Continuous Symmetry Breaking in 1D Long-Range Interacting Quantum Systems

Mohammad F. Maghrebi, Zhe-Xuan Gong, and Alexey V. Gorshkov
Phys. Rev. Lett. 119, 023001 – Published 11 July 2017
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Abstract

Continuous symmetry breaking (CSB) in low-dimensional systems, forbidden by the Mermin-Wagner theorem for short-range interactions, may take place in the presence of slowly decaying long-range interactions. Nevertheless, there is no stringent bound on how slowly interactions should decay to give rise to CSB in 1D quantum systems at zero temperature. Here, we study a long-range interacting spin chain with U(1) symmetry and power-law interactions V(r)1/rα. Using a number of analytical and numerical techniques, we find CSB for α smaller than a critical exponent αc(3) that depends on the microscopic parameters of the model. Furthermore, the transition from the gapless XY phase to the gapless CSB phase is mediated by the breaking of conformal and Lorentz symmetries due to long-range interactions, and is described by a universality class akin to, but distinct from, the Berezinskii-Kosterlitz-Thouless transition. Signatures of the CSB phase should be accessible in existing trapped-ion experiments.

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  • Received 10 November 2016

DOI:https://doi.org/10.1103/PhysRevLett.119.023001

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & OpticalStatistical Physics & Thermodynamics

Authors & Affiliations

Mohammad F. Maghrebi1,2,3, Zhe-Xuan Gong1,2,4, and Alexey V. Gorshkov1,2

  • 1Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
  • 2Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
  • 3Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
  • 4Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA

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Issue

Vol. 119, Iss. 2 — 14 July 2017

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