Dynamics Near Quantum Criticality in Two Space Dimensions

1. Front Matter

   Pages i-xv

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2. Introduction

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   Pages 1-14

3. Dynamics and Conductivity Near Quantum Criticality

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   Pages 15-34

4. Critical Conductivity and Charge Vortex Duality Near Quantum Criticality

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   Pages 35-52

5. Summary and Outlook

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   Pages 53-54

6. Back Matter

   Pages 55-71

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This work addresses dynamical aspects of quantum criticality in two space dimensions. It probes two energy scales: the amplitude (Higgs) mode, which describes fluctuations of the order parameter amplitude in the broken symmetry phase and the dual vortex superfluid stiffness. The results demonstrate that the amplitude mode can be probed arbitrarily close to criticality in the universal line shape of the scalar susceptibility and the optical conductivity. The hallmark of quantum criticality is the emergence of softening energy scales near the phase transition. In addition, the author employs the charge-vortex duality to show that the capacitance of the Mott insulator near the superfluid to insulator phase transition serves as a probe for the dual vortex superfluid stiffness. The numerical methods employed are described in detail, in particular a worm algorithm for O(N) relativistic models and methods for numerical analytic continuation of quantum Monte Carlo data. The predictions obtained are particularly relevant to recent experiments in cold atomic systems and disordered superconductors.

• Charge-vortex duality
• Higgs mode in condensed matter
• Numerical analytic continuation
• Quantum Criticality in Two Dimensions
• Quantum Monte Carlo Data
• Vortex Condensate Stiffness
• Worm Algorithm

• Physics Department, University of California at Berkeley., Berkeley, USA

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