First-Principles Studies Of Quantum Critical Dynamics

Quantum phase transitions (at zero temperature) control the physics over a wide parameter regime in the finite temperature phase diagram, and are important for explain-ing a wide variety of experimental systems. Continuous quantum phase transitions are quite common and particularly more interesting, since they are typically in critical states and exhibit novel critical phenomena. Their most striking feature is universal static and dynamic properties, which is a direct consequence of the emergent long-wave-length scale invariance not only in space but also in time. In this thesis, we study the universal linear response dynamics of quantum critical system. We focus on the two dimensional superfluid-Mott insulator quantum phase transition, which is described by the (2+1) dimensional XY universality class with Lorentz invariance. We employ unbiased quan-tum Monte Carlo calculations to measure the correlation functions in the imaginary time. then use numerical analytic continuation methods to extract the real frequency response functions. We calculate the kinetic energy spectral density in the vicinity of quantum critical point. From the calculation we find that when approaching the quantum criti-cal point from the superfluid side, there’s critically defined resonance structure in the spectral density. The resonance can be interpreted as a damped Higgs mode(Massive Goldstone mode). Similar resonance signals are also found in the Mott-insulator side and even in the normal liquid phase, but the physical meaning behind those signals re-quires further study. Furthermore, we use first principle approach to explore the Higgs mode in ultracold atoms in optical lattices. Our numerical calculations enable a di-rect comparison with a recent experiment and demonstrate a good agreement. Based on our numerical analysis, we formulate the necessary conditions to reveal the Higgs resonance peak experimentally. Another aspect of quantum critical dynamics is the universal transport physics. We calculate the universal AC conductivity in the quantum critical region. For the first time, the shape of the conductivity curve in the Matsubara representation is accurate enough to establish the particle-like nature of charge trans-port, and for a conclusive comparison with a holographic gauge-gravity duality theory. We find that the holographic theory for transport properties can be made compatible with the data if temperature of the horizon of the black brane is different from the tem-perature of the conformal field theory. The requirements for measuring the universal conductivity in a ultracold gas experiment are also determined by our calculation.