Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Equipotential Surfaces and Conductors01:16

Equipotential Surfaces and Conductors

3.3K
For a conductor in which all charges are at rest, the conductor's surface is equipotential. The electric field is always perpendicular to equipotential surfaces. Therefore, in a conductor with static charges, the electric field just outside the conductor is always perpendicular to the conductor's surface. Any tangential component of the electric field will cause charges to move inside the conductor, which will violate the electrostatic nature of the system. In an electrostatic...
3.3K
Equipotential Surfaces and Field Lines01:29

Equipotential Surfaces and Field Lines

3.5K
Electric potential can be pictorially represented as a three-dimensional surface. On such a surface, the electric potential is constant everywhere. The equipotential surface is always perpendicular to the electric field lines, and while it is three-dimensional, it can be treated as an equipotential line in a two-dimensional case. These equipotential lines are also always perpendicular to electric field lines. The term equipotential is often used as a noun, referring to an equipotential line or...
3.5K
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

4.9K
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
4.9K
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

901
Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
901
Divergence and Curl of Electric Field01:25

Divergence and Curl of Electric Field

5.1K
The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as
5.1K
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

796
NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
796

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Topological non-Abelian gauge structures in Cayley-Schreier lattices.

Nature communications·2026
Same author

Topologically enhanced exciton transport.

Nature communications·2025
Same author

Excitonic topology and quantum geometry in organic semiconductors.

Nature communications·2025
Same author

Topologically ordered time crystals.

Nature communications·2024
Same author

Non-Abelian Floquet braiding and anomalous Dirac string phase in periodically driven systems.

Nature communications·2024
Same author

Polar meron-antimeron networks in strained and twisted bilayers.

Nature communications·2023

Related Experiment Video

Updated: May 7, 2025

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
09:00

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

Published on: June 28, 2018

9.8K

Exact projected entangled pair ground states with topological Euler invariant.

Thorsten B Wahl1, Wojciech J Jankowski2, Adrien Bouhon2,3

  • 1TCM Group, Cavendish Laboratory, Department of Physics, Cambridge, UK. tw344@cam.ac.uk.

Nature Communications
|January 2, 2025
PubMed
Summary

We introduce gapped Projected Entangled Pair States (PEPS) with Euler topology, representing the first tensor network for a 2D topological phase. These states offer new avenues for quantum spin liquids and quantum information.

More Related Videos

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
00:07

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

Published on: September 5, 2019

8.3K
Electron Channeling Contrast Imaging for Rapid III-V Heteroepitaxial Characterization
07:50

Electron Channeling Contrast Imaging for Rapid III-V Heteroepitaxial Characterization

Published on: July 17, 2015

10.9K

Related Experiment Videos

Last Updated: May 7, 2025

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
09:00

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

Published on: June 28, 2018

9.8K
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
00:07

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

Published on: September 5, 2019

8.3K
Electron Channeling Contrast Imaging for Rapid III-V Heteroepitaxial Characterization
07:50

Electron Channeling Contrast Imaging for Rapid III-V Heteroepitaxial Characterization

Published on: July 17, 2015

10.9K

Area of Science:

  • Condensed Matter Physics
  • Quantum Information Theory
  • Topological Phases of Matter

Background:

  • Projected Entangled Pair States (PEPS) are crucial tensor network states for simulating quantum many-body systems.
  • Topological phases of matter exhibit properties robust against local perturbations, characterized by topological invariants.
  • Band geometry and quantum geometrical bounds offer insights into the properties of quantum states.

Purpose of the Study:

  • To construct gapped Projected Entangled Pair States (PEPS) exhibiting non-trivial Euler topology.
  • To explore the connection between band geometry, quantum geometrical bounds, and the realization of topological phases in PEPS.
  • To develop interacting variants of these topological PEPS and investigate their properties.

Main Methods:

  • Utilizing optimal conditions related to quantum geometrical bounds for non-interacting systems.
  • Constructing gapped parent Hamiltonians with flat bands and PEPS as unique ground states.
  • Employing unitary circuits to formulate interacting PEPS and their parent Hamiltonians.

Main Results:

  • Demonstrated gapped PEPS with non-trivial Euler topology, protected by crystalline symmetries.
  • Established these PEPS as the first tensor network representation of a non-interacting, gapped two-dimensional topological phase.
  • Identified characteristic entanglement features shared between free-fermionic and interacting topological PEPS.
  • Revealed that these PEPS unexpectedly possess a finite topological invariant.

Conclusions:

  • The developed PEPS models provide a novel platform for studying topological phases in a tensor network framework.
  • These findings pave the way for new research in quantum spin liquids, quantum Hall physics, and quantum information.
  • The study bridges concepts from band geometry, tensor networks, and topological phases of matter.