Spontaneous Symmetry Breaking and Nambu-Goldstone Bosons in Quantum Many-Body Systems

Abstract

Spontaneous symmetry breaking is a general principle, that constitutes the underlying concept of a vast number of physical phenomena ranging from ferromagnetism and superconductivity in condensed matter physics to the Higgs mechanism in the standard model of elementary particles. I focus on manifestations of spontaneously broken symmetries in systems that are not Lorentz invariant, which include both, nonrelativistic systems as well as relativistic systems at nonzero density, providing a self-contained review of the properties of spontaneously broken symmetries specific to such theories. Topics covered include: (i) Introduction to the mathematics of spontaneous symmetry breaking and the Goldstone theorem. (ii) Minimization of Higgs-type potentials for higher-dimensional representations. (iii) Counting rules for Nambu-Goldstone bosons and their dispersion relations. (iv) Construction of effective Lagrangians. Specific examples in both relativistic and nonrelativistic physics are worked out in detail.

49 pages, 2 pdf figures; v2: short discussion of pseudo-NG bosons and some references added + other minor corrections, version to be published

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Cited by in corpus (102)

• Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance
• An Introduction to Spontaneous Symmetry Breaking
• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
• On the number of Nambu-Goldstone bosons and its relation to charge densities
• Compensating strong coupling with large charge
• Effective Lagrangian for Nonrelativistic Systems
• Massive Nambu-Goldstone Bosons
• A relativistic non-relativistic Goldstone theorem: gapped Goldstones at finite charge density
• Counting Rules of Nambu-Goldstone Modes
• Pseudo-Goldstone gaps and order-by-quantum-disorder in frustrated magnets
• Selected Topics in the Large Quantum Number Expansion
• Large charge at large N
• Spin Currents and Magnon Dynamics in Insulating Magnets
• Bogoliubov Theory and Lee-Huang-Yang Corrections in Spin-1 and Spin-2 Bose-Einstein Condensates in the Presence of the Quadratic Zeeman Effect
• A holographic perspective on phonons and pseudo-phonons
• Spontaneous breaking of continuous translational invariance
• Phenomenology of theories of gravity without Lorentz invariance: the preferred frame case
• Mutually attracting spin waves in the square-lattice quantum antiferromagnet
• Spontaneous Symmetry Probing
• Holographic Superfluids and the Landau Criterion
• Effective Field Theory for Finite Systems with Spontaneously Broken Symmetry
• Dispersion relations of Nambu-Goldstone modes at finite temperature and density
• Spontaneous symmetry breaking in inflationary cosmology: on the fate of Goldstone Bosons
• Effective theory for deformed nuclei
• Multicritical Symmetry Breaking and Naturalness of Slow Nambu-Goldstone Bosons
• Asymptotic Symmetries in de Sitter and Inflationary Spacetimes
• Abe homotopy classification of topological excitations under the topological influence of vortices
• Spontaneously magnetized Tomonaga-Luttinger liquid in frustrated quantum antiferromagnets
• Nambu-Goldstone modes in segregated Bose-Einstein condensates
• Effective Lagrangians for quantum many-body systems
• Effective Lagrangian for Nambu-Goldstone modes in nonequilibrium open systems
• Excitations of a trapped two component Bose Einstein Condensate
• Cascading Multicriticality in Nonrelativistic Spontaneous Symmetry Breaking
• Spontaneous Magnetization of an Ideal Ferromagnet: Beyond Dyson's Analysis
• Broken spacetime symmetries and elastic variables
• The low lying modes of triplet-condensed neutron matter and their effective theory
• The a-theorem and conformal symmetry breaking in holographic RG flows
• Topological phase diagrams of exactly solvable non-Hermitian interacting Kitaev chains
• Effective theory for the non-rigid rotor in an electromagnetic field: Toward accurate and precise calculations of E2 transitions in deformed nuclei
• Low-Temperature Properties of Two-Dimensional Ideal Ferromagnets
• The Quantum Yang Baxter conditions: The fundamental relations behind the Nambu-Goldstone theorem
• Completing Lorentz violating massive gravity at high energies
