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arXiv:2304.13624 · Physical review. B./Physical review. B

Quantum many-body scars in spin models with multibody interactions

Kazuyuki Sanada, Yuan Miao, Hosho Katsura

Published Oct 2, 2023• 18 citations
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Abstract

We introduce and study several classes of quantum spin models with multibody interactions that exhibit quantum many-body scars. The models are constructed by two different methods: one exploiting boundary states in integrable spin chains and the other based on a variant of existing methods such as restricted spectrum generating algebras. The first method allows us to construct deformations of the Majumdar-Ghosh and Affleck-Kennedy-Lieb-Tasaki models---prototypes of frustration-free systems. With the second method, we construct a large class of spin-1 models involving scalar spin chirality in both one and two dimensions. Interestingly, in some cases, the models so constructed have towers of scar states of different character. For each example, we show that the scar states behave differently from thermal states by comparing their spectral and dynamical properties with those of other states. We also show that a superposition of the scar states constructed by the second method exhibits perfectly periodic revivals in the dynamics.

DOI
10.1103/physrevb.108.155102

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We introduce and study several classes of quantum spin models with multibody interactions that exhibit quantum many-body scars. The models are constructed by two different methods: one exploiting boundary states in integrable spin chains and the other based on a variant of existing methods such as restricted spectrum generating algebras. The first method allows us to construct deformations of the Majumdar-Ghosh and Affleck-Kennedy-Lieb-Tasaki models---prototypes of frustration-free systems. With the second method, we construct a large class of spin-1 models involving scalar spin chirality in both one and two dimensions. Interestingly, in some cases, the models so constructed have towers of scar states of different character. For each example, we show that the scar states behave differently from thermal states by comparing their spectral and dynamical properties with those of other states. We also show that a superposition of the scar states constructed by the second method exhibits perfectly periodic revivals in the dynamics.
We construct several models with multiple quantum many-body scars (QMBS) using integrable boundary states (IBS). Specifically, we focus on the tilted Néel states, which are parametrized IBS for the spin-1/2 Heisenberg chain, and show that these states can be used to construct a tower of scar states. Our models exhibit periodic revival dynamics, showcasing a characteristic behavior of superpositions of QMBS. Furthermore, the tower of QMBS found in this study possesses a restricted spectrum generating algebra (RSGA) structure, indicating that QMBS are equally spaced in energy. This approach can be extended to two-dimensional models, which can be decomposed into an array of one-dimensional models. In this case, the tilted Néel states again serve as parent states for multiple scar states. These states demonstrate low entanglement entropy, marking them as exact scar states. Notably, their entanglement entropy adheres to the sub-volume law, further solidifying the nonthermal properties of QMBS. Our results provide novel insights into constructing QMBS using IBS, thereby illuminating the connection between QMBS and integrable models.
We propose a class of nonintegrable quantum spin chains that exhibit quantum many-body scars even in the presence of disorder. With the use of the so-called Onsager symmetry, we construct scarred models for arbitrary spin quantum number S. There are two types of scar states, namely, coherent states associated with an Onsager-algebra element and one-magnon scar states. While both of them are highly excited states, they have area-law entanglement and can be written as a matrix product state. Therefore, they explicitly violate the eigenstate thermalization hypothesis. We also investigate the dynamics of the fidelity and entanglement entropy for several initial states. The results clearly show that the scar states are trapped in a perfectly periodic orbit in the Hilbert subspace and never thermalize, whereas other generic states do rapidly. To our knowledge, our model is the first explicit example of disordered quantum many-body scarred models.
The phenomenon of quantum many-body scars has received widespread attention both in theoretical and experimental physics in recent years due to its unique physical properties. In this paper, based on the su(2) algebraic relations, we propose a general method for constructing scar models by combining simple modules. This allows us to investigate many-body scar phenomena in high-spin systems. We numerically verify the thermalization and nonintegrability of this model and demonstrate the dynamical properties of the scar states. We also provide a theoretical analysis of the properties of these scar states. For spin-1 case, we find that our 1D chain model reduces to the famous PXP model [C. J. Turner et al., Phys. Rev. B 98, 155134 (2018)] under special parameter conditions. In addition, due to the continuous tunability of the parameters, our model also enables us to investigate the transitions of quantum many-body scar phenomena from nonintegrable to integrable system.
Quantum many-body scars are highly excited eigenstates of non-integrable Hamiltonians which violate the eigenstate thermalization hypothesis and are embedded in a sea of thermal eigenstates. We provide a general mechanism to construct partially integrable models with arbitrarily large local Hilbert space dimensions, which host exact many-body scars. We introduce designed integrability-breaking terms to several exactly solvable spin chains, whose integrable Hamiltonians are composed of the generators of the Temperley-Lieb algebra. In the non-integrable subspace of these models, we identify a special kind of product states -- the generalized spin helix states as exact quantum many-body scars, which lie in the common null space of the non-Hermitian generators of the Temperley-Lieb algebra and are annihilated by the integrability-breaking terms. Our constructions establish an intriguing connection between integrability and quantum many-body scars, meanwhile provide a systematic understanding of scarred Hamiltonians from the perspective of non-Hermitian projectors.
The discovery of quantum many-body scars (QMBS) both in Rydberg atom simulators and in the Affleck-Kennedy-Lieb-Tasaki spin-1 chain model, have shown that a weak violation of ergodicity can still lead to rich experimental and theoretical physics. In this review, we provide a pedagogical introduction to and an overview of the exact results on weak ergodicity breaking via QMBS in isolated quantum systems with the help of simple examples such as the fermionic Hubbard model. We also discuss various mechanisms and unifying formalisms that have been proposed to encompass the plethora of systems exhibiting QMBS. We cover examples of equally-spaced towers that lead to exact revivals for particular initial states, as well as isolated examples of QMBS. Finally, we review Hilbert space fragmentation, a related phenomenon where systems exhibit a richer variety of ergodic and non-ergodic behaviors, and discuss its connections to QMBS.
We discover a variety of exact quantum many-body scars in higher-spin kinetically constrained models through the recently developed DMRG-S algorithm [Zhang et al., Phys. Rev. Lett. 131, 020402 (2023)]. Specifically, for the higher-spin PXP model on arbitrary bipartite lattices of any spatial dimension, we find exact many-body scars that are equidistantly spaced in the energy spectrum and exhibit similar structures to the ground state of the Affleck-Kennedy-Lieb-Tasaki model. For the one-dimensional Fermi-Hubbard model with a tilted potential in a certain parameter regime, whose effective model is equivalent to a kinetically constrained spin model with four degrees of freedom on each site, we find several many-body scars at energy E=0E=0E=0 and $E=\ifmmode\pm\else\textpm\fi{}\sqrt{2}$ that can be exactly represented as matrix product states with finite bond dimensions. Our results demonstrate that larger local degrees of freedom in the kinetically constrained models provide a much broader space for the emergence of quantum many-body scars and weak ergodicity breaking.