Related papers: Categorical Symmetries at Criticality
Prior work [arXiv:2106.16248] shows that the Standard Model (SM) naturally arises near a gapless quantum critical region between Georgi-Glashow (GG) $su(5)$ and Pati-Salam (PS) $su(4) \times su(2) \times su(2)$ models of quantum vacua (in a…
We introduce a class of non-invertible topological defects in (3+1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1+1)d critical Ising model. As in the lower-dimensional…
The Lie point symmetries of a coupled system of two nonlinear differential-difference equations are investigated. It is shown that in special cases the symmetry group can be infinite dimensional, in other cases up to 10 dimensional. The…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
Quantum measurements performed on a subsystem of a quantum many-body state can generate entanglement for its remaining constituents. The whole system including the measurement record is described by a hybrid mixed state, which can exhibit…
We discuss the behavior of quantum and classical pairwise correlations in critical systems, with the quantumness of the correlations measured by the quantum discord. We analytically derive these correlations for general real density…
The Ising model serves as a canonical platform for exploring emergent symmetry in quantum critical systems. The critical point of the 1D Ising chain is described by a conformal Ising field theory, which remains integrable in the presence of…
We propose a unified framework to classify gapped infra-red (IR) phases with categorical symmetries, leading to a generalized, categorical Landau paradigm. This is applicable in any dimension and gives a succinct, comprehensive, and…
Over the past few decades, tremendous efforts have been devoted to understanding self-duality at the quantum critical point, which enlarges the global symmetry and constrains the dynamics. In this letter, we employ large-scale density…
Gapped phases in 2+1 dimensional quantum field theories with fusion 2-categorical symmetries were recently classified and characterized using the Symmetry Topological Field Theory (SymTFT) approach arXiv:2408.05266, arXiv:2502.20440. In…
Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it…
In this work, we study quantum many-body systems which are self-dual under duality transformation connecting different symmetry protected topological (SPT) phases. We provide a geometric explanation of the criticality of these self-dual…
We study one-dimensional disordered systems with average non-invertible symmetries, where quenched disorder may locally break part of the symmetry while preserving it upon disorder averaging. A canonical example is the random…
The unified mathematical theory of gapped and gapless edges of 2d topological orders was developed by two of the authors. It provides a powerful tool to study pure edge topological phase transitions on the edges of 2d topological orders…
We discuss the boundary critical behaviors of two dimensional quantum phase transitions with fractionalized degrees of freedom in the bulk, motivated by the fact that usually it is the $1d$ boundary that is exposed and can be conveniently…
We explore 1+1 dimensional (1+1D) gapped phases in systems with non-invertible symmetries, focusing on symmetry-protected topological (SPT) phases (defined as gapped phases with non-degenerate ground states), as well as SPT orders (defined…
In this work, we use Ising chain and Kitaev chain to check the validity of an earlier proposal in arXiv:2011.02859 that enriched fusion (higher) categories provide a unified categorical description of all gapped/gapless quantum liquid…
A bosonic non-invertible Symmetry Protected Topological (NISPT) phase in (1+1)-dim is referred to as $\textit{intrinsic}$ if it cannot be mapped, under discrete gauging, to a gapped phase with any invertible symmetry, that is, if it is…
Deconfined criticality and gapless topological states have recently attracted growing attention, as both phenomena go beyond the traditional Landau paradigm. However, the deep connection between these two critical states, particularly in…
We establish a comprehensive framework for characterizing the infrared (IR) phases of a fermionic quantum theory in three spatial dimensions, based on its quantum anomalies associated with a finite symmetry. We uncover a fundamental…