• Symmetry Realization via a Dynamical Inverse Higgs Mechanism
• Simplest phonons and pseudo-phonons in field theory
• Symmetry breaking in interacting ring-shaped superflows of Bose-Einstein condensates
• Scale anomaly of a Lifshitz scalar: a universal quantum phase transition to discrete scale invariance
• Deconfining the rotational Goldstone mode: the superconducting nematic liquid crystal in 2+1D
• Effective field theory and the scattering process for magnons in the ferromagnet, antiferromagnet, and ferrimagnet
• Effective field theory for triaxially deformed nuclei
• Effective Field Theory for Spontaneously Broken Symmetry
• Effective Field Theory of Emergent Symmetry Breaking in Deformed Atomic Nuclei
• Thermodynamics of Two-Dimensional Ideal Ferromagnets - Three-Loop Analysis
• Effective field theory for deformed odd-mass nuclei
• Soft theorems for boosts and other time symmetries
• Properties of Nambu-Goldstone Bosons in a Single-Component Bose-Einstein Condensate
• Higgs Mechanism with Type-II Nambu-Goldstone Bosons at Finite Chemical Potential
• Soft Phonon Theorems
• Spontaneous symmetry breaking and Higgs mode: comparing Gross-Pitaevskii and nonlinear Klein-Gordon equations
• Gapped Goldstones at the cut-off scale: a non-relativistic EFT
• Higgs and Goldstone modes in crystalline solids
• Gauge symmetries and the Higgs mechanism in Quantum Finance
• Spontaneous symmetry breaking via inhomogeneities and the differential surface tension
• Effective field theory of magnon: Dynamics in chiral magnets and Schwinger mechanism
• Nambu-Goldstone bosons characterized by the order parameter in spontaneous symmetry breaking
• Non-linearly realized discrete symmetries
• Low-Temperature Properties of Ferromagnetic Spin Chains in a Magnetic Field
• Criteria for the absence of quantum fluctuations after spontaneous symmetry breaking
• Magnon-Magnon Interactions in O(3) Ferromagnets and Equations of Motion for Spin Operators
• Formation of a supergiant quantum vortex in a relativistic Bose-Einstein condensate driven by rotation and a parallel magnetic field
• Magnetic Catalysis in Antiferromagnetic Films
• Theory of generalized Josephson effects
• Spontaneous symmetry breaking and the flat phase of crystalline membranes
• Magnon Energy Renormalization and Low-Temperature Thermodynamics of O(3) Heisenberg Ferromagnets
• Spin-one color superconductors: collective modes and effective Lagrangian
• Flag manifold sigma models from SU($n$) chains
• Effective field theory of pairing rotations
• Quantum Chromodynamics, Antiferromagnets and XY Models from a Unified Point of View
• Goldstone Boson Interaction in D=2+1 (Pseudo-)Lorentz-Invariant Systems with a Spontaneously Broken Internal Rotation Symmetry
• Systematic Effective Field Theory Analysis of the D=2+1 Quantum XY Model at Low Temperatures
• Ground State Wave Function Overlap in Superconductors and Superfluids
• $\mathcal{N}=2$ supersymmetry and anisotropic scale invariance
• Thermomagnetic Properties of QCD
• Violation of the Spin Statistics Theorem and the Bose-Einstein Condensation of Particles with Half Integer Spin
• Symmetry restoration methods
• Exceptional nonrelativistic effective field theories with enhanced symmetries
• Stability and Absence of a Tower of States in Ferrimagnets
• Mermin-Wagner at the Crossover Temperature
• Quantum black holes as classical space factories
• Models of interacting bosons with exact ground states: a unified approach
• Nuclear condensate and helium white dwarfs
• Engineering Hierarchical Symmetries
• Effective field theories for collective excitations of atomic nuclei
• Thermodynamics of the $d$=3+1 Quantum XY Model
• Dynamics of Frenkel excitons in pentacene
• Entanglement entropy in low-energy field theories at finite chemical potential
• Soft gravitons as Goldstone modes of spontaneously broken asymptotic symmetries in de Sitter spacetimes
• Geometry of Classical Nambu-Goldstone Fields
• Geometrical torque on magnetic moments coupled to a correlated antiferromagnet
• Effective field theory of an anomalous Hall metal from interband quantum fluctuations
• Magnetic correlations in the $SU(3)$ triangular-lattice $t$-$J$ model at finite doping
• The solution to the Black Hole information paradox
• Spontaneous Symmetry Breaking and Frustrated Phases