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Multipartite Entanglement Structure in the Eigenstate Thermalization Hypothesis
Marlon Brenes1, Silvia Pappalardi2,3, John Goold1
1Department of Physics, Trinity College Dublin, Dublin 2, Ireland.
Physical Review Letters
|February 15, 2020
Summary
We explored quantum Fisher information (QFI) in thermal pure states under the eigenstate thermalization hypothesis (ETH). Our findings reveal distinct entanglement structures compared to canonical ensembles, even when local observables appear similar.
Area of Science:
- Quantum Information Theory
- Condensed Matter Physics
- Statistical Mechanics
Background:
- The eigenstate thermalization hypothesis (ETH) describes how isolated quantum systems reach thermal equilibrium.
- Understanding multipartite entanglement in thermal states is crucial for quantum many-body physics.
- Quantum Fisher Information (QFI) quantifies the ultimate precision in estimating quantum states.
Purpose of the Study:
- To investigate the quantum Fisher information (QFI) and multipartite entanglement structure of thermal pure states within the framework of the eigenstate thermalization hypothesis (ETH).
- To compare the entanglement properties derived from ETH with those of the canonical ensemble.
- To provide a numerical example demonstrating extensive QFI in a quantum many-body system under ETH.
Main Methods:
- Explicit calculation of QFI from response functions in both canonical and ETH contexts.
- Theoretical analysis of the relationship between QFI in ETH and canonical ensembles.
- Numerical simulation of a quantum many-body system to illustrate differences in QFI.
Main Results:
- The QFI expression derived from ETH provides an upper bound for the corresponding canonical ensemble expression.
- Despite indistinguishable average values and fluctuations of local observables, the entanglement structures differ significantly between ETH and canonical ensembles.
- A numerical example demonstrates extensive QFI in a quantum many-body system under ETH, while the canonical ensemble QFI vanishes.
Conclusions:
- The entanglement structure of thermal pure states under ETH is fundamentally different from canonical ensembles, with implications for quantum phase transitions.
- These findings are relevant for understanding entanglement in the long-time evolution of quenched quantum many-body systems.
- The study highlights the power of QFI as a sensitive probe of multipartite entanglement in quantum systems beyond equilibrium thermodynamics.
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