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  • Open Access

Capacity of entanglement in Lifshitz theories

Sare Khoshdooni*, Komeil Babaei Velni†, and M. Reza Mohammadi Mozaffar‡

  • *Contact author: sare.khoshdooni@webmail.guilan.ac.ir
  • †Contact author: babaeivelni@guilan.ac.ir
  • ‡Contact author: mmohammadi@guilan.ac.ir
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Phys. Rev. D 112, 026027 – Published 28 July, 2025

DOI: https://doi.org/10.1103/7cg6-m7dn

Abstract

We study the capacity of entanglement in certain integrable scale invariant theories that exhibit Lifshitz scaling symmetry with a generic dynamical exponent z at the critical point. This measure characterizes the width of the eigenvalue spectrum of the reduced density matrix and is a quantum informational counterpart of heat capacity. We explore various aspects of capacity of entanglement, such as the corresponding universal terms for the ground state, its z dependence, and its temporal evolution, after a global quantum quench in two dimensions. We carefully examine the existence of a convenient entropic c-function based on this quantity both in bosonic and fermionic theories. While in the relativistic case the corresponding c-function displays a monotonic behavior under the renormalization group flow, this is not the case for the nonrelativistic theories. We also investigate the dynamics of capacity of entanglement after a mass quench and show that it follows the quasiparticle interpretation for the spreading of entanglement. Finally, we discuss how these results are consistent with the behavior of other entanglement measures, including the entanglement entropy.

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Phys. Rev. D 112, 026027– Published 28 July, 2025
  • Received 14 May 2025
  • Accepted 10 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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