Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Symmetry in Maxwell's Equations

Symmetry in Maxwell's Equations

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...

Symmetry Elements in a Crystal

Symmetry Elements in a Crystal

Crystal symmetry operations are isometric transformations that map objects onto indistinguishable copies while preserving distances, angles, and volumes. The simplest symmetry operation is translation, which shifts the entire infinite crystal lattice parallelly by a translation vector.Crystallographic rotations involve rotations by an angle of 2π/n around an axis without changing the positions of points on the axis. It is called the rotational axis of the symmetry, denoted by n. The combination...

Symmetry

Symmetry

The equation of an ellipse centered at the origin defines all points whose distances from the center maintain a constant ratio between the horizontal and vertical axes. This equation results in a smooth, closed curve that extends further along the x-axis than the y-axis, giving it a horizontal orientation. Such an ellipse demonstrates three kinds of symmetry: across the x-axis, across the y-axis, and about the origin. These symmetries are essential in understanding the graph's structure and...

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:

Hybridization of Atomic Orbitals I

Hybridization of Atomic Orbitals I

The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

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...

You might also read

Related Articles

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

Sort by

Same author

Intervalley-Coupled Twisted Bilayer Graphene from Substrate Commensuration.

Physical review letters·2026

Same author

Spectroscopy of the fractal Hofstadter energy spectrum.

Nature·2025

Same author

Correlated topological flat bands in rhombohedral graphite.

Proceedings of the National Academy of Sciences of the United States of America·2024

Same author

Twistronics of Kekulé Graphene: Honeycomb and Kagome Flat Bands.

Physical review letters·2024

Search research articles

Related Experiment Video

Updated: Jul 8, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Bootstrapping Quantum Hamiltonians with Symmetry.

Michael G Scheer¹

¹Harvard University, Princeton University, Department of Physics, Princeton, New Jersey 08544, USA and Department of Physics, Cambridge, Massachusetts 02138, USA.

Physical Review Letters

|July 7, 2026

Summary

This summary is machine-generated.

We present a new computational method using semidefinite relaxation to find lower bounds for quantum system ground state energies. This approach leverages symmetries to reduce computational cost, showing accurate results for the 1D Hubbard model.

Related Experiment Videos

Last Updated: Jul 8, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Quantum mechanics
Computational physics
Condensed matter physics

Background:

Calculating the ground state energy of quantum Hamiltonians is computationally challenging.
Existing methods often struggle with large or complex systems.
Approximating ground state expectation values is crucial for understanding quantum systems.

Purpose of the Study:

To develop a semidefinite relaxation method for determining lower bounds to ground state energy.
To approximate ground state expectation values for quantum systems.
To investigate the role of symmetry in reducing computational requirements.

Main Methods:

A semidefinite relaxation technique is employed.
Hermitian linear constraints are incorporated.
Various symmetries (unitary, antiunitary, discrete, continuous) are analyzed and utilized.
The method is tested on the 1D Hubbard model.

Main Results:

The method successfully provides lower bounds for ground state energy.
Symmetry considerations significantly decrease computational demands.
Approximations for ground state expectation values are obtained.
Quantitative agreement is achieved with exact diagonalization and the Bethe ansatz for the 1D Hubbard model.

Conclusions:

The described semidefinite relaxation method is effective for quantum ground state energy calculations.
Incorporating symmetries offers a powerful strategy for computational efficiency.
The method shows promise for studying complex quantum models like the 1D Hubbard model.