Topological interactions of Nambu-Goldstone bosons in quantum many-body systems
arXiv:1405.2670 · doi:10.1103/PhysRevD.90.121701
Abstract
We classify effective actions for Nambu-Goldstone (NG) bosons assuming absence of anomalies. Special attention is paid to Lagrangians invariant only up to a surface term, shown to be in a one-to-one correspondence with Chern-Simons (CS) theories for unbroken symmetry. Without making specific assumptions on spacetime symmetry, we give explicit expressions for these Lagrangians, generalizing the Berry and Hopf terms in ferromagnets. Globally well-defined matrix expressions are derived for symmetric coset spaces of broken symmetry. The CS Lagrangians exhibit special properties, on both the perturbative and the global topological level. The order-one CS term is responsible for non-invariance of canonical momentum density under internal symmetry, known as the linear momentum problem. The order-three CS term gives rise to a novel type of interaction among NG bosons. All the CS terms are robust against local variations of microscopic physics.
arXiv comment6+2 pages; v2: substantially rewritten, version to appear as a Rapid Communication in Phys. Rev. D
References in corpus (35)
- Electronic Properties of Graphene in a Strong Magnetic Field
- Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
- On the Foundations of Chiral Perturbation Theory
- General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
- Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance
- Nonrelativistic effective Lagrangians
- Collective Modes and Skyrmion Excitations in Graphene SU(4) Quantum Hall Ferromagnets
- Counting rule for Nambu-Goldstone modes in nonrelativistic systems
- Goldstone and Pseudo-Goldstone Bosons in Nuclear, Particle and Condensed-Matter Physics
- On the number of Nambu-Goldstone bosons and its relation to charge densities
- Effective Lagrangian for Nonrelativistic Systems
- Effective Lagrangian and Topological Interactions in Supersolids
- Massive Nambu-Goldstone Bosons
- A relativistic non-relativistic Goldstone theorem: gapped Goldstones at finite charge density
- More on gapped Goldstones at finite density: More gapped Goldstones
- General Effective Actions
- Spontaneous breaking of spacetime symmetries and the inverse Higgs effect
- Effective theory of chiral two-dimensional superfluids
- General coordinate invariance in quantum many-body systems
- Invariant Effective Actions, Cohomology of Homogeneous Spaces and Anomalies
- Effective Field Theory Approach to Ferromagnets and Antiferromagnets in Crystaline Solids
- Nambu-Goldstone bosons with fractional-power dispersion relations
- Non-relativistic Nambu-Goldstone modes associated with spontaneously broken space-time and internal symmetries
- Spin-Pseudospin Coherence and CP Skyrmions in Bilayer Quantum Hall Ferromagnets
- Multicritical Symmetry Breaking and Naturalness of Slow Nambu-Goldstone Bosons
- Effective Lagrangians for quantum many-body systems
- Pions versus Magnons: From QCD to Antiferromagnets and Quantum Hall Ferromagnets
- Broken spacetime symmetries and elastic variables
- On the Current Carried by `Neutral' Quasiparticles
- Non-relativistic Nambu-Goldstone modes propagating along a skyrmion line
- Effective actions, relative cohomology and Chern Simons forms
- Some topological issues for ferromagnets and fluids
- General 2+1 Dimensional Effective Actions and Soliton Spin Fractionalization
- Quantum Hall Ferromagnets: Induced Topological term and electromagnetic interactions
- Topological term in the non-linear model of the SO(5) spin chains
Cited by in corpus (12)
- Dispersion relations of Nambu-Goldstone modes at finite temperature and density
- Anomalous electrodynamics of neutral pion matter in strong magnetic fields
- Lie-algebraic classification of effective theories with enhanced soft limits
- Effective Lagrangians for quantum many-body systems
- Spontaneously Broken Gauge Theories and the Coset Construction
- Topological Goldstone phases of matter
- Quasi-Nambu-Goldstone modes in nonrelativistic systems
- Gauged Wess-Zumino terms for a general coset space
- Interpolating relativistic and non-relativistic Nambu-Goldstone and Higgs modes
- Exceptional nonrelativistic effective field theories with enhanced symmetries
- Anomalous continuous symmetries and quantum topology of Goldstone modes
- Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum