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Ground State Wave Function Overlap in Superconductors and Superfluids | | Mark P. Hertzberg
; Mudit Jain
; | | Date: |
14 Aug 2019 | | Abstract: | In order to elucidate the role of spontaneous symmetry breaking in condensed
matter systems, we explicitly construct the ground state wave function for a
nonrelativistic theory of a two-fluid system of bosons. This can model either
superconductivity or superfluidity, depending on whether we assign a charge to
the particles or not. Since each nonrelativistic field $Psi_j$ ($j=1,2$)
carries a phase $ heta_j$ and the Lagrangian is formally invariant under
shifts $ heta_j o heta_j+alpha_j$ for independent $alpha_j$, one can
investigate whether these symmetries are spontaneously broken by the ground
state condensate of particles. We explicitly compute the wave function overlap
between a pair of ground states $langle G|G’
angle$ that differ by these
phase shifts. We show that the ground state spontaneously breaks most pairs of
shifts, including $ heta_j o heta_j+m_jepsilon$, where $m_j$ is the mass of
each species. This is associated with a single Goldstone boson (phonon) and is
associated with the conservation of mass. However, we show that the ground
state is unchanged under the transformation $ heta_j o heta_j+q_jepsilon$,
where $q_j$ is the charge of each species, and hence there is no spontaneous
symmetry breaking of the $U(1)_{em}$ associated with electromagnetism. This
construction should remove any residual confusion in the literature, which has
occasionally claimed that $U(1)_{em}$ undergoes spontaneous symmetry breaking
in superconductivity; in fact it does not. | | Source: | arXiv, 1908.4892 | | Services: | Forum | Review | PDF | Favorites | |
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