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

Abstract

We study a one-dimensional spin-$1/2$ model with three-spin interactions and a transverse magnetic field $h$. The model has a $Z_2\times Z_2$ 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 $z$, $\beta$, $\gamma$ and $\nu$, 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. The values obtained for $\beta /\nu$, $\gamma /\nu$, and $\nu$ 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. An analysis on larger systems but with open boundaries using density-matrix renormalization group calculations, however, shows 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 periodic boundary conditions, there are an exponentially large number of exact mid-spectrum zero-energy eigenstates. A subset of these eigenstates have wave functions which are independent of $h$ and have unusual entanglement structure, suggesting that they are quantum many-body scars. The number of such states scales at least linearly with system size. Finally, we study the infinite-temperature autocorrelation functions 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 $h\gg 1$ or $h\ll 1$. If $h$ is close to the critical point, the autocorrelators decay quickly to zero except for an autocorrelator at the end site.

23 pages, 20 figures; corrected some typos

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• Exact Thermal Eigenstates of Nonintegrable Spin Chains at Infinite Temperature
• Sublattice scars and beyond in two-dimensional $U(1)$ quantum link lattice gauge theories
• Emergent symmetries in prethermal phases of periodically driven quantum systems
• Subspace restricted thermalization in a correlated-hopping model with strong Hilbert space fragmentation characterized by irreducible strings
• Universal Upper Bound on Ergotropy and No-Go Theorem by the Eigenstate Thermalization Hypothesis
• Generalized Kramers-Wannier Duality from Bilinear Phase Map
• Exact volume-law entangled zero-energy eigenstates in a large class of spin models
• Prethermalization in the PXP Model under Continuous Quasiperiodic Driving
• Scar-induced imbalance in staggered Rydberg ladders
• Geometric fragmentation and anomalous thermalization in cubic dimer model
• Symmetric tensor scars with tunable entanglement from volume to area law
• Emergent criticality in a constrained boson model
• Metric response of relative entropy: A universal indicator of quantum criticality
• Stable infinite-temperature eigenstates in SU(2)-symmetric nonintegrable models
• Additional quantum many-body scars of the spin-$1$ $XY$ model with Fock-space cages and commutant algebras