Nambu-Goldstone Bosons and Quantum Fisher Information

Abstract

The quantum Fisher matrix and geometric tensor are powerful tools for quantifying the nature of quantum systems. Unfortunately, the formalism needed to compute these quantities is opaque and has limited the development of physical intuition for their behavior, even in the ground state. For quantum systems with continuous symmetries, we know the ground state can be understood in a model-independent and intuitive way from the correlation functions of conserved currents and charges. In this paper, we demonstrate an equivalence between the quantum Fisher matrix associated with the ground states of systems with continuous symmetries and the Nambu-Goldstone. bosons produced by broken generators. We will show that the information metric defined by the Fisher matrix is the same as the Zamolodchikov metric that defines the coset space of the system. Next we show that the Uhlmann curvature associated with multi-parameter estimation is the same as the charge density matrix that defines the difference between type-A and type-B Nambu-Goldstone bosons. We demonstrate these connections in several examples and discuss the generalization to finite temperature.

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BibTeX RIS

BibTeX

@misc{chen2026nambugoldstone,
  title = {{Nambu-Goldstone Bosons and Quantum Fisher Information}},
  author = {Eugene Chen and Daniel Green},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27054},
  eprint = {2610.27054},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27054},
}

RIS

TY  - UNPB
TI  - Nambu-Goldstone Bosons and Quantum Fisher Information
AU  - Eugene Chen
AU  - Daniel Green
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.27054
UR  - https://arxiv.org/abs/2610.27054
AB  - The quantum Fisher matrix and geometric tensor are powerful tools for quantifying the nature of quantum systems. Unfortunately, the formalism needed to compute these quantities is opaque and has limited the development of physical intuition for their behavior, even in the ground state. For quantum systems with continuous symmetries, we know the ground state can be understood in a model-independent and intuitive way from the correlation functions of conserved currents and charges. In this paper, we demonstrate an equivalence between the quantum Fisher matrix associated with the ground states of systems with continuous symmetries and the Nambu-Goldstone. bosons produced by broken generators. We will show that the information metric defined by the Fisher matrix is the same as the Zamolodchikov metric that defines the coset space of the system. Next we show that the Uhlmann curvature associated with multi-parameter estimation is the same as the charge density matrix that defines the difference between type-A and type-B Nambu-Goldstone bosons. We demonstrate these connections in several examples and discuss the generalization to finite temperature.
ER  -

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