Onsager’s Scars in Disordered Spin Chains

Shibata, Naoyuki; Yoshioka, Nobuyuki; Katsura, Hosho

doi:10.1103/physrevlett.124.180604

Cited by 138 publications

(86 citation statements)

References 48 publications

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“…A nonthermalizing oscillation of domain-wall density, which seems to be related to exact scar eigenstates [10], has been observed. A number of recent studies have found the existence of exact scar eigenstates also in other spin models [11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 97%

Exact Floquet quantum many-body scars under Rydberg blockade

Mizuta

Takasan

Kawakami

2020

Phys. Rev. Research

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Quantum many-body scars have attracted much interest as a violation of the eigenstate thermalization hypothesis (ETH) due to recent experimental observation in Rydberg atoms and related theoretical studies. In this paper, we construct a model hosting exact Floquet quantum many-body scars, which violate the Floquet version of ETH. We consider two uniformly driven static Hamiltonians prohibiting neighboring up spins (Rydberg blockade) like the PXP model, and construct a binary drive composed of them. We show that there exists a four-dimensional subspace which completely avoids thermalization to infinite temperature and that any other states, including some special scar states reported in the static PXP model, are vulnerable to heating and relax to infinite temperature. We also construct a more generalized periodic drive composed of time-dependent PXP-type Hamiltonians showing exact Floquet quantum many-body scars and discuss possible experimental realization of the model in Rydberg atoms.

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Section: Introductionmentioning

confidence: 97%

Exact Floquet quantum many-body scars under Rydberg blockade

Mizuta

Takasan

Kawakami

2020

Phys. Rev. Research

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“…Conversely, there are nonintegrable systems with exactly known scar states, such as the Affleck-Kennedy-Lieb-Tasaki (AKLT) model [28][29][30], the spin-1 XY model [31,32], and a spin-1/2 domain-wall-conserving model [33,34], among others [35][36][37][38][39][40][41][42][43], including a framework to make target states as scars in nonintegrable models [35,36]; there is also a growing number of examples of scars in the Floquet setting [41,[44][45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

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

2020

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The η-pairing states are a set of exactly known eigenstates of the Hubbard model on hypercubic lattices, first discovered by Yang [C. N. Yang, Phys. Rev. Lett. 63, 2144 (1989)]. These states are not many-body scar states in the Hubbard model because they occupy unique symmetry sectors defined by the so-called η-pairing SU(2) symmetry. We study an extended Hubbard model with bond-charge interactions, popularized by Hirsch [J. E. Hirsch, Physica C 158, 326 (1989)], where the η-pairing states survive without the η-pairing symmetry and become true scar states. We also discuss similarities between the η-pairing states and exact scar towers in the spin-1 XY model found by Schecter and Iadecola [M. Schecter and T. Iadecola, Phys. Rev. Lett. 123, 147201 (2019)], and systematically arrive at all nearest-neighbor terms that preserve such scar towers in one dimension. We also generalize these terms to arbitrary bipartite lattices. Our study of the spin-1 XY model also leads us to several scarred models, including a spin-1/2 J 1 − J 2 model with Dzyaloshinskii-Moriya interaction, in realistic quantum magnet settings in one and two dimensions.

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“…(1) presents a heuristic for producing models with scar towers. We note that a very recent paper [45] does a subcase of this with their operator Q + being essentially a symmetry of a base Hamiltonian, atop which they add perturbations that annihilate a tower of scar states. In Sec.…”

Section: Discussionmentioning

confidence: 99%

“…In contrast, there are nonintegrable systems with exactly known scar states [36][37][38][39][40][41][42][43][44][45]. In particular, several models are known to host "towers" of exact scar states, where the scar states are known analytically and are equally spaced in energy.…”

Section: Introductionmentioning

confidence: 99%

Unified structure for exact towers of scar states in the Affleck-Kennedy-Lieb-Tasaki and other models

2020

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Quantum many-body scar states are many-body states with finite energy density in non-integrable models that do not obey the eigenstate thermalization hypothesis. Recent works have revealed "towers" of scar states that are exactly known and are equally spaced in energy, specifically in the AKLT and spin-1 XY models, and a spin-1/2 model that conserves the number of domain walls. We provide a common framework to understand and prove known exact towers of scars in these systems, by evaluating the commutator of the Hamiltonian and a ladder operator. In particular, we provide a simple proof of the scar towers in the integer-spin 1D AKLT models by studying two-site spin projectors. Through this picture we deduce a family of Hamiltonians that share the scar tower with the AKLT model, and also find common parent Hamiltonians for the AKLT and XY model scars. We also introduce new towers of exact states, organized in a "pyramid" structure, in the spin-1/2 model through the successive application of a nonlocal ladder operator.

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Onsager’s Scars in Disordered Spin Chains

Cited by 138 publications

References 48 publications

Exact Floquet quantum many-body scars under Rydberg blockade

Exact Floquet quantum many-body scars under Rydberg blockade

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

Unified structure for exact towers of scar states in the Affleck-Kennedy-Lieb-Tasaki and other models

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