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  • Open Access

No Massless Goldstone Bosons in Hamiltonian Time Crystals

Antti J. Niemi*

  • *Contact author: Antti.Niemi@su.se
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Phys. Rev. Lett. 135, 230201 – Published 1 December, 2025

DOI: https://doi.org/10.1103/sytq-kjbr

Abstract

We present a geometric framework for Hamiltonian quantum time crystals, emphasizing the pivotal role of continuous symmetries and their associated conserved charges. In this approach, a time crystal is identified as a minimum-energy ground state that is parallel transported along a family of Fock spaces, with time evolution realized as a symmetry transformation. This parallel transport is implemented via a generalized, time-dependent Bogoliubov transformation, ensuring coherence across the Fock spaces. Revisiting Goldstone’s original analysis, we show that in the presence of a time crystal, the Goldstone mode acquires a mass and its direction oscillates periodically in Higgs space. Our formulation circumvents existing no-go theorems that would otherwise forbid quantum time-crystalline order. We place time crystals within the broader context of quantum many-body physics and field theory, drawing analogies to superconductivity and quantum field theory in time-dependent backgrounds.

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Phys. Rev. Lett. 135, 230201– Published 1 December, 2025
  • Received 12 March 2025
  • Accepted 14 November 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 Bibsam.

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