Effective Lagrangians for quantum many-body systems
arXiv:1406.3439 · doi:10.1007/JHEP08(2014)088
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 (31)
- On the Foundations of Chiral Perturbation Theory
- The Mesonic Chiral Lagrangian of Order
- Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance
- Nonrelativistic effective Lagrangians
- Extension of the Chiral Perturbation Theory Meson Lagrangian to Order
- Counting rule for Nambu-Goldstone modes in nonrelativistic systems
- Kaon Condensation and Goldstone's Theorem
- Spontaneous Symmetry Breaking and Nambu-Goldstone Bosons in Quantum Many-Body Systems
- Goldstone and Pseudo-Goldstone Bosons in Nuclear, Particle and Condensed-Matter Physics
- Chiral Perturbation Theory Beyond One Loop
- Spontaneous Symmetry Breaking with Abnormal Number of Nambu-Goldstone Bosons and Kaon Condensate
- Effective Lagrangian for Nonrelativistic Systems
- Massive Nambu-Goldstone Bosons
- Diquark Condensate in QCD with Two Colors at Next-to-Leading Order
- Thermodynamics of chiral symmetry at low densities
- General Effective Actions
- Invariant Effective Actions, Cohomology of Homogeneous Spaces and Anomalies
- Effective Field Theory Approach to Ferromagnets and Antiferromagnets in Crystaline Solids
- Systematic Low-Energy Effective Theory for Magnons and Charge Carriers in an Antiferromagnet
- Two-Hole Bound States from a Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet
- Effective Analysis of the O(N) Antiferromagnet: Low Temperature Expansion of the Order Parameter
- Spontaneous Magnetization of the O(3) Ferromagnet at Low Temperatures
- Spin Waves in Canted Phases: An Application to Doped Manganites
- Spontaneous Magnetization of an Ideal Ferromagnet: Beyond Dyson's Analysis
- Effective Field Theories
- Thermodynamics of O(N) Antiferromagnets in 2+1 Dimensions
- Effective actions, relative cohomology and Chern Simons forms
- Topological interactions of Nambu-Goldstone bosons in quantum many-body systems
- Thermodynamics of Two-Dimensional Ideal Ferromagnets - Three-Loop Analysis
- Low-Temperature Properties of Ferromagnetic Spin Chains in a Magnetic Field
- Thermodynamics of Ferromagnetic Spin Chains in a Magnetic Field: Impact of the Spin-Wave Interaction
Cited by in corpus (21)
- General coordinate invariance in quantum many-body systems
- Dispersion relations of Nambu-Goldstone modes at finite temperature and density
- Lie-algebraic classification of effective theories with enhanced soft limits
- Field theories with higher-group symmetry from composite currents
- Quasi-Nambu-Goldstone modes in nonrelativistic systems
- Topological interactions of Nambu-Goldstone bosons in quantum many-body systems
- Nonrelativistic effective field theories with enhanced symmetries and soft behavior
- Effective Field Theory for Spontaneously Broken Symmetry
- Effective field theory and the scattering process for magnons in the ferromagnet, antiferromagnet, and ferrimagnet
- Scattering amplitudes of massive Nambu-Goldstone bosons
- Effective field theory of magnon: Dynamics in chiral magnets and Schwinger mechanism
- Magnetic Catalysis in Antiferromagnetic Films
- Exceptional nonrelativistic effective field theories with enhanced symmetries
- Effective field theory of fluctuating wall in open systems: from a kink in Josephson junction to general domain wall
- Two-loop free energy of three-dimensional antiferromagnets in external magnetic and staggered fields
- Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum
- Thermodynamics of Antiferromagnetic Solids in Magnetic Fields
- Thermodynamics of the =3+1 Quantum XY Model
- Nonrelativistic Banks-Casher relation and random matrix theory for multi-component fermionic superfluids
- Square-Lattice Antiferromagnet Subjected to a Magnetic Field Aligned with the Order Parameter
- Geometry of Classical Nambu-Goldstone Fields