Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models

Iyoda, Eiki; Katsura, Hosho; Sagawa, Takahiro

doi:10.1103/physrevd.98.086020

Cited by 22 publications

(29 citation statements)

References 72 publications

(109 reference statements)

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“…At spin-1/2, this coincides with the Hamiltonian obtained in Ref. 45 or the "Wishart-SYK" model [58], and can consequently be derived as a special case of the integrable spin-1/2 Hamiltonians considered in the recent work Ref. 46.…”

Section: Integrability At ∆ = 0 and ∆ =supporting

confidence: 79%

Integrable and Chaotic Dynamics of Spins Coupled to an Optical Cavity

et al. 2019

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We show that a class of random all-to-all spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram due to the pairwise separable nature of the couplings. By controlling the experimental parameters, one can tune between integrable and chaotic dynamics on the one hand, and between classical and quantum regimes on the other hand. For two special values of a spin-anisotropy parameter, the model exhibits rational-Gaudin type integrability and it is characterized by an extensive set of spin-bilinear integrals of motion, independent of the spin size. More generically, we find a novel integrable structure with conserved charges that are not purely bilinear. Instead, they develop "dressing tails" of higher-body terms, reminiscent of the dressed local integrals of motion found in Many-Body Localized phases. Surprisingly, this new type of integrable dynamics found in finite-size spin-1/2 systems disappears in the large-S limit, giving way to classical chaos. We identify parameter regimes for characterizing these different dynamical behaviors in realistic experiments, in view of the limitations set by cavity dissipation. arXiv:1904.10966v3 [cond-mat.stat-mech]

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Section: Integrability At ∆ = 0 and ∆ =supporting

confidence: 79%

Integrable and Chaotic Dynamics of Spins Coupled to an Optical Cavity

et al. 2019

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“…One may also develop approaches analogous to ours for the so-called complex SYK model [1,27,82]. This model has ordinary (i.e., complex), instead of Majorana (real) fermions, and may be viewed as arising at the end of a one-dimensional system that admits a Z 4 topological classification.…”

Section: Discussionmentioning

confidence: 99%

Tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model

2019

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The Sachdev-Ye-Kitaev (SYK) model, in its simplest form, describes k Majorana fermions with random all-to-all four-body interactions. We consider the SYK model in the framework of a manybody Altland-Zirnbauer classification that sees the system as belonging to one of eight (real) symmetry classes depending on the value of k mod 8. We show that, depending on the symmetry class, the system may support exact many-body zero modes with the symmetries also dictating whether these may have a nonzero contribution to Majorana fermions, i.e., single-particle weight. These zero modes appear in all but two of the symmetry classes. When present, they leave clear signatures in physical observables that go beyond the threefold (Wigner-Dyson) possibilities for level spacing statistics studied earlier. Signatures we discover include a zero-energy peak or hole in the single-particle spectral function, depending on whether symmetries allow or forbid zero modes to have single-particle weight. The zero modes are also shown to influence the many-body dynamics, where signatures include a nonzero long-time limit for the out-of-time-order correlation function. Furthermore, we show that the extension of the four-body SYK model by quadratic terms can be interpreted as realizing the remaining two complex symmetry classes; we thus demonstrate how the entire tenfold Altland-Zirnbauer classification may emerge in the SYK model.

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“…Above, G ± ≡ G ± (0) = L i=1 g i S ± i , and (1/2 ± S z 0 ) projects the central spin along the z direction. Hamiltonians of the form G ± G ∓ arise in the study of topological superconductivity and superfluidity [51][52][53], neutron pairing [54], and Sachdev-Ye-Kitaev-like models [55]. These are Richardson-Gaudin integrable, and all results for their eigenstates and conserved charges can be found in, e.g., Refs.…”

mentioning

confidence: 99%

“…These are Richardson-Gaudin integrable, and all results for their eigenstates and conserved charges can be found in, e.g., Refs. [24,25,38,[55][56][57][58].…”

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confidence: 99%

Integrability and dark states in an anisotropic central spin model

Villazon

Chandran

Claeys

2020

Phys. Rev. Research

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Central spin models describe a variety of quantum systems in which a spin-1 2 qubit interacts with a bath of surrounding spins, as realized in quantum dots and defect centers in diamond. We show that the fully anisotropic central spin Hamiltonian with (XX) Heisenberg interactions is integrable. Building on the class of integrable Richardson-Gaudin models, we derive an extensive set of conserved quantities and obtain the exact eigenstates using the Bethe ansatz. These states divide into two exponentially large classes: bright states, where the qubit is entangled with the bath, and dark states, where it is not. We discuss how dark states limit qubit-assisted spin bath polarization and provide a robust long-lived quantum memory for qubit states.

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Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models

Cited by 22 publications

References 72 publications

Integrable and Chaotic Dynamics of Spins Coupled to an Optical Cavity

Integrable and Chaotic Dynamics of Spins Coupled to an Optical Cavity

Tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model

Integrability and dark states in an anisotropic central spin model

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