Higher-form symmetry breaking at Ising transitions

Abstract

In recent years, new phases of matter that are beyond the Landau paradigm of symmetry breaking are mountaining, and to catch up with this fast development, new notions of global symmetry are introduced. Among them, the higher-form symmetry, whose symmetry charges are spatially extended, can be used to describe topologically ordered phases as the spontaneous breaking of the symmetry, and consequently unify the unconventional and conventional phases under the same conceptual framework. However, such conceptual tools have not been put into quantitative test except for certain solvable models, therefore limiting its usage in the more generic quantum manybody systems. In this work, we study Z2 higher-form symmetry in a quantum Ising model, which is dual to the global (0-form) Ising symmetry. We compute the expectation value of the Ising disorder operator, which is a non-local order parameter for the higher-form symmetry, analytically in free scalar theories and through unbiased quantum Monte Carlo simulations for the interacting fixed point in (2+1)d. From the scaling form of this extended object, we confirm that the higher-form symmetry is indeed spontaneously broken inside the paramagnetic, or quantum disordered phase (in the Landau sense), but remains symmetric in the ferromagnetic/ordered phase. At the Ising critical point, we find that the higher-form symmetry is also spontaneously broken, even though the 0-form symmetry is preserved. We discuss examples where both the global 0-form symmetry and the dual higher-form symmetry are preserved, in systems with a codimension-1 manifold of gapless points in momentum space. These results provide non-trivial working examples of higher-form symmetry operators, including the first computation of one-form order parameter in an interacting conformal field theory, and open the avenue for their generic implementation in quantum many-body systems.

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• Non-Invertible Duality Defects in 3+1 Dimensions
• Quantum criticality under decoherence or weak measurement
• Gapless topological phases and symmetry-enriched quantum criticality
• Scaling of entanglement entropy at deconfined quantum criticality
• Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
• Scaling of disorder operator at deconfined quantum criticality
• Universal Features of Higher-Form Symmetries at Phase Transitions
• Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
• Scaling of disorder operator at $(2+1)d$ U(1) quantum criticality
• Decorated Defect Construction of Gapless-SPT States
• Topological Disorder Parameter
• Tensor network approach to electromagnetic duality in (3+1)d topological gauge models
• Entanglement order parameters and critical behavior for topological phase transitions and beyond
• Unlocking the general relationship between energy and entanglement spectra via the wormhole effect
• Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation
• Extracting subleading corrections in entanglement entropy at quantum phase transitions
• Different temperature-dependence for the edge and bulk of entanglement Hamiltonian
• Sampling reduced density matrix to extract fine levels of entanglement spectrum and restore entanglement Hamiltonian
• Reweight-annealing method for evaluating the partition function via quantum Monte Carlo calculations
• Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry
• Distinguishing Quantum Phases through Cusps in Full Counting Statistics
• Bipartite Fluctuations of Critical Fermi Surfaces
• Measuring the Boundary Gapless State and Criticality via Disorder Operator
• A Multicritical Point with Infinite Fractal Symmetries
• Generalized Landau Paradigm for quantum phases and phase transitions
• Disorder operators in two-dimensional Fermi and non-Fermi liquids through multidimensional bosonization
• Addressing general measurements in quantum Monte Carlo
• Finite Correlation Length Scaling of Disorder Parameter at Quantum Criticality
• Lieb-Robinson bounds with exponential-in-volume tails
• Multiparty Entanglement Microscopy of Quantum Ising models in 1d, 2d and 3d
• Bell sampling in Quantum Monte Carlo simulations