2022/12/29 by Arkya Chatterjee, Chatterjee, Arkya, Wenjie Ji +3 · 18 citations
Computer Science · Mathematics · Physics and Astronomy · #Anyon #Combinatorics #Condensed matter physics #Critical point (mathematics) #FOS: Physical sciences #Fibonacci number #Gapless playback #Geometry #Global symmetry #High Energy Physics - Theory (hep-th) #Ising model #Mathematical Physics (math-ph) #Mathematics #Order (exchange) #Physics #Potts model #Quantum #Quantum many-body systems #Quantum mechanics #Spontaneous symmetry breaking #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el) #Symmetry (geometry) #Symmetry breaking #Symmetry protected topological order #Theoretical and Computational Physics #Theoretical physics #Topological and Geometric Data Analysis #Topological order #Topological quantum computer #Topology (electrical circuits)
paper · pdf · doi:10.48550/arxiv.2212.14432
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2022/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A characteristic property of a gapless liquid state is its emergent symmetry and dual symmetry, associated with the conservation laws of symmetry charges and symmetry defects respectively. These conservation laws, considered on an equal footing, can't be described simply by the representation theory of a group (or a higher group). They are best described in terms of a topological order (TO) with gappable boundary in one higher dimension; we call this the symTO of the gapless state. The symTO can thus be considered a fingerprint of the gapless state. We propose that a largely complete characterization of a gapless state, up to local-low-energy equivalence, can be obtained in terms of its maximal emergent symTO. In this paper, we review the symmetry/topological-order (Symm/TO) correspondence and propose a precise definition of maximal symTO. We discuss various examples to illustrate these ideas. We find that the 1+1D Ising critical point has a maximal symTO described by the 2+1D double-Ising topological order. We provide a derivation of this result using symmetry twists in an exactly solvable model of the Ising critical point. The critical point in the 3-state Potts model has a maximal symTO of double (6,5)-minimal-model topological order. As an example of a noninvertible symmetry in 1+1D, we study the possible gapless states of a Fibonacci anyon chain with emergent double-Fibonacci symTO. We find the Fibonacci-anyon chain without translation symmetry has a critical point with unbroken double-Fibonacci symTO. In fact, such a critical theory has a maximal symTO of double (5,4)-minimal-model topological order. We argue that, in the presence of translation symmetry, the above critical point becomes a stable gapless phase with no symmetric relevant operator.