Related papers: Higher-Form Anomalies on Lattices
We define an 't Hooft anomaly index for a group acting on a 2d quantum lattice system by finite-depth circuits. It takes values in the degree-4 cohomology of the group and is an obstruction to on-siteability of the group action. We…
't Hooft anomalies impose fundamental constraints on quantum matter and often lead to emergent symmetry structures upon gauging. We analyze a lattice model with four global symmetries realizing a mixed anomaly described by $\sim a_1\wedge…
An internal symmetry in a lattice model is said to be onsiteable if it can be disentangled into an onsite action by introducing ancillas and conjugating with a finite-depth circuit. A standard lore holds that onsiteability is equivalent to…
We analyze lattice Hamiltonian systems whose global symmetries have 't Hooft anomalies. As is common in the study of anomalies, they are probed by coupling the system to classical background gauge fields. For flat fields (vanishing field…
In this work, we explore topological phases of matter obtained by effectively gauging or fermionizing a system, where the Gauss law constraint is only enforced energetically. In contrast to conventional gauging or fermionization, the…
We study four-dimensional gauge theories with arbitrary simple gauge group with $1$-form global center symmetry and $0$-form parity or discrete chiral symmetry. We canonically quantize on $\mathbb{T}^3$, in a fixed background field gauging…
We consider quantum many body systems with generalized symmetries, such as the higher form symmetries introduced recently, and the "tensor symmetry". We consider a general form of lattice Hamiltonians which allow a certain level of…
We study gauging interfaces and their defect descendants in lattice models with generalized symmetries in higher dimensions. We construct explicit interface Hamiltonians for gauging a $\mathbb Z_2^{(0)}$ symmetry in $(2+1)d$ and a $\mathbb…
We examine higher-form symmetries of quantum lattice gauge theories through the lens of homotopy theory and operator algebras. We show that in the operator-algebraic approach both higher-form symmetries and 't Hooft anomalies arise from…
The Hilbert space of a quantum system with internal global symmetry $G$ decomposes into sectors labelled by irreducible representations of $G$. If the system is chaotic, the energies in each sector should separately resemble ordinary random…
We study higher-form global symmetries and a higher-group structure of a low-energy limit of $(3+1)$-dimensional axion electrodynamics in a gapped phase described by a topological action. We argue that the higher-form symmetries should have…
We show that certain 't~Hooft anomalies that evade detection on commonly used closed four-dimensional manifolds become visible when a quantum field theory is placed on asymptotically locally Euclidean (ALE) spaces. As a concrete example, we…
Symmetry protected topological (SPT) states have boundary 't Hooft anomalies that obstruct an effective boundary theory realized in its own dimension with UV completion and an on-site $G$-symmetry. In this work, yet we show that a certain…
We explore higher-form symmetries of M- and F-theory compactified on elliptic fibrations, determined by the topology of their asymptotic boundaries. The underlying geometric structures are shown to be equivalent to known characterizations…
The usual condensed matter lattice theories do not include dynamical electromagnetic (EM) field and do not have higher symmetries naturally (unless we engineer fine-tuned toy models to realize higher symmetries). However, for gapped…
We show that certain global anomalies can be detected in an elementary fashion by analyzing the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory. Distinct anomalous behaviours imprinted in the Hilbert…
We describe a method for computing the anomaly of any finite unitary symmetry group $G$ acting by finite-depth quantum circuits on a two-dimensional lattice system. The anomaly is characterized by an index valued in the cohomology group…
We investigate (-1)-form symmetries using the framework of symmetry topological field theories. Previous studies of (-1)-form symmetries have primarily focused on SymTFTs with topological point operators. Here we examine SymTFTs devoid of…
The Lieb-Schultz-Mattis theorem dictates that a trivial symmetric insulator in lattice models is prohibited if lattice translation symmetry and $U(1)$ charge conservation are both preserved. In this paper, we generalize the…
In the realm of invertible symmetry, the topological approach based on classifying spaces dominates the classification of 't Hooft anomalies and symmetry protected topological phases. We explore the alternative algebraic approach based on…