Spread complexity in free fermion models

Gautam, Mamta; Jaiswal, Nitesh; Gill, Ankit

doi:10.1140/epjb/s10051-023-00636-6

Eur. Phys. J. B

2024

DOI: 10.1140/epjb/s10051-023-00636-6

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Spread complexity in free fermion models

Mamta Gautam,

Nitesh Jaiswal,

Ankit Gill

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2024

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Cited by 3 publications

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Krylov Complexity of Fermionic and Bosonic Gaussian States

Adhikari,

Rijal,

Aryal

et al. 2024

Fortschritte der Physik

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The concept of complexity has become pivotal in multiple disciplines, including quantum information, where it serves as an alternative metric for gauging the chaotic evolution of a quantum state. This paper focuses on Krylov complexity, a specialized form of quantum complexity that offers an unambiguous and intrinsically meaningful assessment of the spread of a quantum state over all possible orthogonal bases. This study is situated in the context of Gaussian quantum states, which are fundamental to both Bosonic and Fermionic systems and can be fully described by a covariance matrix. While the covariance matrix is essential, it is insufficient alone for calculating Krylov complexity due to its lack of relative phase information is shown. The relative covariance matrix can provide an upper bound for Krylov complexity for Gaussian quantum states is suggested. The implications of Krylov complexity for theories proposing complexity as a candidate for holographic duality by computing Krylov complexity for the thermofield double States (TFD) and Dirac field are also explored.

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Krylov Complexity of Fermionic and Bosonic Gaussian States

Adhikari,

Rijal,

Aryal

et al. 2024

Fortschritte der Physik

View full text Add to dashboard Cite

show abstract

Complexity in two-point measurement schemes

Gill,

Pal,

Pal

et al. 2024

Phys. Rev. B

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Krylov complexity of modular Hamiltonian evolution

Caputa,

Magan,

Patramanis

et al. 2024

Phys. Rev. D

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Spread complexity in free fermion models

Cited by 3 publications

References 44 publications

Krylov Complexity of Fermionic and Bosonic Gaussian States

Krylov Complexity of Fermionic and Bosonic Gaussian States

Complexity in two-point measurement schemes

Krylov complexity of modular Hamiltonian evolution

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