Imaginary-Time Quantum Relaxation Critical Dynamics with Semi-Ordered Initial States

We explore the imaginary-time relaxation dynamics near quantum critical points with semi-ordered initial states. Different from the case with homogeneous ordered initial states, in which the order parameter M decays homogeneously as M proportional to tau (-beta/nu z ), here M depends on the location x, showing rich scaling behaviors. Similar to the classical relaxation dynamics with an initial domain wall in model A, which describes the purely dissipative dynamics, here as the imaginary time evolves, the domain wall expands into an interfacial region with growing size. In the interfacial region, the local order parameter decays as M proportional to tau (-beta/nu z ), with beta (1) being an additional dynamic critical exponent. Far away from the interfacial region the local order parameter decays as M proportional to tau (-beta/nu z ) in the short-time stage, then crosses over to the scaling behavior of M proportional to tau (-beta/nu z ) when the location x is absorbed in the interfacial region. A full scaling form characterizing these scaling properties is developed. The quantum Ising model in both one and two dimensions are taken as examples to verify the scaling theory. In addition, we find that for the quantum Ising model the scaling function is an analytical function and beta (1) is not an independent exponent.

Automated summary

We investigate the relaxation dynamics near quantum critical points with semi-ordered initial states in imaginary time. The behavior differs from that with homogeneous ordered initial states, where the order parameter M decays homogeneously. Instead, M depends on the location x, exhibiting rich scaling behaviors. As the imaginary time evolves, a domain wall expands into an interfacial region, where the local order parameter decays as M proportional to tau (-beta/nu z), with beta (1) as an additional dynamic critical exponent. A full scaling form is developed to characterize these scaling properties, and the quantum Ising model is used as examples to validate the scaling theory.