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Euclidian Crystals in Many-Body Systems: Breakdown of Goldstone’s Theorem

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Abstract

It is proven via modification of the Nambu–Goldstone theorem, based on the Ward–Takahashi identity that Goldstone’s bosons of the quantum order could be massive. The quantum order parameter (QOP), introduced previously as the instantonic crystal in Euclidian space (Mukhin, J. Supercond. Nov. Magn. 24:1165–1171, 2011), breaks Matsubara’s time translational invariance while possessing zero classical expectation value and vanishing scattering cross-section (“hidden order”). The amplitude of the mass-gap can be calculated from the eigenmodes spectrum of the effective Euclidian action for a particular self-consistent QOP solution in the fermionic repulsive Hubbard model. Theoretical results are discussed in relation with possible linking together of the two phenomena that previously were considered separately, i.e., “hidden order” fingerprints in ARPES measurements and the “neutron resonance” feature in the magnetic spectrum in lightly hole-doped copper oxides.

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Acknowledgements

The author acknowledges useful discussions with Professor Jan Zaanen and Dr. Michail Fistul, as well as partial support of this work by the Russian Ministry of Science and Education grant no. 14A18.21.1936, MISIS grant 3400022, and RFFI grant 12-02-01018.

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  1. Theoretical Physics and Quantum Technologies Department, Moscow Institute for Steel and Alloys, Leninskii avenue 4, 119049, Moscow, Russia

    S. I. Mukhin

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  1. S. I. Mukhin
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Correspondence to S. I. Mukhin.

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Mukhin, S.I. Euclidian Crystals in Many-Body Systems: Breakdown of Goldstone’s Theorem. J Supercond Nov Magn 27, 945–950 (2014). https://doi.org/10.1007/s10948-013-2416-9

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  • DOI: https://doi.org/10.1007/s10948-013-2416-9

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