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Exact quantum scars in the chiral nonlinear Luttinger liquid

Frank Schindler, Nicolas Regnault, and B. Andrei Bernevig
Phys. Rev. B 105, 035146 – Published 26 January 2022

Abstract

While the chiral linear Luttinger liquid is integrable via bosonization, its nonlinear counterpart does not admit for an analytic solution. In this work, we find a subextensive number of exact eigenstates for a large family of density-density interaction terms. These states are embedded in a continuum of strongly correlated excited states. The real-space entanglement entropy of some exact states scales logarithmically with system size while that of others has volume-law scaling. We introduce momentum-space entanglement as an unambiguous differentiator between these exact states and the remaining excited states. With regard to momentum space, the exact states behave as bona fide quantum many-body scars: they exhibit identically zero momentum-space entanglement, while typical eigenstates behave thermally. We corroborate this finding by a level statistics analysis. Furthermore, we detail the general formalism for systematically finding all interaction terms and associated exact states, and present a number of infinite exact state sequences extending to arbitrarily high energies. Unlike many previous examples of quantum many-body scars, the exact states uncovered here do not lie at equidistant energies and do not follow from a special operator algebra. Instead, they are uniquely enabled by the interplay of Fermi statistics and chirality.

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  • Received 7 November 2021
  • Accepted 14 January 2022

DOI:https://doi.org/10.1103/PhysRevB.105.035146

©2022 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Frank Schindler1, Nicolas Regnault2, and B. Andrei Bernevig2,3,4

  • 1Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
  • 2Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
  • 3Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
  • 4IKERBASQUE, Basque Foundation for Science, Bilbao, Spain

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Issue

Vol. 105, Iss. 3 — 15 January 2022

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