Symmetry-respecting real-space renormalization for the quantum Ashkin-Teller model

Abstract

We use a simple real-space renormalization group approach to investigate the critical behavior of the quantum Ashkin-Teller model, a one-dimensional quantum spin chain possessing a line of criticality along which critical exponents vary continuously. This approach, which is based on exploiting the on-site symmetry of the model, has been shown to be surprisingly accurate for predicting some aspects of the critical behavior of the quantum transverse-field Ising model. Our investigation explores this approach in more generality, in a model where the critical behavior has a richer structure but which reduces to the simpler Ising case at a special point. We demonstrate that the correlation length critical exponent as predicted from this real-space renormalization group approach is in broad agreement with the corresponding results from conformal field theory along the line of criticality. Near the Ising special point, the error in the estimated critical exponent from this simple method is comparable to that of numerically-intensive simulations based on much more sophisticated methods, although the accuracy decreases away from the decoupled Ising model point.

Kibble-Zurek exponent and chiral transition of the period-4 phase of Rydberg chains

“…We compare the values of λ and ν obtained to fit the hard-boson model with the conformal field theory result of Kohmoto et al 28,29 in Fig. 9b.…”

“…The dark blue line shows the exact result of refs. 28 , 29 . The open red circle is the numerical result of this work ν ≃ 0.777 (result for N = 3001 shown in panel a , finite-size error do not exceed ±0.02) and λ ≃ 0.57 ± 0.01 as shown in Fig.…”

“…b Critical exponent ν as a function of the Ashkin-Teller asymmetry parameter λ. The dark blue line shows the exact result of refs 28,29. .…”

“…if , irrelevant otherwise. Now, the exponent ν is known exactly as a function of λ 28 , 29 : At λ = 0, the model is known as the four-state clock model and corresponds to two decoupled transverse-field Ising chains. In that case, ν = 1: The chiral perturbation is relevant, and it is known to drive the system immediately into a critical phase.…”

“…if ν > ν c ¼ ð1 þ ffiffi ffi 3 p Þ=4 ' 0:683, irrelevant otherwise. Now, the exponent ν is known exactly as a function of λ 28,29 :…”