Higgs Condensates are Symmetry-Protected Topological Phases: II. $U(1)$
Gauge Theory and Superconductors
- URL: http://arxiv.org/abs/2303.08136v1
- Date: Tue, 14 Mar 2023 17:59:42 GMT
- Title: Higgs Condensates are Symmetry-Protected Topological Phases: II. $U(1)$
Gauge Theory and Superconductors
- Authors: Ryan Thorngren, Tibor Rakovszky, Ruben Verresen, and Ashvin Vishwanath
- Abstract summary: We show that a Higgs phase in $d$ spatial dimensions is in a non-trivial $U(1)$ SPT class protected by a global $U(1)$ symmetry associated with the Higgs field.
The signature properties of superconductors -- Higgs phases for electromagnetism -- can be reproduced from this SPT response.
We also treat generalizations to partial-Higgs phases, including "2e" condensates in electronic superconductors.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Classifying Higgs phases within the landscape of gapped and symmetry
preserving states of matter presents a conceptual challenge. We argue that
$U(1)$ Higgs phases are symmetry-protected topological (SPT) phases and we
derive their topological response theory and boundary anomaly -- applicable to
superconductors treated with dynamical electromagnetic field. This generalizes
the discussion of discrete gauge theories by Verresen et al., arXiv:2211.01376.
We show that a Higgs phase in $d$ spatial dimensions is in a non-trivial SPT
class protected by a global $U(1)$ symmetry associated with the Higgs field,
and a $d-2$ form $U(1)$ magnetic symmetry, associated with the absence of
magnetic monopoles. In $d=2$, this gives an SPT with a mixed Hall response
between conventional symmetries, whereas in $d=3$ we obtain a novel SPT
protected by a 0-form and 1-form symmetry whose 2+1d boundary anomaly is
satisfied by a superfluid. The signature properties of superconductors -- Higgs
phases for electromagnetism -- can be reproduced from this SPT response. For
instance, the Josephson effect directly arises from the aforementioned boundary
superfluid. In addition to this minimalist approach being complementary to
Landau-Ginzburg theory, its non-perturbative nature is useful in situations
where fluctuations are significant. We substantiate this by predicting the
stability of the Josephson effect upon introducing monopoles in $U(1)$ lattice
gauge theory, where tuning from the charge-1 Higgs phase to the confined phase
leads to a quantum critical point in the junction. Furthermore, this
perspective reveals unexpected connections, such as how persistent currents at
the surface of a superconductor arise from generalized Thouless pumps. We also
treat generalizations to partial-Higgs phases, including "2e" condensates in
electronic superconductors, corresponding to symmetry-enriched topological
orders.
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