Related Experiment Video
Updated: Jun 3, 2025
06:26
Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets
Published on: May 15, 2017
7.1K
Entropic Order Parameters for Categorical Symmetries in 2D-CFT
Javier Molina-Vilaplana1, Pablo Saura-Bastida1, Germán Sierra2
1Departamento de Automática, Ingeniería Eléctrica y Tecnología Electrónica, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain.
Entropy (Basel, Switzerland)
|January 8, 2025
Summary
We introduce an information-theoretic tool to detect categorical symmetries in quantum field theories. This method uses quantum relative entropy to distinguish between different symmetry-broken phases.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
- Condensed Matter Physics
Background:
- Categorical symmetries are advanced structures in quantum field theories.
- Understanding symmetry breaking is crucial for characterizing phases of matter.
- Rational Conformal Field Theories (RCFTs) provide a framework for studying these phenomena.
Purpose of the Study:
- To develop a novel information-theoretic order parameter.
- To characterize the presence and breaking of categorical symmetries in (1+1)-d RCFTs.
- To distinguish between different symmetry-broken phases.
Main Methods:
- Computation of quantum relative entropy.
- Analysis of ground states at phase transition critical points.
- Focus on theories with categorical symmetries.
Main Results:
- The quantum relative entropy, at leading order in the high-temperature limit, depends on quantum dimensions of topological operators.
- This dependence is directly linked to the implementation of categorical symmetry.
Conclusions:
- The proposed information-theoretic order parameter effectively characterizes categorical symmetries.
- It provides a method to distinguish between different broken phases in (1+1)-d theories with categorical symmetries.
More Related Videos
Related Concept Videos
01:20Gauss's Law: Cylindrical Symmetry
7.4K
A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
7.4K
01:34Woodward–Hoffmann Selection Rules and Microscopic Reversibility
3.0K
Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
3.0K
01:27Gauss's Law: Planar Symmetry
7.8K
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
7.8K
01:28Symmetry in Maxwell's Equations
3.3K
Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
3.3K
02:11Conformations of Cyclohexane
12.1K
Cyclohexane does not exist in a planar form due to the high angle and torsional strain it would experience in the planar structure. Instead, it adopts non-planar chair and boat conformations.
The chair form is the most stable and derives its name from its resemblance to the “easy chair.” In the chair conformation, two carbon atoms are arranged out-of-plane — one above and one below, minimizing the torsional strain. In the chair form, the bond angle is very close to the ideal...
The chair form is the most stable and derives its name from its resemblance to the “easy chair.” In the chair conformation, two carbon atoms are arranged out-of-plane — one above and one below, minimizing the torsional strain. In the chair form, the bond angle is very close to the ideal...
12.1K
01:16Thermal Sigmatropic Reactions: Overview
2.1K
Sigmatropic rearrangements are a class of pericyclic reactions in which a σ bond migrates from one part of a π system to another. These are intramolecular rearrangements where the total number of σ and π bonds remain unchanged.
Sigmatropic shifts are classified based on an order term [i, j ], where i and j indicate the number of atoms across which each end of the σ bond migrates. Below are examples of a [3,3] sigmatropic shift in...
Sigmatropic shifts are classified based on an order term [i, j ], where i and j indicate the number of atoms across which each end of the σ bond migrates. Below are examples of a [3,3] sigmatropic shift in...
2.1K