Modulated symmetries are internal that act in a non-uniform, spatially modulated way and generalizations of, for example, dipole symmetries. In this paper, we systematically study the gauging of finite Abelian {1+1} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> dimensions. Working with local Hamiltonians spin chains, explore dual after their potential new spatial modulations. We...

Projective symmetries are ubiquitous in quantum lattice models and can be leveraged to constrain their phase diagram entanglement structure. In this paper, we investigate the consequences of projective algebras formed by non-invertible translations a generalized 1+1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> D XY model based on group-valued qudits. This is specified finite...

In the 1+1D ultralocal lattice Hamiltonian for staggered fermions with a finite-dimensional Hilbert space, there are two conserved, integer-valued charges that flow in continuum limit to vector and axial of massless Dirac fermion perturbative anomaly. Each generates an ordinary U(1) global symmetry acts locally on operators can be gauged individually. Interestingly, they do not commute finite generate Onsager algebra, but their commutator goes zero limit. The chiral anomaly is matched by...

Although condensed matter systems usually do not have higher-form symmetries, we show that, unlike 0-form symmetry, symmetries can emerge as exact at low energies and long distances. In particular, emergent zero temperature are robust to arbitrary local UV perturbations in the thermodynamic limit. This result is true for both invertible noninvertible symmetries. Therefore symmetries: they but constrain low-energy dynamics if were. Since phases of defined limit, this implies that a theory...

We explore the rich landscape of higher-form and non-invertible symmetries that emerge at low energies in generic ordered phases. Using their charge is carried by homotopy defects (i.e., domain walls, vortices, hedgehogs, etc.), absence walls we find symmetry D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math> -dimensional spacetime are described (D-1) display="inline"><mml:mrow><mml:mo stretchy="false"...

We investigate how symmetry and topological order are coupled in the ${2+1}$d $\mathbb{Z}_{N}$ rank-2 toric code for general $N$, which is an exactly solvable point Higgs phase of a symmetric $U(1)$ gauge theory. The enriched present has non-trivial realization square-lattice translation (and rotation/reflection) symmetry, where anyons on different lattice sites have types belong to superselection sectors. call such particles "position-dependent excitations." As result, can hop by one site...

Although condensed matter systems usually do not have higher-form symmetries, we show that, unlike 0-form symmetry, symmetries can emerge as exact at low energies and long distances. In particular, emergent zero temperature are robust to arbitrary local UV perturbations in the thermodynamic limit. This result is true for both invertible non-invertible symmetries. Therefore, $\textit{exact symmetries}$: they but constrain low-energy dynamics if were. Since phases of defined limit, this...

Rank-2 toric code (R2TC), a prototypical archetype of the discrete rank-2 symmetric gauge theory, has properties that differ from those standard code. Specifically, it features blending UV and IR in its ground state, restricted mobility quasiparticles, variations braiding statistics quasiparticles based on their position. In this paper, we investigate various aspects $\mathbb{Z}_N$ theory ${(2+1)}$-dimensional spacetime. Firstly, demonstrate $U(1)$ can arise ${U(1)\times U(1)}$ rank-1 after...

We consider compact ${U}^{\ensuremath{\kappa}}(1)$ gauge theory in $3+1$ dimensions with a general $2\ensuremath{\pi}$-quantized topological term ${\ensuremath{\sum}}_{I,J=1}^{\ensuremath{\kappa}}\frac{{K}_{IJ}}{4\ensuremath{\pi}}{\ensuremath{\int}}_{{M}^{4}}{F}^{I}\ensuremath{\wedge}{F}^{J}$, where $K$ is an integer symmetric matrix even diagonal elements and ${F}^{I}=d{A}^{I}$. At energies below the charges' gaps but above monopoles' gaps, this field has emergent...

In this note, we classify topological solitons of n <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math> -brane fields, which are nonlocal fields that describe -dimensional extended objects. We consider a class formally define homomorphism from the -fold loop space \Omega^n X_D display="inline"><mml:mrow><mml:msup><mml:mi>Ω</mml:mi><mml:mi>n</mml:mi></mml:msup><mml:msub><mml:mi>X</mml:mi><mml:mi>D</mml:mi></mml:msub></mml:mrow></mml:math>...

Condensed-matter systems provide alternative "vacua" exhibiting emergent low-energy properties drastically different from those of the standard model. A case in point is quantum electrodynamics (QED) fractionalized topological magnet known as spin ice, whose magnetic monopoles set it apart familiar QED world we live in. Here, show that two greatly differ their fine structure constant α, which parametrizes how strongly matter couples to light: αQSI more than an order magnitude greater...

Dualities of quantum field theories are challenging to realize in lattice models qubits. In this work, we explore one the simplest dualities, T-duality compact boson CFT, and its realization spin chains. special case XX model, uncover an exact T-duality, which is associated with a non-invertible symmetry that exchanges two U(1) symmetries. The latter symmetries flow momentum winding mixed anomaly CFT. However, charge operators do not commute on instead generate Onsager algebra. We discuss...

