Ph.D Thesis

Ph.D StudentSnir Gazit
SubjectDynamics near Quantum Criticality in Two Space Dimensions
DepartmentDepartment of Physics
Supervisor Professor Podolsky Daniel
Full Thesis textFull thesis text - English Version


Quantum phase transitions are ubiquitous in condensed matter and cold atomic systems. Some physical systems undergo a zero temperature phase transition between a disordered and a broken symmetry phase, which is tuned by a non-thermal parameter. A remarkable signature of continuous phase transitions, both in classical and in quantum systems, is the emergence of universality. In the quantum case, not only static properties are universal but also dynamical properties. In this thesis we study dynamical aspects of quantum criticality in two space dimensions. Our focus is on systems with relativistic dynamics and O(N) symmetry that is spontaneously broken in the ordered phase. To study the real time dynamics we employ a large scale quantum Monte Carlo simulation combined with numerical analytic continuation. We compute the universal scaling function of two experimentally pertinent response functions: the scalar susceptibility and the optical conductivity. From this analysis we deduce that the amplitude (Higgs) mode is a universal spectral feature that can be probed arbitrarily close to the critical point. Moreover, we characterize the universal properties of the amplitude mode line shape and determine the universal amplitude ratio between the amplitude mode mass and the single particle gap in the disordered phase. In addition, we study the charge-vortex duality at finite frequency near the superfluid to insulator transition. Using a generalized reciprocity relation between charge and vortex conductivities at complex frequencies, we identify the capacitance in the insulating phase as a measure of vortex condensate stiffness. We compute the ratio of boson superfluid stiffness to vortex condensate stiffness for the relativistic O(2) model. The product of dynamical conductivities at mirror points is used as a test of charge-vortex duality. Our predictions motivate future experiments that probe dynamical properties near quantum criticality.