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Universal entanglement crossover of coupled quantum wires
Romain Vasseur1, Jesper Lykke Jacobsen2, Hubert Saleur3
1Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA and Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
Physical Review Letters
|April 1, 2014
Summary
We reveal the universal scaling of entanglement entropy in quantum impurity systems. This provides a new analytical understanding of entanglement evolution across weak and strong coupling regimes, crucial for quantum many-body systems.
Area of Science:
- Condensed Matter Physics
- Quantum Information Theory
- Many-Body Physics
Background:
- Investigates entanglement in one-dimensional quantum wires (Luttinger liquids) coupled via a quantum impurity.
- The system exhibits a crossover between weak and strong coupling regimes, preventing standard conformal field theory application.
- Entanglement evolution in this crossover is poorly understood analytically.
Purpose of the Study:
- To determine the universal scaling form of entanglement entropy in a quantum impurity-controlled Luttinger liquid system.
- To analytically derive the universal function governing entanglement entropy evolution across coupling regimes.
- To provide a theoretical framework for understanding entanglement in interacting quantum systems.
Main Methods:
- Utilizes conformal field theory concepts and recent advances in form factor calculations.
- Employs a defect massless-scattering formalism for analytical derivation.
- Compares theoretical predictions with extensive numerical simulations.
Main Results:
- Proposes a universal scaling form for entanglement entropy: ∂S/∂lnL = f(LTB), where TB is the characteristic energy scale.
- Analytically derives the universal function f(LTB) in a refermionizable regime.
- Confirms the theoretical findings through rigorous numerical simulations.
Conclusions:
- The derived universal scaling form provides a new analytical insight into entanglement entropy evolution.
- The study bridges the gap between weak and strong coupling regimes in quantum impurity systems.
- Offers a foundation for further theoretical and numerical investigations of entanglement in complex quantum systems.
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