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Chirality

Chirality

Chirality is a term that describes the lack of mirror symmetry in an object. In other words, chiral objects cannot be superposed on their mirror images. For example, our feet are chiral, as the mirror image of the left foot, the right foot, cannot be superposed on the left foot.
Chiral objects exhibit a sense of handedness when they interact with another chiral object. For example, our left foot can only fit in the left shoe and not in the right shoe. Achiral objects — objects that have...

Prochirality

Prochirality

The concept of prochirality leads to the nomenclature of the individual faces of a molecule and plays a crucial role in the enantioselective reaction. It is a concept where two or more achiral molecules react to produce chiral products. A typical process is the reaction of an achiral ketone to generate a chiral alcohol. Here, the achiral reactant reacts with an achiral reducing agent, sodium borohydride, to generate an equimolar mixture of the chiral enantiomers of the product. For example, an...

Chirality at Nitrogen, Phosphorus, and Sulfur

Chirality at Nitrogen, Phosphorus, and Sulfur

Chirality is most prevalent in carbon-based tetrahedral compounds, but this important facet of molecular symmetry extends to sp3-hybridized nitrogen, phosphorus and sulfur centers, including trivalent molecules with lone pairs. Here, the lone pair behaves as a functional group in addition to the other three substituents to form an analogous tetrahedral center that can be chiral.
A consequence of chirality is the need for enantiomeric resolution. While this is theoretically possible for all...

Chirality in Nature

Chirality in Nature

Chirality is the most intriguing yet essential facet of nature, governing life’s biochemical processes and precision. It can be observed from a snail shell pattern in a macroscopic world to an amino acid, the minutest building block of life. Most of the snails around the world have right-coiled shells because of the intrinsic chirality in their genes. All the amino acids present in the human body exist in an enantiomerically pure state, except for glycine - the sole achiral amino acid.

The Pauli Exclusion Principle

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:

¹H NMR Chemical Shift Equivalence: Enantiotopic and Diastereotopic Protons

¹H NMR Chemical Shift Equivalence: Enantiotopic and Diastereotopic Protons

Replacing each alpha-hydrogen in chloroethane by bromine (or a different functional group) yields a pair of enantiomers. Such protons are called prochiral or enantiotopic and are related by a mirror plane. Enantiotopic protons are chemically equivalent in an achiral environment. Because most proton NMR spectra are recorded using achiral solvents, enantiotopic hydrogens yield a single signal.
In chiral compounds such as 2-butanol, replacing the methylene hydrogens at C3 produces a pair of...

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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

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Published on: September 5, 2019

Chiral projected entangled-pair state with topological order.

Shuo Yang^1,2, Thorsten B Wahl¹, Hong-Hao Tu¹

¹Max-Planck Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany.

Physical Review Letters

|March 28, 2015

Summary

Projected entangled-pair states (PEPS) can describe chiral topological order in 2D systems. A novel PEPS construction reveals symmetry linked to topological properties and edge conformal field theory characteristics.

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Area of Science:

Condensed matter physics
Quantum information theory

Background:

Topologically ordered phases are exotic states of matter with unique properties.
Projected entangled-pair states (PEPS) are a powerful tensor network tool for describing 2D quantum many-body systems.

Purpose of the Study:

To demonstrate that PEPS can effectively describe chiral topologically ordered phases.
To construct a simple PEPS for spin-1/2 particles on a 2D lattice.

Main Methods:

Construction of a novel Projected Entangled-Pair State (PEPS) for spin-1/2 particles.
Analysis of the local projector's symmetry within the PEPS.
Application of the bulk-boundary correspondence.

Main Results:

Successfully described chiral topologically ordered phases using PEPS.
Identified a symmetry in the PEPS local projector responsible for global topological character.
Extracted characteristic quantities of the edge conformal field theory.

Conclusions:

PEPS provide a viable framework for studying chiral topological order.
The identified symmetry is crucial for realizing topological properties in PEPS.
The bulk-boundary correspondence is effective for probing edge physics from bulk properties.