dorsal/arxiv
View SchemaSpontaneous symmetry breaking and response functions
| Authors | A. Beraudo, A. De Pace, M. Martini, A. Molinari |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0409039 |
| URL | https://arxiv.org/abs/nucl-th/0409039 |
| DOI | 10.1016/j.aop.2004.12.002 |
| Journal | Annals Phys. 317 (2005) 444-473 |
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.
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"abstract": "We study the quantum phase transition occurring in an infinite homogeneous\nsystem of spin 1/2 fermions in a non-relativistic context. As an example we\nconsider neutrons interacting through a simple spin-spin Heisenberg force. The\ntwo critical values of the coupling strength -- signaling the onset into the\nsystem of a finite magnetization and of the total magnetization, respectively\n-- are found and their dependence upon the range of the interaction is\nexplored. The spin response function of the system in the region where the\nspin-rotational symmetry is spontaneously broken is also studied. For a\nferromagnetic interaction the spin response along the direction of the\nspontaneous magnetization occurs in the particle-hole continuum and displays,\nfor not too large momentum transfers, two distinct peaks. The response along\nthe direction orthogonal to the spontaneous magnetization displays instead,\nbeyond a softened and depleted particle-hole continuum, a collective mode to be\nidentified with a Goldstone boson of type II. Notably, the random phase\napproximation on a Hartree-Fock basis accounts for it, in particular for its\nquadratic -- close to the origin -- dispersion relation. It is shown that the\nGoldstone boson contributes to the saturation of the energy-weighted sum rule\nfor ~25% when the system becomes fully magnetized (that is in correspondence of\nthe upper critical value of the interaction strength) and continues to grow as\nthe interaction strength increases.",
"arxiv_id": "nucl-th/0409039",
"authors": [
"A. Beraudo",
"A. De Pace",
"M. Martini",
"A. Molinari"
],
"categories": [
"nucl-th"
],
"doi": "10.1016/j.aop.2004.12.002",
"journal_ref": "Annals Phys. 317 (2005) 444-473",
"title": "Spontaneous symmetry breaking and response functions",
"url": "https://arxiv.org/abs/nucl-th/0409039"
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