Ashkin-Teller Chain Research Articles

Critical properties of the quantum Ashkin-Teller chain with chiral perturbations

Critical properties of the quantum Ashkin-Teller chain with chiral perturbations

Monte Carlo simulations of the disordered three-color quantum Ashkin-Teller chain

We investigate the zero-temperature quantum phase transitions of the disordered three-color quantum Ashkin-Teller spin chain by means of large-scale Monte Carlo simulations. We find that the first-order phase transitions of the clean system are rounded by the quenched disorder. For weak inter-color coupling, the resulting emergent quantum critical point between the paramagnetic phase and the magnetically ordered Baxter phase is of infinite-randomness type and belongs to the universality class of the random transverse-field Ising model, as predicted by recent strong-disorder renormalization group calculations. We also find evidence for unconventional critical behavior in the case of strong inter-color coupling, even though an unequivocal determination of the universality class is beyond our numerical capabilities. We compare our results to earlier simulations, and we discuss implications for the classification of phase transitions in the presence of disorder.

Numerical evidence of the double-Griffiths phase of the random quantum Ashkin-Teller chain

The random quantum Ashkin-Teller chain is studied numerically by means of time-dependent Density-Matrix Renormalization Group. The critical lines are estimated as the location of the peaks of the integrated autocorrelation times, computed from spin-spin and polarization-polarization autocorrelation functions. Disorder fluctuations of magnetization and polarization are observed to be maximum on these critical lines. Entanglement entropy leads to the same phase diagram, though with larger Finite-Size effects. The decay of spin-spin and polarization-polarization autocorrelation functions provides numerical evidence of the existence of a double Griffiths phase when taking into account finite-size effects. The two associated dynamical exponents z increase rapidly as the critical lines are approached, in agreement with the recent conjecture of a divergence at the two transitions in the thermodynamic limit.

Universal behavior of the Shannon and Rényi mutual information of quantum critical chains

We study the Shannon and R\'enyi mutual information (MI) in the ground state (GS) of different critical quantum spin chains. Despite the apparent basis dependence of these quantities we show the existence of some particular basis (we will call them conformal basis) whose finite-size scaling function is related to the central charge $c$ of the underlying conformal field theory of the model. In particular, we verified that for large index $n$, the MI of a subsystem of size $\ensuremath{\ell}$ in a periodic chain with $L$ sites behaves as $\frac{c}{4}\frac{n}{n\ensuremath{-}1}ln[\frac{L}{\ensuremath{\pi}}sin(\frac{\ensuremath{\pi}\ensuremath{\ell}}{L})]$, when the ground-state wave function is expressed in these special conformal basis. This is in agreement with recent predictions. For generic local basis, we will show that, although in some cases ${b}_{n}ln[\frac{L}{\ensuremath{\pi}}sin(\frac{\ensuremath{\pi}\ensuremath{\ell}}{L})]$ is a good fit to our numerical data, in general, there is no direct relation between ${b}_{n}$ and the central charge of the system. We will support our findings with detailed numerical calculations for the transverse field Ising model, $Q=3,4$ quantum Potts chain, quantum Ashkin-Teller chain, and the XXZ quantum chain. We will also present some additional results of the Shannon mutual information ($n=1$), for the parafermionic ${Z}_{Q}$ quantum chains with $Q=5,6,7$, and 8.

Quantum Ashkin-Teller model near the decoupling limit

The critical properties and the spectrum of the quantum Ashkin-Teller chain are investigated by perturbation expansion around the exactly soluble Ising decoupling limit. The critical exponents are found to satisfy the hyperscaling relation and they are consistent with the conjectured values. The critical Hamiltonian in the finite-size scaling limit is transformed into a two-band spin-1/2 Fermi system, where the interaction energy in first order is the product of the band magnetizations. The complete spectrum is shown to exhibit a conformal structure with infinite primary operators, the anomalous dimensions of which are consistent with a Gaussian form.

Conformal invariance and the spectrum of the quantum Ashkin-Teller chain near the decoupling point

The complete spectrum of the critical quantum Ashkin-Teller chain is solved exactly in the finite size scaling limit near the Ising decoupling point. The model is transformed into two spin 1 2 fermion systems, where the interaction energy in first order is proportional to the product of the subsystem magnetizations. The spectrum of the model consists of infinitely many conformal towers, and the anomalous dimensions of the different operators are consistent with the Gaussian form.

Superconformal invariance in the Ashkin-Teller quantum chain with free boundary conditions

The finite-size limit of the lower part of the spectrum of the Ashkin-Teller chain with free boundary conditions is studied numerically and interpreted from the point of view of conformal invariance. Several irreducible representations of the Virasoro algebra with the central charge c=1 are identified. For two special values of the coupling constant, higher degeneracies occur and the whole spectrum can be understood in terms of a few irreducible representations of the N=2 superconformal algebra.