Theory of smeared quantum phase transitions

TL;DR

This paper develops an analytical strong-disorder renormalization group theory for the dissipative random transverse-field Ising chain, revealing how Ohmic dissipation smears the quantum critical point and detailing the phase diagram and observable behaviors.

Contribution

It provides the first analytical solution for the renormalization flow equations in this context, demonstrating the destruction of the quantum critical point by dissipation.

Findings

Ohmic dissipation destroys the quantum critical point.

Analytical solutions for low-temperature properties are obtained.

The phase diagram near the smeared transition is characterized.

Abstract

We present an analytical strong-disorder renormalization group theory of the quantum phase transition in the dissipative random transverse-field Ising chain. For Ohmic dissipation, we solve the renormalization flow equations analytically, yielding asymptotically exact results for the low-temperature properties of the system. We find that the interplay between quantum fluctuations and Ohmic dissipation destroys the quantum critical point by smearing. We also determine the phase diagram and the behavior of observables in the vicinity of the smeared quantum phase transition.