Theory of Smeared Quantum Phase Transitions

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.

Figure 1

Zero-temperature phase diagram and magnetization of the dissipative random transverse-field Ising chain as a function of the typical transverse field $h_{\mathrm{typ}}$. SO and SD denote the strongly ordered and disordered conventional phases; WO and WD are the weakly ordered and disordered quantum Griffiths phases. (a) No dissipation: sharp QCP. (b) Ohmic dissipation: smeared transition with the inhomogeneously ordered (IO) phase replacing the WD Griffiths phase. (c) Distributions of the bonds $J$ and fields $h_{\mathrm{eff}}$ in the various phases. The shaded area quantifies the fraction $w$ of $J$’s bigger than $h_{\mathrm{eff}}$’s [see Eq. (10)].