Effective Lagrangians for quantum many-body systems

Abstract

The low-energy and low-momentum dynamics of systems with a spontaneously broken continuous symmetry is dominated by the ensuing Nambu-Goldstone bosons. It can be conveniently encoded in a model-independent effective field theory whose structure is fixed by symmetry up to a set of effective coupling constants. We construct the most general effective Lagrangian for the Nambu-Goldstone bosons of spontaneously broken global internal symmetry up to the fourth order in derivatives. Rotational invariance and spatial dimensionality of one, two or three are assumed in order to obtain compact explicit expressions, but our method is completely general and can be applied without modifications to condensed matter systems with a discrete space group as well as to higher-dimensional theories. The general low-energy effective Lagrangian for relativistic systems follows as a special case. We also discuss the effects of explicit symmetry breaking and classify the corresponding terms in the Lagrangian. Diverse examples are worked out in order to make the results accessible to a wide theoretical physics community.

45 pages

References in corpus (4)

• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
• Chiral Perturbation Theory Beyond One Loop
• Two-Hole Bound States from a Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet
• Topological interactions of Nambu-Goldstone bosons in quantum many-body systems

Cited by in corpus (5)

• General coordinate invariance in quantum many-body systems
• Dispersion relations of Nambu-Goldstone modes at finite temperature and density
• Quasi-Nambu-Goldstone modes in nonrelativistic systems
• Topological interactions of Nambu-Goldstone bosons in quantum many-body systems
• Two-loop free energy of three-dimensional antiferromagnets in external magnetic and staggered fields