bibkey: ariasdigiuliokeskivakkuritonni2023capacity
authors: Raúl Arias; Giuseppe Di Giulio; Esko Keski-Vakkuri; Erik Tonni
year: 2023
title: "Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement"
doi: 10.1007/JHEP03(2023)175
url: https://arxiv.org/abs/2301.02117v1
claim: "The paper studies the capacity of entanglement and the Schur-concave entanglement monotones built from it along renormalization-group flows, in charge sectors of theories with a U(1) symmetry and after quantum quenches; it decomposes a reduced density matrix that commutes with the subsystem charge into normalized charge blocks and asks whether a majorization order between two density matrices survives this decomposition."
strata_touched:
  - D5/S3/Entropy/ChargeSectorMajorizationRefutation
license: citation-only
triage: anchor

Arias, Di Giulio, Keski-Vakkuri and Tonni, majorization in charge sectors

R. Arias, G. Di Giulio, E. Keski-Vakkuri and E. Tonni, arXiv:2301.02117v1 [cond-mat.stat-mech] (5 January 2023); JHEP 03 (2023) 175. Quotations are from the v1 TeX source, with cross-references omitted.

Charge sectors (Section 6): for a system with a $U(1)$ charge $Q=Q_A\oplus Q_B$ in an eigenstate of $Q$, $[{\rho }_A,Q_A]=0$, and

${\rho }_A={⨁}_{q}p(q){\rho }_A(q),$

where each block ${\rho }_A(q)$ corresponds to an eigenvalue $q$ of $Q_A$ and $p(q)=\mathrm{Tr}{\Pi }_q{\rho }_A$ is the probability of finding $q$ in a measurement of $Q_A$.

The question (Section 7, “Symmetry-resolved related issues”):

For instance, given two density matrices such that $\rho \succ \sigma$, we may ask whether this majorization order survives once we decompose $\rho$ and $\sigma$ according to (6.1). One can try to diagnose this aspect using $M_A^{(n)}(q)$, given that these quantities are entanglement monotones also in a fixed charge sector. We leave this analysis for future investigations.

Verified locator

Source: https://arxiv.org/abs/2301.02117v1

• DOI: https://doi.org/10.1007/JHEP03(2023)175 (JHEP 03 (2023) 175; author list, journal, issue and article number from Crossref).
• URL: https://arxiv.org/abs/2301.02117v1 (the e-print is a gzipped tar archive; member CDraft-Final.tex, 5204 lines, md5 5739b2bdf5eab61756172c2a3f55d9e0):
  • Schur concavity and the majorization order, l. 854–857;
  • the charge-sector decomposition, eq. (6.1), l. 3550–3567;
  • the question, l. 4140.
• The arXiv version date is from the arXiv metadata.