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arXiv:2307.11161 · Physical review. B./Physical review. B

Weak universality, quantum many-body scars, and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality

Adithi Udupa, Samudra Sur, Sourav Nandy, Arnab Sen, Diptiman Sen

Published Dec 26, 2023• 18 citations
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Abstract

We study a one-dimensional spin-$1/2$ model with three-spin interactions and a transverse magnetic field $h$. The model is known to have a ${Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ symmetry and a duality between $h$ and $1/h$. The self-dual point at $h=1$ is a quantum critical point with a continuous phase transition. We compute the critical exponents $z, \ensuremath{\beta}, \ensuremath{\gamma}$, and $\ensuremath{\nu}$, and the central charge $c$ numerically using exact diagonalization (ED) for systems with periodic boundary conditions. We find that both $z$ and $c$ are equal to 1, implying that the critical point is governed by a conformal field theory with a marginal operator. The values obtained for $\ensuremath{\beta}/\ensuremath{\nu}, \ensuremath{\gamma}/\ensuremath{\nu}$, and $\ensuremath{\nu}$ from ED suggest that the model exhibits Ashkin-Teller criticality with an effective coupling that is intermediate between the four-state Potts model and two decoupled transverse field Ising models. A more careful analysis on much larger systems but with open boundaries using density-matrix renormalization group (DMRG) calculations, however, reveals important additive and multiplicative logarithmic corrections at and near criticality, and we present evidence that the self-dual point may be in the same universality class as the four-state Potts model. An energy level spacing analysis shows that the model is not integrable. For a system with an even number of sites and periodic boundary conditions, there are exact mid-spectrum zero-energy eigenstates whose number grows exponentially with the system size. A subset of these eigenstates have wave functions that are independent of the value of $h$ and have unusual entanglement structures; hence these can be considered to be quantum many-body scars. The number of such quantum scars scales at least linearly with system size. Finally, we study the infinite-temperature autocorrelation functions at sites close to one end of an open system. We find that some of the autocorrelators relax anomalously in time, with pronounced oscillations and very small decay rates if $h\ensuremath{\gg}1$ or $h\ensuremath{\ll}1$. If $h$ is close to the critical point, the autocorrelators decay quickly to zero except for an autocorrelator at the end site.

DOI
10.1103/physrevb.108.214430

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The qqq-state Potts chain with ferromagnetic couplings, J=1J=1J=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>4q>4q>4. Here we introduce a qqq-periodic alternating longitudinal field of strength hhh 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=0T=0T=0. We considered the q=3q=3q=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 $h<q/(q\ensuremath{-}1)$.
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