Universal conductivity in a two-dimensional superfluid-to-insulator quantum critical system

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory
• String Theory

Background:

• The (2+1)-dimensional XY universality class describes superfluid-to-Mott insulator transitions.
• AdS/CFT correspondence offers a framework to test quantum critical phenomena.

Purpose of the Study:

• To compute the universal conductivity of the (2+1)-dimensional XY universality class.
• To test the holographic gauge-gravity duality by comparing simulation data with theoretical predictions.
• To determine experimental requirements for measuring universal conductivity in cold gas systems.

Main Methods:

• Large-scale Monte Carlo simulations of the classical (2+1)-dimensional J-current model.
• Simulations of the two-dimensional Bose-Hubbard model.
• Analysis of the conductivity in the Matsubara representation.

Main Results:

• Precise determination of the universal conductivity on the quantum critical plateau: σ(∞) = 0.359(4)σQ.
• The calculated conductivity curve is accurate enough for conclusive comparison with holographic models.
• Evidence for particle-like charge transport established.
• Compatibility of holographic gauge-gravity duality with data achieved when black brane horizon temperature differs from CFT temperature.

Conclusions:

• The study provides a precise value for universal conductivity, crucial for testing quantum critical theories.
• Findings support the particle-like nature of charge transport in this system.
• The research bridges theoretical models (AdS/CFT) with experimental possibilities in cold atom systems.