Synopsis: Counting Broken Symmetries

Theorists obtain a general theorem that predicts the number of Goldstone modes generated by spontaneous symmetry breaking in nonrelativistic systems.

From superconductivity in condensed-matter physics to electroweak symmetry breaking in particle physics, some of the richest phenomena in modern physics can be understood within the paradigm of spontaneous breaking of symmetries, i.e., the quantum mechanical scenario of the ground state of a quantum system being less symmetric than the corresponding Hamiltonian. A telltale sign of broken symmetries are massless bosonic excitations known as Nambu-Goldstone bosons (NGB). The number of such distinct bosonic excitations are generally taken to be a measure of how many of the original symmetries are dynamically broken. Despite decades of research on the subject, a general formula that predicts the number of different NGBs in a given dynamical system with broken symmetries has eluded theorists.

Now, in a paper in Physical Review Letters, Haruki Watanabe and Hitoshi Murayama (both jointly at the University of California, Berkeley, and the University of Tokyo, Japan) provide a general theorem that relates the number of NGBs to that of broken symmetries. The latter are characterized by the number of generators of the symmetry group of the Hamilonian (as well as their mutual commutation relations) that do not leave invariant the vacuum of the dynamical system under consideration. The power of this result lies in the fact that it applies to all dynamical systems subject to spontaneous symmetry breaking (under some minimal assumptions specified in the paper). While the relativistic analog of this result has been known for a long time, this is the first result of its kind that is applicable to nonrelativistic systems of interest in condensed-matter physics. This result should provide crucial insights, particularly in the study of quantum many-body systems and investigations into quantum criticality. – Abhishek Agarwal


Features

More Features »

Announcements

More Announcements »

Subject Areas

Particles and Fields

Previous Synopsis

Atomic and Molecular Physics

Ephemeral Fermions

Read More »

Next Synopsis

Related Articles

Viewpoint: Dark Matter Still at Large
Cosmology

Viewpoint: Dark Matter Still at Large

No dark matter particles have been observed by two of the world’s most sensitive direct-detection experiments, casting doubt on a favored dark matter model. Read More »

Viewpoint: Connecting the Bright and Dark Sides of Galaxies
Cosmology

Viewpoint: Connecting the Bright and Dark Sides of Galaxies

A universal law shows that the rotation of a disk galaxy is determined entirely by the visible matter it contains, even if the disk is mostly filled with dark matter. Read More »

Viewpoint: Cosmic-Ray Showers Reveal Muon Mystery
Particles and Fields

Viewpoint: Cosmic-Ray Showers Reveal Muon Mystery

The Pierre Auger Observatory has detected more muons from cosmic-ray showers than predicted by the most up-to-date particle-physics models. Read More »

More Articles