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

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...

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:

Molecular Orbital Theory II

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

Fermi Level

Fermi Level

The Fermi-Dirac function is represented by an S-shaped curve indicating the probability of an energy state being occupied by an electron at a given temperature. The Fermi level is the energy level at which there is a fifty percent chance of finding an electron, and it is positioned between the lower-energy valence band and the higher-energy conduction band.
At absolute zero temperature, electrons fill all energy states up to the Fermi level, leaving upper states empty. As the temperature rises,...

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

Hückel's Rule Diagram of π MOs: Frost Circle

Hückel's Rule Diagram of π MOs: Frost Circle

The Frost circle or the inscribed polygon method is a graphical method for determining the relative energies of π molecular orbitals (MOs) for planar, fully conjugated, and monocyclic compounds. This method was first described by A. A. Frost and Boris Musulin in 1953.
A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so...

You might also read

Related Articles

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

Sort by

Same author

Haldane Gap of the Three-Box Symmetric SU(3) Chain.

Physical review letters·2020

Same author

Rashba Cavity QED: A Route Towards the Superradiant Quantum Phase Transition.

Physical review letters·2019

Same author

Chiral Spin Liquids in Triangular-Lattice SU(N) Fermionic Mott Insulators with Artificial Gauge Fields.

Physical review letters·2016

Same author

Exact Diagonalization of Heisenberg SU(N) models.

Physical review letters·2014

Same author

Comment on "Superradiant phase transitions and the standard description of circuit QED".

Physical review letters·2012

Same author

Protected quantum computation with multiple resonators in ultrastrong coupling circuit QED.

Physical review letters·2011

Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026

Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026

Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026

Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026

Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026

Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 27, 2025

Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Exact Diagonalization of SU(N) Fermi-Hubbard Models.

Thomas Botzung¹, Pierre Nataf¹

¹Laboratoire de Physique et Modélisation des Milieux Condensés, Université Grenoble Alpes and CNRS, 25 avenue des Martyrs, 38042 Grenoble, France.

Physical Review Letters

|April 29, 2024

Summary

This summary is machine-generated.

Researchers developed a new method for exact diagonalizations of SU(N) Fermi-Hubbard models using representation theory. This approach simplifies calculations and reveals new insights into SU(N) phases, including a color ordered phase for N=4.

More Related Videos

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics

Published on: September 28, 2016

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Related Experiment Videos

Last Updated: Jun 27, 2025

Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics

Published on: September 28, 2016

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Area of Science:

Condensed matter physics
Quantum many-body systems
Strongly correlated electron systems

Background:

Exact diagonalization is crucial for understanding quantum many-body models.
SU(N) Fermi-Hubbard models are relevant for studying systems with multiple internal "colors" or flavors.
Previous methods faced challenges in scaling with system size and particle number.

Purpose of the Study:

To develop an efficient method for exact diagonalization of SU(N) Fermi-Hubbard models.
To utilize representation theory for simplifying Hamiltonian matrix elements.
To investigate the stability of SU(N) phases under varying interaction strengths.

Main Methods:

Employed representation theory of the unitary group U(L).
Constructed an orthonormal basis using semistandard Young tableaux or Gelfand-Tsetlin patterns.
Performed exact diagonalizations on L-site clusters for various SU(N) symmetries.

Main Results:

Demonstrated a simplified Hamiltonian in the chosen basis.
Investigated the robustness of SU(N) phases by decreasing on-site interaction U.
Observed the emergence of a long-range color ordered phase for N=4 at 1/4 filling on a triangular lattice.

Conclusions:

The developed method provides a powerful tool for studying SU(N) Fermi-Hubbard models.
Representation theory offers a systematic way to handle complex many-body systems.
The findings highlight the rich phase diagram of SU(N) models, with potential for new emergent phenomena.