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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
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Entanglement in Nonunitary Quantum Critical Spin Chains.
Romain Couvreur1,2, Jesper Lykke Jacobsen1,3,2, Hubert Saleur2,4
1Laboratoire de physique théorique, Département de physique de l'ENS, École normale supérieure, UPMC Univ. Paris 06, CNRS, PSL Research University, 75005 Paris, France.
Physical Review Letters
|January 18, 2018
Summary
We extend entanglement entropy to nonunitary quantum mechanics using spin chains. This approach defines Rényi entropies and clarifies central charges in conformal field theory (CFT) models.
Area of Science:
- Quantum Information Theory
- Condensed Matter Physics
- Quantum Field Theory
Background:
- Entanglement entropy is crucial for understanding quantum criticality.
- Nonunitary quantum mechanics is gaining interest in diverse fields.
- Extending entanglement entropy to nonunitary systems is a key challenge.
Purpose of the Study:
- To propose and investigate an extension of entanglement entropy to nonunitary quantum mechanics.
- To define Rényi entropies for quantum group symmetric and supergroup symmetric spin chains.
- To interpret these entropies geometrically and analyze their scaling properties.
Main Methods:
- Focusing on one-dimensional quantum group/supergroup symmetric spin chains.
- Utilizing left and right eigenstates with specific trace definitions.
- Connecting the entropy definition to related loop models.
- Calculating scaling in conformal field theory (CFT) cases.
Main Results:
- A natural definition of Rényi entropies for a variety of nonunitary models.
- Geometric interpretation of Rényi entropies via loop models.
- Distinguishing central charge and effective central charge in CFT.
- Defining an effective central charge for less understood models.
- Detailed analysis of the sl(2|1) alternating spin chain for percolation.
Conclusions:
- The proposed extension provides a robust framework for studying nonunitary quantum systems.
- The geometric interpretation offers new insights into entanglement in these systems.
- The effective central charge definition is valuable for characterizing nonunitary CFTs.
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