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 strongrandomness 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 = 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.

Strong-disorder renormalization group for periodically driven systems

“…Interactions within the 0 and π Ising chains flow towards 0 under RG much faster than the other couplings and are therefore irrelevant 89,260 . While interactions also permit Floquet-umklapp termsγ 0 iγ 0 jγ π kγ π l that would couple the critical 0 and π chains at the multicritical point, such terms are also irrelevant, and so can be ignored as long as interactions are relatively weak 72,89,20,233 . While weak interactions are irrelevant at the multicritical point, and very strong interactions are likely to drive thermalization, we leave open the possibility that intermediate interactions might drive the system to a new infinite-randomness critical point in the universality class of the random Ashkin-Teller model 20 .…”

“…Since we expect a renormalized Floquet operator of form e iθ e φÕ , withÕ some operator, we recover e iθ by simply takingÕ → 0, or equivalently γ i → 0 for all i. Thus, 20) where c = ±1 picks the P + or P − branch, respectively. In the limit Ω 1, we can expand this expression and check that it reproduces the energy shift in the static case 192 : Figure 3.6: (a) An exact transformation of each domain wall reveals that we can view the π and 0 puddles as being connected by 2nd order terms (see below for details).…”

Floquet quantum criticality

“…Interactions within the 0 and π Ising chains flow towards 0 under RG much faster than the other couplings and are therefore irrelevant [35,47]. While interactions also permit Floquet-umklapp termsγ 0 iγ 0 jγ π kγ π l that would couple the critical 0 and π chains at the multicritical point, such terms are also irrelevant, and so can be ignored as long as interactions are relatively weak [47,[58][59][60]. While weak interactions are irrelevant at the multicritical point, and very strong interactions are likely to drive thermalization, we leave open the possibility that intermediate interactions might drive the system to a new infiniterandomness critical point in the universality class of the random Ashkin-Teller model [59].…”

Emerging critical behavior at a first‐order phase transition rounded by disorder

“…As a quantum version of the Aizenman-Wehr theorem has been proven [40], the first-order character of the transition in the clean problem must change upon the introduction of disorder. Recent strong-disorder renormalization group approaches predict continuous transitions governed by infinite-randomness critical points in different universality classes, depending on the coupling strength [41][42][43]. Furthermore, in the case of two colors an exotic strong-disorder infinite-coupling phase [44] is predicted to appear for large .…”