Universal contributions to charge fluctuations in spin chains at finite temperature

Abstract

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 $Q$ can be succinctly captured by the generating function $G(\theta )=⟨e^{i\theta Q}⟩$. For a 1D translation-invariant spin chain, in the thermodynamic limit the magnitude $|G(\theta )|$ scales with the system size $L$ as $\ln |G(\theta )|=-\alpha (\theta )L+\gamma (\theta )$, where $\gamma (\theta )$ 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 $\gamma (\theta )$ when the system is periodic. We find that $\gamma (\theta )$ only takes nonzero values at isolated points of $\theta$, which is $\theta =\pi$ for all our examples. In two exemplary lattice systems we show that $\gamma (\pi )$ 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 $\gamma (\theta )$ depends on microscopic conditions (such as the filling factor) in field theory and exactly solvable lattice models.

21 pages, 5 figures, published version

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