Dynamics at and near conformal quantum critical points

TL;DR

This paper investigates the dynamical properties of conformal quantum critical points in two-dimensional systems, revealing their instability under perturbations and how their dynamical exponents vary across different models.

Contribution

It demonstrates the instability of CQCPs under generic perturbations and characterizes their dynamical exponents through numerical studies of coupled models.

Findings

CQCPs are generally unstable and flow to the 2D Ising critical point.

The dynamical critical exponent z is 2 along the quantum Lifshitz line.

z varies continuously along the Z_2 symmetric line.

Abstract

We explore the dynamical behavior at and near a special class of two-dimensional quantum critical points. Each is a conformal quantum critical point (CQCP), where in the scaling limit the equal-time correlators are those of a two-dimensional conformal field theory. The critical theories include the square-lattice quantum dimer model, the quantum Lifshitz theory, and a deformed toric code model. We show that under generic perturbation the latter flows toward the ordinary Lorentz-invariant (2+1) dimensional Ising critical point, illustrating that CQCPs are generically unstable. We exploit a correspondence between the classical and quantum dynamical behavior in such systems to perform an extensive numerical study of two lines of CQCPs in a quantum eight-vertex model, or equivalently, two coupled deformed toric codes. We find that the dynamical critical exponent z remains 2 along the U(1)-symmetric quantum Lifshitz line, while it continuously varies along the line with only Z_2 symmetry. This illustrates how two CQCPs can have very different dynamical properties, despite identical equal-time ground-state correlators. Our results equally apply to the dynamics of the corresponding purely classical models.