Strong-randomness phenomena in quantum Ashkin-Teller models

Abstract

The $N$-color quantum Ashkin-Teller spin chain is a prototypical model for the study of strong-randomness phenomena at first-order and continuous quantum phase transitions. In this paper, we first review the existing strong-disorder renormalization group approaches to the random quantum Ashkin-Teller chain in the weak-coupling as well as the strong-coupling regimes. We then introduce a novel general variable transformation that unifies the treatment of the strong-coupling regime. This allows us to determine the phase diagram for all color numbers $N$, and the critical behavior for all $N\ne 4$. In the case of two colors, $N=2$, a partially ordered product phase separates the paramagnetic and ferromagnetic phases in the strong-coupling regime. This phase is absent for all $N>2$, i.e., there is a direct phase boundary between the paramagnetic and ferromagnetic phases. In agreement with the quantum version of the Aizenman-Wehr theorem, all phase transitions are continuous, even if their clean counterparts are of first order. We also discuss the various critical and multicritical points. They are all of infinite-randomness type, but depending on the coupling strength, they belong to different universality classes.

8 pages, 2 eps figures included, final version as published, unifies and further develops the theories of arXiv:1208.0471 and arXiv:1310.4864

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• Activated scaling in disorder rounded first-order quantum phase transitions
• Monte Carlo simulations of the disordered three-color quantum Ashkin-Teller chain
• Numerical evidence of a super-universality of the 2D and 3D random quantum Potts models
• Numerical evidences of a universal critical behavior of 2D and 3D random quantum clock and Potts models
• Emerging critical behavior at a first-order phase transition rounded by disorder
• Emergent universal critical behavior of the 2D $N$-color Ashkin-Teller model in the presence of correlated disorder