Coexistence of ergodic and nonergodic behavior and level spacing statistics in a one-dimensional model of a flat band superconductor

Meri Teeriaho; Ville Vertti Linho; Koushik Swaminathan; Sebastiano Peotta

doi:10.1103/PhysRevResearch.7.013318

Coexistence of ergodic and nonergodic behavior and level spacing statistics in a one-dimensional model of a flat band superconductor

Meri Teeriaho
, Ville Vertti Linho
, Koushik Swaminathan
, Sebastiano Peotta^*

^*Corresponding author for this work

University of Helsinki

Research output: Contribution to journal › Article › Scientific › peer-review

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Abstract

Motivated by recent studies of the projected dice lattice Hamiltonian [K. Swaminathan, Phys. Rev. Res. 5, 043215 (2023)2643-156410.1103/PhysRevResearch.5.043215], we introduce the on-site/bond singlet (OBS) model, a one-dimensional model of a flat band superconductor, in order to better understand the quasiparticle localization and interesting coexistence of ergodic and nonergodic behavior present in the former model. The OBS model is the sum of terms that have direct counterparts in the projected dice lattice Hamiltonian, each of which is parameterized by a coupling constant. Exact diagonalization reveals that the energy spectrum and nonequilibrium dynamics of the OBS model are essentially the same as that of the dice lattice for some values of the coupling constants. The quasiparticle localization and breaking of ergodicity manifest in a striking manner in the level spacing distribution. Its near Poissonian form provides evidence for the existence of local integrals of motion and establishes the OBS model as a nontrivial integrable generalization of the projected Creutz ladder Hamiltonian. These results show that level spacing statistics is a promising tool to study quasiparticle excitations in flat band superconductors.

Original language	English
Article number	013318
Pages (from-to)	1-17
Number of pages	17
Journal	Physical Review Research
Volume	7
Issue number	1
DOIs	https://doi.org/10.1103/PhysRevResearch.7.013318
Publication status	Published - Jan 2025
MoE publication type	A1 Journal article-refereed

Funding

We acknowledge support from the Research Council of Finland under Grants No. 330384, No. 336369, and No. 358150. We acknowledge the computational resources provided by the Aalto Science-IT project.

Keywords

Condensed Matter - Superconductivity
Condensed Matter - Statistical Mechanics

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Coexistence_of_ergodic_and_nonergodic_behavior_and_level_spacing_statistics_in_a_one-dimensional_model_of_a_flat_band_superconductorFinal published version, 1.63 MBLicence: CC BY
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http://adsabs.harvard.edu/abs/2024arXiv241109196T

Cite this

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title = "Coexistence of ergodic and nonergodic behavior and level spacing statistics in a one-dimensional model of a flat band superconductor",

abstract = "Motivated by recent studies of the projected dice lattice Hamiltonian [K. Swaminathan, Phys. Rev. Res. 5, 043215 (2023)2643-156410.1103/PhysRevResearch.5.043215], we introduce the on-site/bond singlet (OBS) model, a one-dimensional model of a flat band superconductor, in order to better understand the quasiparticle localization and interesting coexistence of ergodic and nonergodic behavior present in the former model. The OBS model is the sum of terms that have direct counterparts in the projected dice lattice Hamiltonian, each of which is parameterized by a coupling constant. Exact diagonalization reveals that the energy spectrum and nonequilibrium dynamics of the OBS model are essentially the same as that of the dice lattice for some values of the coupling constants. The quasiparticle localization and breaking of ergodicity manifest in a striking manner in the level spacing distribution. Its near Poissonian form provides evidence for the existence of local integrals of motion and establishes the OBS model as a nontrivial integrable generalization of the projected Creutz ladder Hamiltonian. These results show that level spacing statistics is a promising tool to study quasiparticle excitations in flat band superconductors.",

keywords = "Condensed Matter - Superconductivity, Condensed Matter - Statistical Mechanics",

author = "Meri Teeriaho and Linho, \{Ville Vertti\} and Koushik Swaminathan and Sebastiano Peotta",

note = "Publisher Copyright:{\textcopyright} 2025 authors. Published by the American Physical Society.",

year = "2025",

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doi = "10.1103/PhysRevResearch.7.013318",

language = "English",

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AU - Teeriaho, Meri

AU - Linho, Ville Vertti

AU - Swaminathan, Koushik

AU - Peotta, Sebastiano

PY - 2025/1

Y1 - 2025/1

N2 - Motivated by recent studies of the projected dice lattice Hamiltonian [K. Swaminathan, Phys. Rev. Res. 5, 043215 (2023)2643-156410.1103/PhysRevResearch.5.043215], we introduce the on-site/bond singlet (OBS) model, a one-dimensional model of a flat band superconductor, in order to better understand the quasiparticle localization and interesting coexistence of ergodic and nonergodic behavior present in the former model. The OBS model is the sum of terms that have direct counterparts in the projected dice lattice Hamiltonian, each of which is parameterized by a coupling constant. Exact diagonalization reveals that the energy spectrum and nonequilibrium dynamics of the OBS model are essentially the same as that of the dice lattice for some values of the coupling constants. The quasiparticle localization and breaking of ergodicity manifest in a striking manner in the level spacing distribution. Its near Poissonian form provides evidence for the existence of local integrals of motion and establishes the OBS model as a nontrivial integrable generalization of the projected Creutz ladder Hamiltonian. These results show that level spacing statistics is a promising tool to study quasiparticle excitations in flat band superconductors.

AB - Motivated by recent studies of the projected dice lattice Hamiltonian [K. Swaminathan, Phys. Rev. Res. 5, 043215 (2023)2643-156410.1103/PhysRevResearch.5.043215], we introduce the on-site/bond singlet (OBS) model, a one-dimensional model of a flat band superconductor, in order to better understand the quasiparticle localization and interesting coexistence of ergodic and nonergodic behavior present in the former model. The OBS model is the sum of terms that have direct counterparts in the projected dice lattice Hamiltonian, each of which is parameterized by a coupling constant. Exact diagonalization reveals that the energy spectrum and nonequilibrium dynamics of the OBS model are essentially the same as that of the dice lattice for some values of the coupling constants. The quasiparticle localization and breaking of ergodicity manifest in a striking manner in the level spacing distribution. Its near Poissonian form provides evidence for the existence of local integrals of motion and establishes the OBS model as a nontrivial integrable generalization of the projected Creutz ladder Hamiltonian. These results show that level spacing statistics is a promising tool to study quasiparticle excitations in flat band superconductors.

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Coexistence of ergodic and nonergodic behavior and level spacing statistics in a one-dimensional model of a flat band superconductor

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Superfluidity, topology and disorder in lattice models with flat bands - SUPERFLAT

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