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Universal contributions to charge fluctuations in spin chains at finite temperature
At finite temperature, conserved charges undergo thermal fluctuations in a
quantum many-body system in the grand canonical ensemble. The full structure of
the fluctuations of the total U(1) charge can be succinctly captured by the
generating function . For a
1D translation-invariant spin chain, in the thermodynamic limit the magnitude
scales with the system size as , where is the
scale-invariant contribution and may encode universal information about the
underlying system. In this work we investigate the behavior and physical
meaning of when the system is periodic. We find that
only takes non-zero values at isolated points of ,
which is for all our examples. In two exemplary lattice systems we
show that takes quantized values when the U(1) symmetry exhibits
a specific type of 't Hooft anomaly with other symmetries. In other cases, we
investigate how depends on microscopic conditions (such as the
filling factor) in field theory and exactly solvable lattice models.Comment: 19 pages, 2 figure
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