Room Salle des séminaires du FAST et du LPTMS, bâtiment Pascal n°530
Speaker's Last Name Barthel
Speaker's First Name Thomas
Speaker's Email Address
Speaker's Institution Duke University
Title Crossover functions for entanglement entropy in many-body energy eigenstates and universality
Abstract We consider the entanglement entropies of energy eigenstates in quantum many-body systems. For the typical models that allow for a field-theoretical description of the long-range physics, we find that the entanglement entropy of (almost) all eigenstates is described by a single crossover function. The eigenstate thermalization hypothesis (ETH) implies that such crossover functions can be deduced from subsystem entropies of thermal ensembles and that they assume universal scaling forms in quantum-critical regimes. They describe the full crossover from the groundstate entanglement scaling for low energies and small subsystem size (area or log-area law) to the extensive volume-law regime for high energies or large subsystem size. For critical 1d systems, the scaling function follows from conformal field theory (CFT). We use it to also deduce the scaling function for Fermi liquids in d>1 dimensions. These analytical results are complemented by numerics for large non-interacting systems of fermions in d=1,2,3 and the harmonic lattice model (free scalar field theory) in d=1,2. Lastly, we demonstrate ETH for entanglement entropies and the validity of the scaling arguments in integrable and non-integrable interacting spin chains. [1] « Eigenstate entanglement: Crossover from the ground state to volume laws”, Phys. Rev. Lett. 127, 040603 (2021) [2] « Scaling functions for eigenstate entanglement crossovers in harmonic lattices », Phys. Rev. A 104, 022414 (2021) [3] « Eigenstate entanglement scaling for critical interacting spin chains”, Quantum 6, 642 (2022)
arXiv Preprint Number
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