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

Udupa, A and Sur, S and Nandy, S and Sen, A and Sen, D (2023) Weak universality, quantum many-body scars, and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality. In: Physical Review B, 108 (21).

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Official URL: https://doi.org/10.1103/PhysRevB.108.214430


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 Z2�Z2 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, β, γ, and ν, 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 β/ν, γ/ν, and ν 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�1 or h�1. If h is close to the critical point, the autocorrelators decay quickly to zero except for an autocorrelator at the end site. © 2023 American Physical Society.

Item Type: Journal Article
Publication: Physical Review B
Publisher: American Physical Society
Additional Information: The copyright for this article belongs to Author.
Keywords: Autocorrelation; Boundary conditions; Criticality (nuclear fission); Ising model; Quantum entanglement; Statistical mechanics, Auto correlation; Autocorrelators; Exact diagonalization; Four-state Potts model; Many body; One-dimensional; Periodic boundary conditions; Self-dual; Spin models; System size, Wave functions
Department/Centre: Others
Date Deposited: 01 Mar 2024 09:56
Last Modified: 01 Mar 2024 09:56
URI: https://eprints.iisc.ac.in/id/eprint/84020

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