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arXiv:2306.09127 · Physical review. B./Physical review. B

Quantum Potts chain in alternating field

Péter Lajkó, Wedad Alaaeldin Yehia, Ferenc Iglói

Published Oct 2, 2023• 0 citations
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Abstract

The $q$-state Potts chain with ferromagnetic couplings, $J=1$, in the presence of a transverse field $\mathrm{\ensuremath{\Gamma}}$ has a quantum phase transition at $\mathrm{\ensuremath{\Gamma}}/q=1$, which is continuous for $q\ensuremath{\le}4$ and of first order for $q>4$. Here we introduce a $q$-periodic alternating longitudinal field of strength $h$ and study the phase diagram and the critical properties of the model. For $h<q/(q\ensuremath{-}1)$, there is a ferromagnetic ordered phase, for $\mathrm{\ensuremath{\Gamma}}<{\mathrm{\ensuremath{\Gamma}}}_{c}(h)$, and at $h=q/(q\ensuremath{-}1)$, there is a classical endpoint at $\mathrm{\ensuremath{\Gamma}}=0$, with finite entropy at $T=0$. We considered the $q=3$ model and using density matrix renormalization group techniques, we calculated the low-lying spectrum of the Hamiltonian, the transverse magnetization, and the spin-spin correlation function, all of which signal a diverging correlation length at the transition point with the exponent of the three-state Potts model. In the vicinity of the classical endpoint, the model is mapped to a quantum hard rod model, which also belongs to the universality class of the ferromagnetic three-state Potts model. Also, the spectrum of the critical Hamiltonian is found in agreement with conformal invariance. At the same time, the correlation function shows a jump at the transition point, and thus the transition is of mixed order for $h<q/(q\ensuremath{-}1)$.

DOI
10.1103/physrevb.108.144403

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