We sketch a procedure to capture general non-invertible symmetries of d-dimensional quantum field theory in the data higher-category, which captures local properties topological defects associated symmetries. also discuss fusions defects, involve condensations/gaugings higher-categorical localized on worldvolumes defects. Recently some were discussed literature where dimension seems jump under fusion. This is not possible standard description higher-categories. explain that...

Non-invertible symmetries have by now seen numerous constructions in higher dimensional Quantum Field Theories (QFT). In this paper we provide an depth study of gauging 0-form the presence non-invertible symmetries. The starting point our analysis is a theory with $G$ symmetry, and propose description sequential partial gaugings sub-symmetries. implements theta-symmetry defects companion [1]. resulting network symmetry structures related will be called web. Our formulation makes direct...

We present a framework to systematically investigate higher categorical symmetries in two-dimensional spin systems. Though exotic, such generalised have been shown naturally arise as dual upon gauging invertible symmetries. Our relies on an approach dualities whereby quantum lattice models only differ choice of module 2-category over some input fusion 2-category. Given arbitrary system with ordinary symmetry, we explain how perform the (twisted) any its sub-symmetries. then demonstrate that...

The spin-1/2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, debated to possess spin-liquid ground state when only nearest-neighbor antiferromagnetic interactions are present. Here, we contest this hypothesis extensive numerical investigation using both exact diagonalization and complementary variational techniques. Specifically, employ resonating-valence-bond-like,...

As exemplified by the growing interest in quantum anomalous Hall effect, research on topology as an organizing principle of matter is greatly enriched from interplay with magnetism. In this vein, we present a combined electrical and thermoelectrical transport study magnetic Weyl semimetal ${\mathrm{EuCd}}_{2}{\mathrm{As}}_{2}$. Unconventional contribution to Nernst effects were observed both above below transition temperature ${\mathrm{EuCd}}_{2}{\mathrm{As}}_{2}$, indicating existence...

We consider a 2D quantum spin model with ring-exchange interaction that has subsystem symmetries associated to conserved magnetization along rows and columns of square lattice, which implies the conservation global dipole moment. The is not integrable, but violates eigenstate thermalization hypothesis through an extensive Hilbert space fragmentation, including exponential number inert subsectors trivial dynamics, arising from kinetic constraints. While are quite restrictive for we show they...

We consider exactly solvable models in (3+1)d whose ground states are described by topological lattice gauge theories. Using simplicial arguments, we emphasize how the consistency condition of unitary map performing a local change triangulation is equivalent to coherence relation pentagonator 2-morphism monoidal 2-category. By weakening some axioms such 2-category, obtain cohomological model underlying 1-category 2-group. Topological from 2-groups together with their realization then studied...

We discuss (2+1)-dimensional gapless surface theories of bulk (3+1)-dimensional topological phases, such as the BF theory at level $\mathrm{K}$, and its generalization. In particular, we put these on a flat (2+1) dimensional torus $T^3$ parameterized by modular parameters, compute partition functions obeying various twisted boundary conditions. show are transformed into each other under $SL(3,\mathbb{Z})$ transformations, furthermore establish bulk-boundary correspondence in (3+1) dimensions...

While driven interacting quantum matter is generically subject to heating and scrambling, certain classes of systems evade this paradigm. We study such an exceptional class in periodically critical (1 + 1)-dimensional with a spatially modulated, but disorder-free time evolution operator. Instead complete the excitations system remain well-defined. Their propagation analogous along light cones curved space-time obtained by two Schwarzschild black holes. The Hawking temperature serves as order...

We analyze $2+1d$ and $3+1d$ bosonic symmetry protected topological (SPT) phases of matter by onsite group $G$ using dual bulk boundary approaches. In the bulk, we study an effective field theory, which upon coupling to a background flat gauge furnishes purely response theory. The action evaluated on certain manifolds, with appropriate choice field, defines set SPT invariants. Further, SPTs can be gauged summing over all isomorphism classes fields obtain Dijkgraaf-Witten theories. These...

The paradigm of topological band theory has been recently challenged by the discovery nodes with non-Abelian charges. Here, authors simplify description topology using elementary geometric rules, and they use them to prove a relation between monopole charge linking structure nodal-line rings. Furthermore, establish novel braiding phenomenon induced interaction Berry phase. analysis suggests unexpected richness structures in $\mathcal{P}\phantom{\rule{0}{0ex}}\mathcal{T}$-symmetric systems.

We analyze the topological properties of a chiral p+ip superconductor for two-dimensional metal and semimetal with four Dirac points. Such system has been proposed to realize second-order superconductivity host corner Majorana modes. show that an additional C4 rotational symmetry, is in intrinsic higher-order phase, lower C2 boundary-obstructed phase. The boundary obstruction protected by bulk Wannier gap. However, we well-known nested Wilson loop general unquantized despite particle-hole...

