相关论文: Categorical Symmetries at Criticality

These notes were prepared for a series of intensive lectures delivered at Hokkaido University, Nagoya University, Kyoto University, and Kyushu University. We begin with a brief review of higher-form symmetries, anomalies, and discrete gauge…

Quantum phase transitions take place between distinct phases of matter at zero temperature. Near the transition point, exotic quantum symmetries can emerge that govern the excitation spectrum of the system. A symmetry described by the E8…

Quantum phase transitions are a fascinating area of condensed matter physics. The extension through complexification not only broadens the scope of this field but also offers a new framework for understanding criticality and its statistical…

The $d$-dimensional long-range Ising model, defined by spin-spin interactions decaying with the distance as the power $1/r^{d+s}$, admits a second order phase transition with continuously varying critical exponents. At $s = s_*$, the phase…

We study generalized symmetries of quantum field theories in 1+1D generated by topological defect lines with no inverse. This paper follows our companion paper on gapped phases and anomalies associated with these symmetries. In the present…

The tricritical Ising model serves as an example of emergent spacetime supersymmetry, which can arise in condensed matter systems. In this work, we present a variational quantum algorithm to create this tricritical state on a digitized…

Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…

We present practical and formal methods for gauging non-invertible symmetries in (2+1)d topological quantum field theories. Along the way, we generalize various aspects of invertible 0-form gauging, including symmetry fractionalization,…

We present a framework to systematically investigate higher categorical symmetries in two-dimensional spin systems. Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible…

The ordering of charges on half-filled hypercubic lattices is investigated numerically, where electroneutrality is ensured by background charges. This system is equivalent to the $s = 1/2$ Ising lattice model with antiferromagnetic $1/r$…

The thermal dynamics of the two-dimensional Ising model and quantum dynamics of the one-dimensional transverse-field Ising model (TFIM) are mapped to one another through the transfer-matrix formalism. We show that the fermionised TFIM…

The simplest topologically ordered phase in 2+1D is the deconfined phase of $Z_2$ gauge theory, realized for example in the toric code. This phase permits a duality that exchanges electric and magnetic excitations (``$e$'' and ``$m$''…

Critical edge states appear at the bulk gap closing points of topological transitions. Their emergence signify the existence of topologically nontrivial critical points, whose descriptions fall outside the scope of gapped topological…

Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to…

We study several models of $d$-dimensional fermions ($d=1,2,3$) with an emphasis on the properties of their gapless (metallic) phase. It occurs at $T = 0$ as a continuous transition when zeros of the partition function reach the real range…

We study properties of boundary conditions (BCs) in theories with categorical (or non-invertible) symmetries. We describe how the transformation properties, or (generalized) charges, of BCs are captured by topological BCs of Symmetry…

The second-order phase transitions in the Ising model and liquid-gas systems share a universality class and critical exponents, despite the absence of $Z_2$ symmetry in the liquid-gas Hamiltonian. This discrepancy highlights a central…

In this paper we study a hierarchical supersymmetric model for a class of gapless, three-dimensional, weakly disordered quantum systems, displaying pointlike Fermi surface and conical intersections of the energy bands in the absence of…

Gauging a finite subgroup of a global symmetry can map conventional phases and phase transitions to unconventional ones. In this work, we study, as a concrete example, an emergent $\mathbb{Z}_2$-gauged system with global symmetry $U(1)$,…

Anomalies of global symmetries provide important information on the quantum dynamics. We show the dynamical constraints can be organized into three classes: genuine anomalies, fractional topological responses, and integer responses that can…