Fractional domain wall statistics in spin chains with anomalous symmetries
arxiv(2024)
摘要
We study the statistics of domain wall excitations in quantum spin chains. We
focus on systems with finite symmetry groups represented by matrix product
unitaries (MPUs), i.e. finite depth quantum circuits. Such symmetries can be
anomalous, in which case gapped phases which they support must break the
symmetry. The lowest lying excitations of those systems are thus domain wall
excitations. We investigate the behavior of these domain walls under exchange,
and find that they can exhibit non-trivial exchange statistics. This statistics
is completely determined by the anomaly of the symmetry, and we provide a
direct relation between the known classification of MPU symmetry actions on
ground states and the domain wall statistics. Already for the simplest case of
a ℤ_2 symmetry, we obtain that the presence of an anomalous MPU
symmetry gives rise to domain wall excitations which behave neither as bosons
nor as fermions, but rather exhibit fractional statistics. Finally, we show
that the exchange statistics of domain walls is a physically accessible
quantity, by devising explicit measurement operators through which it can be
determined.
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