Symmetry breaking on a supercomputer

4 June 2007

The Japan Lattice QCD Collaboration has used numerical simulations to reproduce spontaneous chiral symmetry breaking (SCSB) in quantum chromodynamics (QCD). This idea underlies the widely accepted explanation for the masses of particles made from the lighter quarks, but it has not yet been proven theoretically starting from QCD. Now using a new supercomputer and an appropriate formulation of lattice QCD, Shoji Hashimoto from KEK and colleagues have realized an exact chiral symmetry on the lattice, and observe the effects of symmetry breaking.

Chiral symmetry distinguishes right-hand spinning quarks from left-handed and is exact only if the quarks move at c and are therefore massless. In 1961 Yoichiro Nambu and Giovanni Jona-Lasinio proposed the idea of SCSB, inspired by the Bardeen–Cooper–Schrieffer mechanism of superconductivity in which spin-up and spin-down electrons pair up and condense into a lower energy level. In QCD a quark and an antiquark pair up, leading to a vacuum full of condensed quark–antiquark pairs. The result is that chiral symmetry is broken, so that the quarks – and the particles they form – acquire masses.

In their simulation the group employed the overlap fermion formulation for quarks on the lattice, proposed by Herbert Neuberger in 1998. While this is an ideal formulation theoretically, it is numerically difficult to implement, requiring more than 100 times the computer power of other fermion formulations. However, the group used the new IBM System BlueGene Solution supercomputer installed at KEK in March 2006, as well as steady improvements of numerical algorithms


The group’s simulation included extremely light quarks to give eigenvalues of the quarks. The results reproduce predictions (see figure) indicating that chiral symmetry breaking gives rise to light pions that behave as expected.

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