We demonstrate that genuinely non-Hermitian topological phases and corresponding phase transitions can be naturally realized in monitored quantum circuits, exemplified by the paradigmatic Su-Schrieffer-Heeger model. emulate this model a 1D chain of spinless electrons evolving under unitary dynamics subject to periodic measurements are stochastically invoked. The topology is visible invariants adapted context circuits. For instance, diagram realization obtained from biorthogonal polarization...

Topological quantum chemistry (TQC) is a successful framework for identifying (noninteracting) topological materials. Based on the symmetry eigenvalues of Bloch eigenstates at maximal momenta, which are attainable from first principles calculations, band structure can either be classified as an atomic limit, in other words adiabatically connected to independent electronic orbitals respective crystal lattice, or it topological. For interacting systems, there no single-particle and hence, TQC...

We study the heating dynamics of a generic one dimensional critical system when driven quasiperiodically. Specifically, we consider Fibonacci drive sequence comprising Hamiltonian uniform conformal field theory (CFT) describing such systems and its sine-square deformed counterpart. The asymptotic is dictated by Lyapunov exponent which has fractal structure embedding Cantor lines where exactly zero. Away from these lines, typically heats up fast to infinite energy in non-ergodic manner...

We show that the chiral Dirac and Majorana hinge modes in three-dimensional higher-order topological insulators (HOTIs) superconductors (HOTSCs) can be gapped while preserving protecting $\mathsf{C}_{2n}\mathcal T$ symmetry upon introduction of non-Abelian surface order. In both cases, order on a single side breaks time reversal symmetry, but appears with its time-reversal conjugate alternating sides pattern. absence HOTI/HOTSC bulk, such pattern necessarily involves gapless hinges between...

Many of the experiments in twisted bilayer graphene (TBG) differ from each other terms details their phase diagrams. Few controllable aspects aside, this discrepancy is largely believed to be arising presence a varying degree twist angle inhomogeneity across different samples. Real space maps indeed reveal TBG devices splitting into several large domains angles. Motivated by these observations, we study quantum mechanical tunneling domain wall (DW) that separates two such regions. We show...

The multiflavor $\mathit{BF}$ theories in (3+1) dimensions with cubic or quartic coupling are the simplest topological quantum field that can describe fractional braiding statistics between looplike excitations (three-loop four-loop statistics). In this paper, by canonically quantizing these theories, we study algebra of Wilson loop and surface operators, multiplets ground states on three-torus. particular, coupled three-torus, explicitly calculate $\mathcal{S}$ $\mathcal{T}$ matrices, which...

We propose a diagnostic tool for detecting non-trivial symmetry protected topological (SPT) phases by group $G$ in 2+1 dimensions. Our method is based on directly studying the 1+1-dimensional anomalous edge conformal field theory (CFT) of SPT phases. claim that if CFT an phase, then there must be obstruction to cutting it open. This manifests in-existence boundary states preserves both and global $G$. discuss relation between edgeability, ability find consistent state, gappability, gap out...

Excitations in (3+1)-dimensional [(3+1)D] topologically ordered phases have very rich structures. (3+1)D topological support both pointlike and stringlike excitations, particular the loop (closed string) excitations may admit knotted linked In this work, we ask following question: How do different types of contribute to entanglement entropy or, alternatively, can use detect structure further obtain information underlying order? We are mainly interested order that be realized Dijkgraaf-Witten...

We prove two Lieb-Schultz-Mattis type theorems that apply to any translationally invariant and local fermionic $d$-dimensional lattice Hamiltonian for which fermion-number conservation is broken down the of fermion parity. show when internal symmetry group ${G}_{f}^{\phantom{\rule{0.16em}{0ex}}}$ realized locally (in a repeat unit cell lattice) by nontrivial projective representation, then ground state cannot be simultaneously nondegenerate, symmetric (with respect translations...

We propose that doped Weyl semimetals with {time-reversal and certain crystalline symmetries} are natural candidates to realize higher-order topological superconductors, which exhibit a fully gapped bulk while the surface hosts robust gapless chiral hinge states. show in such semimetal, featureless finite-range attractive interaction favors p+ip pairing symmetry. By analyzing its properties, we identify state as superconductor, depending on existence of four-fold rotoinversion symmetry, is...

We investigate the gauging of higher-form finite Abelian symmetries and their sub-groups in quantum spin models spatial dimensions d=2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> 3. Doing so, we naturally uncover gauged with dual higher-group potential mixed ‘t Hooft anomalies. demonstrate that anomalies manifest as symmetry fractionalization participating anomaly. Gauging is...

The recently introduced topological quantum chemistry (TQC) framework has provided a description of universal properties all possible band insulators in space groups based on crystalline unitary symmetries and time reversal. While this formalism filled the gap between mathematical classification practical diagnosis materials, an obvious limitation is that it only applies to weakly interacting systems-which can be described within theory. It open question which extent generalized correlated...