The Dynamics of Quantum Criticality Revealed by Quantum Monte Carlo and Holography

June 12, 2014
Figure 4: Holographic continuation

Holographic continuation: a, The black points represent Monte Carlo data for the conductivity at the superfluid–insulator QCP at imaginary frequencies. b, Real part of the holographic conductivity evaluated at complex frequencies, where the imaginary/real axis dependence is highlighted by the green/blue line. The arrow represents the continuation procedure. c, Resulting conductivity at real frequencies (solid blue line). The dashed line is the vortex-like response obtained for γ =−0.08. [Figure reprinted by permission from Macmillan Publishers Ltd: W. Witczak-Krempa, E.S. Sørensen, S. Sachdev, "The dynamics of quantum criticality revealed by quantum Monte Carlo and holography," Nature Physics 10, 361–366 (2014) doi:10.1038/nphys2913 ©2014.]

Understanding the dynamics of quantum systems without long-lived excitations (quasiparticles) constitutes an important yet challenging problem. Although numerical techniques can yield results for the dynamics in imaginary time, their reliable continuation to real time has proved difficult. Professor Subir Sachdev and colleagues from Perimeter Institute for Theoretical Physics and McMaster University, Ontario, tackled this issue using the superfluid–insulator quantum critical point of bosons on a two-dimensional lattice, where quantum fluctuations destroy quasiparticles. I a recent article in Nature Physics, the researchers presented quantum Monte Carlo simulations for two separate lattice realizations. Their low-frequency conductivities turned out to have the same universal dependence on imaginary frequency and temperature. Using the structure of the real-time dynamics of conformal field theories described by the holographic gauge/gravity duality, they then made progress on the problem of analytically continuing the numerical data to real time. This method has yielded quantitative and experimentally testable results on the frequency-dependent conductivity near the quantum critical point.