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 (103)

• 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
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• 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
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• Spontaneous Symmetry Probing
• Mutually attracting spin waves in the square-lattice quantum antiferromagnet
• 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
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• Effective theory for deformed nuclei
• Asymptotic Symmetries in de Sitter and Inflationary Spacetimes
• Multicritical Symmetry Breaking and Naturalness of Slow Nambu-Goldstone Bosons
• 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
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• Effective field theory for deformed odd-mass nuclei
• Soft theorems for boosts and other time symmetries
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• Soft Phonon Theorems
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• Higgs Mechanism with Type-II Nambu-Goldstone Bosons at Finite Chemical Potential
• Gapped Goldstones at the cut-off scale: a non-relativistic EFT
• Higgs and Goldstone modes in crystalline solids
• Effective field theory of magnon: Dynamics in chiral magnets and Schwinger mechanism
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• Spontaneous symmetry breaking via inhomogeneities and the differential surface tension
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• Magnetic Catalysis in Antiferromagnetic Films
• Theory of generalized Josephson effects
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• Magnon Energy Renormalization and Low-Temperature Thermodynamics of O(3) Heisenberg Ferromagnets
• Systematic Effective Field Theory Analysis of the D=2+1 Quantum XY Model at Low Temperatures
• Goldstone Boson Interaction in D=2+1 (Pseudo-)Lorentz-Invariant Systems with a Spontaneously Broken Internal Rotation Symmetry
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• Ground State Wave Function Overlap in Superconductors and Superfluids
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