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 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.

8 pages, 5 figures, comments welcome; v2 fixed an error in the analytic expression against which we compare our numerical results, added new references; v3 published version

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• Tensor network states and algorithms in the presence of a global U(1) symmetry
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Cited by in corpus (10)

• Kibble-Zurek exponent and chiral transition of the period-4 phase of Rydberg chains
• Anomalies and entanglement renormalization
• Weak universality, quantum many-body scars and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality
• Tunable quantum criticality in multicomponent Rydberg arrays
• Strong and weak symmetries and their spontaneous symmetry breaking in mixed states emerging from the quantum Ising model under multiple decoherence
• Critical properties of the quantum Ashkin-Teller chain with chiral perturbations
• Spontaneous breaking of finite group symmetries at all temperatures
• Probing universal critical scaling with scan-DMRG
• Stacked quantum Ising systems and quantum Ashkin-Teller model
• Emergent criticality in a constrained boson model