Detection of anyon braiding through pump-probe spectroscopy

Abstract

We show that the braiding of anyons in a quantum spin liquid leaves a distinct dynamical signature in the nonlinear pump-probe response. Using a combination of exact diagonalization and matrix product state techniques, we study the nonlinear pump-probe response of the toric code in a magnetic field, a model which hosts mobile electric $e$ and magnetic $m$ anyonic excitations. While the linear response signal oscillates and decays with time like $\sim t^{-1.3}$, the amplitude of the nonlinear signal for ${\chi }_{XZZ}^{(3)}$ features a linear-in-time enhancement at early times. The comparison between ${\chi }_{XZZ}^{(3)}$, which involves the non-trivial braiding of $e$ and $m$ anyons, and ${\chi }_{XXX}^{(3)}$ that involves the trivial braiding of the same types of anyons, serves to distinguish the braiding statistics of anyons. We support our analysis by constructing a hard-core anyon model with statistical gauge fields to develop further insights into the time dependence of the pump-probe response. Pump-probe spectroscopy provides a distinctive new probe of quantum spin liquid states, beyond the inconclusive broad features observed in single spin flip inelastic neutron scattering.

17 pages, 11 figures. References updated; discussion in "Time Scales" section expanded

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Cited by in corpus (1)

• Tunable anyonic permeability across ${\mathbb{Z}}_2$ spin liquid junctions