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Coherence generation, symmetry algebras, and Hilbert space fragmentation

Faidon Andreadakis1,* and Paolo Zanardi1,2,†

  • 1Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA
  • 2Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532, USA

  • *fandread@usc.edu
  • †zanardi@usc.edu
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Phys. Rev. A 107, 062402 – Published 2 June, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.062402

Abstract

Hilbert space fragmentation is a novel type of ergodicity breaking in closed quantum systems. Recently, an algebraic approach was utilized to provide a definition of Hilbert space fragmentation characterizing families of Hamiltonian systems based on their (generalized) symmetries. In this paper we reveal a simple connection between the aforementioned classification of physical systems and their coherence generation properties, quantified by the coherence generating power (CGP). The maximum CGP (in the basis associated with the algebra of each family of Hamiltonians) is exactly related to the number of independent Krylov subspaces K, which is precisely the characteristic used in the classification of the system. In order to gain further insight, we numerically simulate paradigmatic models with both ordinary symmetries and Hilbert space fragmentation, comparing the behavior of the CGP in each case with the system dimension. More generally, allowing the time evolution to be any unitary channel in a specified algebra, we show analytically that the scaling of the Haar averaged value of the CGP depends only on K. These results illustrate the intuitive relationship between coherence generation and symmetry algebras.

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Phys. Rev. A 107, 062402– Published 2 June, 2023
  • Received 3 February 2023
  • Accepted 9 May 2023
Article part of CHORUS
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