Smeared phase transition in the dissipative random quantum Ashkin-Teller model

TL;DR

The paper investigates how Ohmic dissipation interacts with quenched disorder in the one-dimensional random quantum Ashkin–Teller model. Using a combination of adiabatic renormalization and strong-disorder renormalization group methods, it shows that dissipation smears two of the three quantum phase transitions (PM–PROD and PROD–FM) by freezing dynamics of ferromagnetic rare regions, while the PROD–PM transition remains sharp because the intertwined product order is not generically damped. The analysis relies on product-variable reformulations, RG flow of couplings and dissipation strengths, and careful accounting of how rare-region dynamics couple to the baths. The findings imply that composite (intertwined) orders can evade dissipation-induced smearing, with potential relevance to other systems exhibiting nematic or quadrupolar-like order; the SDRG framework used here is robust to variations in dissipation and couplings and extends to higher dimensions.

Abstract

We study the effects of dissipation in the phase diagram of the random quantum Ashkin-Teller model by means of a generalization of the strong-disorder renormalization group combined with adiabatic renormalization. This model has three phases and three quantum phase transitions. We demonstrate that the combined effect of Ohmic dissipation and quenched disorder smears two out of the three quantum phase transitions. Our analytical theory allows us to understand why one of the phase transitions remains sharp. This is due to a cancellation of the dissipation effects on the nontrivial nature of the intertwined order parameter of one of the phases.

Figures (2)

• Figure 1: (a) Schematic phase diagram of the RQAT chain without dissipation. The dashed lines indicate crossovers from conventional FM, PM and product phases to Griffiths phases. GFM and GPM denote the Griffiths ferromagnetic and paramagnetic phases, respectively. DG corresponds to the double Griffiths phase, characterized by the presence of rare regions in both $\sigma$ and $\eta$ variables. GPROD denotes the Griffiths product phase, where rare regions form in the $\sigma$ variable near the PM transition and in the $\eta$ variable near the FM transition. (b) Schematic phase diagram of the RQAT chain with dissipation. The transitions where rare regions are formed in the original spin variable are smeared. In the strong-coupling regime, the GFM phase is replaced by a weakly ordered (WO) phase and the GPROD phase is replaced by an inhomogeneous ferromagnetic (IFM) phase.
• Figure 2: Decimation procedure when the two largest local energy scales in the system are (a) $g_{2}$ and $K_{2}$, (b) $g_{2}$ and $h_{2}$, and (c) $K_{2}$ and $J_{2}$ [in the main text, these correspond to the decimation cases (ii), (iii) and (iv), respectively]. The couplings to the oscillator baths also renormalized and are not illustrated here.