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-pairing states as true scars in an extended Hubbard model

Mark, Daniel K.; Motrunich, Olexei I.

doi:10.1103/physrevb.102.075132

Cited by 102 publications

(74 citation statements)

References 90 publications

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“…Therefore, except a factor around 2, our bound gives the correct log-volume scaling of the EEs of the scar states. Similar results are also obtained for scar states in the extended Fermi-Hubbard model [26,27].…”

Section: Fig 2 Comparison Between the Upper Bound Of The Bipartite Eessupporting

confidence: 85%

Bounding Entanglement Entropy Using Zeros of Local Correlation Matrices

Yao,

Pan,

Liu

et al. 2022

Preprint

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Correlation functions and entanglement are two different aspects to characterize quantum manybody states. While many correlation functions are experimentally accessible, entanglement entropy (EE), the simplest characterization of quantum entanglement, is usually difficult to measure. In this letter, we propose a protocol to bound the subsystem EE by local measurements. This protocol utilizes the local correlation matrix and focuses on its (approximate) zero eigenvalues. Given a quantum state, each (approximate) zero eigenvalue can be used to define a local projection operator. An auxiliary Hamiltonian can then be constructed by summing these projectors. When the construction only involves projectors of zero eigenvalues, we prove the EE of a subsystem is bounded by the ground state degeneracy of the auxiliary Hamiltonian on this subsystem. When projectors of small eigenvalues are included, we show the EE can be bounded by a thermal entropy of the subsystem. Our protocol can be applied experimentally to investigate exotic quantum many-body states prepared in a quantum simulator.

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Section: Fig 2 Comparison Between the Upper Bound Of The Bipartite Eessupporting

confidence: 85%

Bounding Entanglement Entropy Using Zeros of Local Correlation Matrices

Yao,

Pan,

Liu

et al. 2022

Preprint

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“…While breaking the thermalization rendered ergodicity, the QMBS states are distinct from the quantum states in classically integrable systems and from quantum many-body localized states as well [17][18][19][20]. Theoretically, QMBS states have been studied in diverse systems ranging from the Heisenberg spin [21,22], Affleck-Kennedy-Lieb-Tasaki [23,24], extended Hubbard [25][26][27] and Ising [28] models to frustrated [29,30] and topological [31,32] lattices, quantum Hall systems [33,34], Floquet-driven systems [35,36], systems with a flat band [29,37,38], and two-dimensional systems [39]. General theoretical frameworks were developed, in which QMBS states are constructed based on the embedding method [40,41] and quasi-symmetry groups [42].…”

Section: Introductionmentioning

confidence: 99%

Many-body Hilbert space scarring on a superconducting processor

Zhang¹,

Dong²,

Gao³

et al. 2022

Preprint

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Thermalization in complex and strongly interacting quantum many-body systems represents an obstacle to applications. It was recently suggested theoretically that quantum many-body scarring (QMBS) states embedded in the thermalized energy spectrum can overcome this difficulty. Here, by programming a superconducting circuit of two-dimensional multiqubit array with tunable couplings, we experimentally investigate the slow quantum thermalization dynamics associated with QMBS states in the paradigmatic settings of chain and comb tensor topologies, which are effectively described by the unconstrained spin model. Robust QMBS states have been successfully observed in a superconducting circuit of up to 30 qubits with an extraordinarily large Hilbert space for exact diagonalization simulations of classical computers. The QMBS states can be readily distinguished from the conventional thermalized states through the population dynamics, the entanglement entropy, and the fidelity, paving the way to exploiting these states for mitigating quantum thermalization for significant applications in quantum information science and technology.

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“…We mention that the fragmentation of the Hilbert space in the folded XXZ model could be related to the existence of additional non-abelian conservation laws, potentially associated with the emergence of the integrable analogue (cf. Refs [38][39][40]) of quantum many-body scars [15,[41][42][43][44][45].…”

Section: Overview Of the Modelmentioning

confidence: 99%

Measurement catastrophe and ballistic spread of charge density with vanishing current

Zadnik,

Bocini,

Bidzhiev

et al. 2021

Preprint

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One of the features of many-body quantum systems with Hilbert-space fragmentation are stationary states manifesting quantum jamming. It was recently shown that these are "states with memory", in which, e.g., measuring a localised observable has everlasting macroscopic effects. We study such a measurement catastrophe with an example that stands out for its clarity. We show in particular that at late times the expectation value of a charge density becomes a nontrivial function of the ratio between distance and time notwithstanding the corresponding current approaching zero.

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η -pairing states as true scars in an extended Hubbard model

Cited by 102 publications

References 90 publications

Bounding Entanglement Entropy Using Zeros of Local Correlation Matrices

Bounding Entanglement Entropy Using Zeros of Local Correlation Matrices

Many-body Hilbert space scarring on a superconducting processor

Measurement catastrophe and ballistic spread of charge density with vanishing current

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