Non-local order parameters for states with topological electromagnetic response

Abstract

Chern insulators are states of matter characterized by a quantized Hall conductance, gapless edge modes but also a singular response to monopole configurations of an external electromagnetic field. In this paper, we describe the nature of such a singular response and show how it can be used to define a class of operators acting as non-local order parameters. These operators characterize the Chern-insulator states in the following way: for a given state, there exists a corresponding operator which has an algebraically decaying two-point function in that particular state, while it decays exponentially in all other states. The behaviour of the order parameter is defined only in terms of the electromagnetic response, and not from any microscopic properties, and we therefore claim to have found a generic order parameter for the Chern insulating states. We support this claim by numerically evaluating the order parameters for different insulating states. We also show how our construction can be generalized to other states with topological electromagnetic response, and use the states with a quantized magnetoelectric effect in three dimensions as an example. Besides providing novel insights into topological states of matter, our construction can be exploited to efficiently diagnose such states numerically.

arXiv comment12 pages, 3 figures

References in corpus (22)

• Topological Insulators in Three Dimensions
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Classification of topological quantum matter with symmetries
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological invariants of time-reversal-invariant band structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• Topological orders and Edge excitations in FQH states
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
• Chiral Topological Insulators, Superconductors and other competing orders in three dimensions
• Effective field theories for topological insulators by functional bosonization
• Momentum space metric, non-local operator, and topological insulators
• Topological Excitations in Compact Maxwell-Chern-Simons Theory
• Effective hydrodynamic field theory and condensation picture of topological insulators
• Confinement, brane symmetry and the Julia-Toulouse approach for condensation of defects
• Monopoles in the presence of the Chern-Simons term via the Julia-Toulouse approach
• Characterization of two-dimensional fermionic insulating states
• Off-Diagonal Long Range Order and Scaling in a Disordered Quantum Hall System

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