Effective Lagrangian for Nonrelativistic Systems
arXiv:1402.7066 · doi:10.1103/PhysRevX.4.031057
Abstract
The effective Lagrangian for Nambu-Goldstone bosons (NGBs) in systems without Lorentz invariance has a novel feature that some of the NGBs are canonically conjugate to each other, hence describing dynamical degree of freedom by two NGB fields. We develop explicit forms of their effective Lagrangian up to the quadratic order in derivatives. We clarify the counting rules of NGB degrees of freedom and completely classify possibilities of such canonically conjugate pairs based on the topology of the coset spaces. Its consequence on the dispersion relations of the NGBs is clarified. We also present simple scaling arguments to see whether interactions among NGBs are marginal or irrelevant, which justifies a lore in the literature about the possibility of symmetry breaking in dimensions.
34 pages, 5 tables, 2 figures; v2: published version (to appear in Physical Review X)
References in corpus (17)
- General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
- Counting rule for Nambu-Goldstone modes in nonrelativistic systems
- Spin dynamics in a one-dimensional ferromagnetic Bose gas
- Effective Lagrangian and Topological Interactions in Supersolids
- Spin waves in a one-dimensional spinor Bose gas
- Spontaneous breaking of spacetime symmetries and the inverse Higgs effect
- Superfluidity in a Three-flavor Fermi Gas with SU(3) Symmetry
- Spectral functions of strongly interacting isospin-1/2 bosons in one dimension
- Nonlinear realizations of symmetries and unphysical Goldstone bosons
- Nambu-Goldstone bosons with fractional-power dispersion relations
- Spontaneously magnetized Tomonaga-Luttinger liquid in frustrated quantum antiferromagnets
- Noncommuting Momenta of Topological Solitons
- Remarks on nonrelativistic Goldstone bosons
- Broken spacetime symmetries and elastic variables
- Goldstone bosons in presence of charge density
- Dynamical stabilization of runaway potentials at finite density
- Relativistic Bose gases at finite density
Cited by in corpus (74)
- Keldysh Field Theory for Driven Open Quantum Systems
- An Introduction to Spontaneous Symmetry Breaking
- Heavy Hadrons in Nuclear Matter
- Detectability of Axion Dark Matter with Phonon Polaritons and Magnons
- Selected Topics in the Large Quantum Number Expansion
- Scalar Field Theories with Polynomial Shift Symmetries
- Structure of near-threshold quasi-bound states
- Colloquium: Hydrodynamics and holography of charge density wave phases
- Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting
- Magnetophonons & type-B Goldstones from Hydrodynamics to Holography
- Spontaneous symmetry breaking and Nambu-Goldstone modes in dissipative systems
- Dispersion relations of Nambu-Goldstone modes at finite temperature and density
- Lie-algebraic classification of effective theories with enhanced soft limits
- Effective Field Theory for Quasicrystals and Phasons Dynamics
- Low-energy effective theory of non-thermal fixed points in a multicomponent Bose gas
- Counting Nambu-Goldstone modes of higher-form global symmetries
- Effective Lagrangians for quantum many-body systems
- Homogeneous Holographic Viscoelastic Models & Quasicrystals
- Effective Lagrangian for Nambu-Goldstone modes in nonequilibrium open systems
- Spontaneous symmetry breaking and Nambu-Goldstone modes in open classical and quantum systems
- Spontaneously Broken Gauge Theories and the Coset Construction
- Cascading Multicriticality in Nonrelativistic Spontaneous Symmetry Breaking
- Field theories with higher-group symmetry from composite currents
- Gauged Wess-Zumino terms for a general coset space
- Emergent generalized symmetries in ordered phases and applications to quantum disordering
- Quasi-Nambu-Goldstone modes in nonrelativistic systems
- "Quantum Geometric Nesting" and Solvable Model Flat-Band Systems
- Non-relativistic Nambu-Goldstone modes propagating along a skyrmion line
- Nambu-Goldstone bosons and the Higgs mechanism without Lorentz invariance: Analysis based on constrained-system theory
- The Quantum Yang Baxter conditions: The fundamental relations behind the Nambu-Goldstone theorem
- Symmetry Realization via a Dynamical Inverse Higgs Mechanism
- Topological interactions of Nambu-Goldstone bosons in quantum many-body systems
- Effective Field Theory for Spontaneously Broken Symmetry
- Nonrelativistic effective field theories with enhanced symmetries and soft behavior
- Goldstino in supersymmetric Bose-Fermi mixtures in the presence of Bose Einstein condensate
- A Note on Holographic Non-Relativistic Goldstone Bosons
- Interpolating relativistic and non-relativistic Nambu-Goldstone and Higgs modes
- Soft Phonon Theorems
- Englert-Brout-Higgs Mechanism in Nonrelativistic Systems
- Quasi-Nambu-Goldstone modes in many-body scar models
- Scattering amplitudes of massive Nambu-Goldstone bosons
- Spontaneous breaking of U(1) symmetry at zero temperature in one dimension
- Effective field theory of magnon: Dynamics in chiral magnets and Schwinger mechanism
- Formation of a supergiant quantum vortex in a relativistic Bose-Einstein condensate driven by rotation and a parallel magnetic field
- Generalized symmetries in singularity-free nonlinear models and their disordered phases
- Goldstino spectrum in an ultracold Bose-Fermi mixture with explicitly broken supersymmetry
- Solving puzzles of spontaneously broken spacetime symmetries
- Kaon Condensation in Baryonic Fermi Liquid at High Density
- Spontaneous symmetry breaking and the flat phase of crystalline membranes
- Flag manifold sigma models from SU() chains
- Fractons in effective field theories for spontaneously broken translations
- Ground State Wave Function Overlap in Superconductors and Superfluids
- Rainbow Nambu-Goldstone modes under a shear flow
- Unstable Nambu-Goldstone modes
- Fractal dimension and the counting rule of the Goldstone modes
- Emergence of the Unconventional Type-II Nambu-Goldstone Modes with Topological Origin in Bose Superfluids
- Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum
- Stability and Absence of a Tower of States in Ferrimagnets
- Effective field theory of fluctuating wall in open systems: from a kink in Josephson junction to general domain wall
- Exact Ground State of Lieb-Mattis Hamiltonian as a Superposition of Néel states
- Nonlinear Lifshitz Photon Theory in Condensed Matter Systems
- Entanglement entropy in low-energy field theories at finite chemical potential
- Spin-orbit coupled bosons in one dimension: emergent gauge field and Lifshitz transition
- Nonrelativistic Banks-Casher relation and random matrix theory for multi-component fermionic superfluids
- Fractals and spontaneous symmetry breaking with type-B Goldstone modes: a perspective from entanglement
- Magnon-induced long-range correlations and their neutron-scattering signature in quantum magnets
- Entanglement-enabled symmetry-breaking orders
- Geometry of Classical Nambu-Goldstone Fields
- An introduction to Goldstone boson physics and to the coset construction
- Goldstone modes and the golden spiral in the ferromagnetic spin-1 biquadratic model
- Effective field theory for dissipative photons from higher-form symmetries
- Nonrelativistic Yang-Mills Theory for a Naturally Light Higgs Boson
- Superfluidity of Total Angular Momentum
- Spontaneous Symmetry Breaking and Frustrated Phases