Spontaneous symmetry breaking and response functions
arXiv:nucl-th/0409039 · doi:10.1016/j.aop.2004.12.002
Abstract
We study the quantum phase transition occurring in an infinite homogeneous system of spin 1/2 fermions in a non-relativistic context. As an example we consider neutrons interacting through a simple spin-spin Heisenberg force. The two critical values of the coupling strength -- signaling the onset into the system of a finite magnetization and of the total magnetization, respectively -- are found and their dependence upon the range of the interaction is explored. The spin response function of the system in the region where the spin-rotational symmetry is spontaneously broken is also studied. For a ferromagnetic interaction the spin response along the direction of the spontaneous magnetization occurs in the particle-hole continuum and displays, for not too large momentum transfers, two distinct peaks. The response along the direction orthogonal to the spontaneous magnetization displays instead, beyond a softened and depleted particle-hole continuum, a collective mode to be identified with a Goldstone boson of type II. Notably, the random phase approximation on a Hartree-Fock basis accounts for it, in particular for its quadratic -- close to the origin -- dispersion relation. It is shown that the Goldstone boson contributes to the saturation of the energy-weighted sum rule for ~25% when the system becomes fully magnetized (that is in correspondence of the upper critical value of the interaction strength) and continues to grow as the interaction strength increases.
36 pages, 17 figures
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Cited by in corpus (13)
- Spontaneous Symmetry Breaking and Nambu-Goldstone Bosons in Quantum Many-Body Systems
- Linear response of homogeneous nuclear matter with energy density functionals
- Nuclear response for the Skyrme effective interaction with zero range tensor terms
- Nuclear response for the Skyrme effective interaction with zero-range tensor terms. II. Sum rules and instabilities
- Nuclear response for the Skyrme effective interaction with zero-range tensor terms. III. Neutron matter and neutrino propagation
- Spin ordered phase transitions in isospin asymmetric nuclear matter
- Goldstone boson counting in linear sigma models with chemical potential
- Spontaneous symmetry breaking in the linear sigma model at finite chemical potential: One-loop corrections
- Spin polarized states in neutron matter at a strong magnetic field
- Goldstone bosons in presence of charge density
- Finite temperature effects in antiferromagnetism of nuclear matter
- Unusual temperature behavior of entropy of antiferromagnetic spin state in nuclear matter with effective finite range interaction
- Spontaneous symmetry breaking in strong and electroweak interactions