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تسجيل مستخدم جديدWeak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 XY Magnets
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We study the spin-1 XY model on a hypercubic lattice in $d$ dimensions and show that this well-known nonintegrable model hosts an extensive set of anomalous finite-energy-density eigenstates with remarkable properties. Namely, they exhibit subextensive entanglement entropy and spatiotemporal long-range order, both believed to be impossible in typical highly excited eigenstates of nonintegrable quantum many-body systems. While generic initial states are expected to thermalize, we show analytically that the eigenstates we construct lead to weak ergodicity breaking in the form of persistent oscillations of local observables following certain quantum quenches--in other words, these eigenstates provide an archetypal example of so-called quantum many-body scars. This work opens the door to the analytical study of the microscopic origin, dynamical signatures, and stability of such phenomena.
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Recent discovery of persistent revivals in quantum simulators based on Rydberg atoms have pointed to the existence of a new type of dynamical behavior that challenged the conventional paradigms of integrability and thermalization. This novel collecti
ve effect has been named quantum many-body scars by analogy with weak ergodicity breaking of a single particle inside a stadium billiard. In this overview, we provide a pedagogical introduction to quantum many-body scars and highlight the newly emerged connections with the semiclassical quantization of many-body systems. We discuss the relation between scars and more general routes towards weak violations of ergodicity due to embedded algebras and non-thermal eigenstates, and highlight possible applications of scars in quantum technology.
We study a kinetically constrained pair hopping model that arises within a Landau level in the quantum Hall effect. At filling $ u = 1/3$, the model exactly maps onto the so-called PXP model, a constrained model for the Rydberg atom chain that is num
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The discovery of Quantum Many-Body Scars (QMBS) both in Rydberg atom simulators and in the Affleck-Kennedy-Lieb-Tasaki (AKLT) spin-1 chain model, have shown that a weak violation of ergodicity can still lead to rich experimental and theoretical physi
cs. 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 revisit the $eta$-pairing states in Hubbard models and explore their connections to quantum many-body scars to discover a universal scars mechanism. $eta$-pairing occurs due to an algebraic structure known as a Spectrum Generating Algebra (SGA), g
iving rise to equally spaced towers of eigenstates in the spectrum. We generalize the original $eta$-pairing construction and show that several Hubbard-like models on arbitrary graphs exhibit SGAs, including ones with disorder and spin-orbit coupling. We further define a Restricted Spectrum Generating Algebra (RSGA) and give examples of perturbations to the Hubbard-like models that preserve an equally spaced tower of the original model as eigenstates. The states of the surviving tower exhibit a sub-thermal entanglement entropy, and we analytically obtain parameter regimes for which they lie in the bulk of the spectrum, showing that they are exact quantum many-body scars. The RSGA framework also explains the equally spaced towers of eigenstates in several well-known models of quantum scars, including the AKLT model.
In this letter, we study the PXP Hamiltonian with an external magnetic field that exhibits both quantum scar states and quantum criticality. It is known that this model hosts a series of quantum many-body scar states violating quantum thermalization
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