Fractionalized conductivity and emergent self-duality near topological phase transitions

Abstract

The experimental discovery of the fractional Hall conductivity in two-dimensional electron gases revealed new types of quantum particles, called anyons, which are beyond bosons and fermions as they possess fractionalized exchange statistics. These anyons are usually studied deep inside an insulating topological phase. It is natural to ask whether such fractionalization can be detected more broadly, say near a phase transition from a conventional to a topological phase. To answer this question, we study a strongly correlated quantum phase transition between a topological state, called a ${\mathbb{Z}}_2$ quantum spin liquid, and a conventional superfluid using large-scale quantum Monte Carlo simulations. Our results show that the universal conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulator-to-superfluid transition. Moreover, a dynamically self-dual optical conductivity emerges at low temperatures above the transition point, indicating the presence of the elusive vison particles. Our study opens the door for the experimental detection of anyons in a broader regime, and has ramifications in the study of quantum materials, programmable quantum simulators, and ultra-cold atomic gases. In the latter case, we discuss the feasibility of measurements in optical lattices using current techniques.

9+4 pages, 4+3 figures. v3: New results regarding emergent dynamical self-duality due to visons. New figure of vison-pair spectra. Extended discussion and appendices

References in corpus (11)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Quantum critical transport, duality, and M-theory
• Quantum phases of Rydberg atoms on a kagome lattice
• Choreographed entangle dances: topological states of quantum matter
• Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography
• The quasi-normal modes of quantum criticality
• Spin liquid phase in a $S=1/2$ quantum magnet on the kagome lattice
• Amplitude Mode in Quantum Magnets via Dimensional Crossover
• Critical capacitance and charge-vortex duality near the superfluid to insulator transition
• Correlation holes and slow dynamics induced by fractional statistics in gapped quantum spin liquids
• Nonlinear coupling of reversed shear Alfven eigenmode and toroidal Alfven eigenmode during current ramp

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