Related papers: Higher-Form Anomalies on Lattices

Higher-Form Anomalies on Lattices

URL: http://arxiv.org/abs/2509.12304v1
Date: Mon, 15 Sep 2025 18:00:00 GMT
Title: Higher-Form Anomalies on Lattices
Authors: Yitao Feng, Ryohei Kobayashi, Yu-An Chen, Shinsei Ryu,
Abstract summary: We present a general method for defining the 't Hooft anomaly of higher-form symmetries in lattice models built on a tensor product Hilbert space.<n>We show how to characterize the 't Hooft anomaly of the symmetry action by an index valued in $Hd+2(Bp+1G, U(1))$.
Score: 3.3032850807618197
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
Abstract: Higher-form symmetry in a tensor product Hilbert space is always emergent: the symmetry generators become genuinely topological only when the Gauss law is energetically enforced at low energies. In this paper, we present a general method for defining the 't Hooft anomaly of higher-form symmetries in lattice models built on a tensor product Hilbert space. In (2+1)D, for given Gauss law operators realized by finite-depth circuits that generate a finite 1-form $G$ symmetry, we construct an index representing a cohomology class in $H^4(B^2G, U(1))$, which characterizes the corresponding 't Hooft anomaly. This construction generalizes the Else-Nayak characterization of 0-form symmetry anomalies. More broadly, under the assumption of a specified formulation of the $p$-form $G$ symmetry action and Hilbert space structure in arbitrary $d$ spatial dimensions, we show how to characterize the 't Hooft anomaly of the symmetry action by an index valued in $H^{d+2}(B^{p+1}G, U(1))$.

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