We explore the rich landscape of higher-form and non-invertible symmetries that emerge at low energies in generic ordered phases. Using their charge is carried by homotopy defects (i.e., domain walls, vortices, hedgehogs, etc.), absence walls we find symmetry ${D}$-dimensional spacetime are described ${(D-1)}$-representations a ${(D-1)}$-group depends only on spontaneous symmetry-breaking (SSB) pattern phase. These emergent not spontaneously broken show breaking them induces phase transition...

We study the nonlinear $\sigma$-model in ${(d+1)}$-dimensional spacetime with connected target space $K$ and show that, at energy scales below singularities (e.g., vortices, hedgehogs, etc.), it has an emergent non-invertible higher symmetry. The symmetry defects of are described by $d$-representations a discrete $d$-group $\mathbb{G}^{(d)}$, so is dual invertible $\mathbb{G}^{(d)}$ determined such that its classifying $B\mathbb{G}^{(d)}$ given $d$-th Postnikov stage $K$. In $(2+1)$D for...

Since their proposal nearly half a century ago, physicists have sought axions in both high energy and condensed matter settings. Despite intense growing efforts, to date, experimental success has been limited, with the most prominent results arising context of topological insulators. Here, we propose novel mechanism whereby can be realized quantum spin liquids. We discuss necessary symmetry requirements identify possible realizations candidate pyrochlore materials. In this context, couple...

Projective symmetries are ubiquitous in quantum lattice models and can be leveraged to constrain their phase diagram entanglement structure. In this paper, we investigate the consequences of projective algebras formed by non-invertible translations a generalized $1+1$D XY model based on group-valued qudits. This is specified finite group $G$ enjoys $\mathsf{Rep}(G)\times Z(G)$ translation symmetry, where symmetry operators obey algebra presence defects. For invertible symmetries, such imply...

We study the nonlinear $\ensuremath{\sigma}$-model in $(d+1)$-dimensional space-time with connected target space $K$ and show that, at energy scales below singular field configurations (such as vortices), it has an emergent noninvertible higher symmetry. The symmetry defects of are described by $d$-representations a discrete $d$-group ${\mathbb{G}}^{(d)}$ (i.e., is dual invertible symmetry). determined such that its classifying $B{\mathbb{G}}^{(d)}$ given $d\mathrm{th}$ Postnikov stage $K$....

Modulated symmetries are internal that act in a non-uniform, spatially modulated way and generalizations of, for example, dipole symmetries. In this paper, we systematically study the gauging of finite Abelian ${1+1}$ dimensions. Working with local Hamiltonians spin chains, explore dual after their potential new spatial modulations. We establish sufficient conditions existence an isomorphism between dual, naturally implemented by lattice reflections. For instance, systems prime qudits,...

We perform a thorough investigation of the first FPUT recurrence in $\beta$-FPUT chain for both positive and negative $\beta$. show numerically that rescaled time $T_{r}=t_{r}/(N+1)^{3}$ depends, large $N$, only on parameter $S\equiv E\beta(N+1)$. Our numerics also reveal small $\left|S\right|$, $T_{r}$ is linear $S$ with slope For proportional to $\left|S\right|^{-1/2}$ $\beta$ but different multiplicative constants. In continuum limit, approaches modified Korteweg-de Vries (mKdV) equation,...

We numerically investigate the existence and stability of higher-order recurrences (HoRs), including super-recurrences, super-super-recurrences, etc., in α β Fermi-Pasta-Ulam-Tsingou (FPUT) lattices for initial conditions fundamental normal mode. Our results represent a considerable extension pioneering work Tuck Menzel on super-recurrences. For fixed lattice sizes, we observe study apparent singularities periods these HoRs, speculated to be caused by nonlinear resonances. Interestingly,...

Rank-2 toric code (R2TC), a prototypical archetype of the discrete rank-2 symmetric gauge theory, has properties that differ from those standard code. Specifically, it features blending UV and IR in its ground state, restricted mobility quasiparticles, variations braiding statistics quasiparticles based on their position. In this paper, we investigate various aspects $\mathbb{Z}_N$ theory ${(2+1)}$-dimensional spacetime. Firstly, demonstrate $U(1)$ can arise ${U(1)\times U(1)}$ rank-1 after...

In the 1+1D ultra-local lattice Hamiltonian for staggered fermions with a finite-dimensional Hilbert space, there are two conserved, integer-valued charges that flow in continuum limit to vector and axial of massless Dirac fermion perturbative anomaly. Each generates an ordinary U(1) global symmetry acts locally on operators can be gauged individually. Interestingly, they do not commute finite generate Onsager algebra, but their commutator goes zero limit. The chiral anomaly is matched by...

Dualities of quantum field theories are challenging to realize in lattice models qubits. In this work, we explore one the simplest dualities, T-duality compact boson CFT, and its realization spin chains. special case XX model, uncover an exact T-duality, which is associated with a non-invertible symmetry that exchanges two U(1) symmetries. The latter symmetries flow momentum winding mixed anomaly CFT. However, charge operators do not commute on instead generate Onsager algebra. We discuss...

Since their proposal nearly half a century ago, physicists have sought axions in both high energy and condensed matter settings. Despite intense growing efforts, to date experimental success has been limited, with the most prominent results arising context of topological insulators. Here we propose novel mechanism whereby can be realized quantum spin liquids. We discuss necessary symmetry requirements identify possible realizations candidate pyrochlore materials. In this context, couple...