Quantum field theory for the chiral clock transition in one spatial dimension

Seth Whitsitt, Rhine Samajdar, and Subir Sachdev
Phys. Rev. B 98, 205118 – Published 9 November 2018

Abstract

We describe the quantum phase transition in the N-state chiral clock model in spatial dimension d=1. With couplings chosen to preserve time-reversal and spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-dimensional chain of trapped ultracold alkali atoms. For such couplings and N=3, the clock model is expected to have a direct phase transition from a gapped phase with a broken global ZN symmetry, to a gapped phase with the ZN symmetry restored. The transition has dynamical critical exponent z1, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in d=1, involving the onset of a single-boson condensate in the background of a higher-dimensional N-boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in 2d, with 4N chosen to be of order 2d. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for N=3, finding good evidence for a direct phase transition, and obtain estimates for z and the correlation length exponent ν.

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  • Received 30 August 2018

DOI:https://doi.org/10.1103/PhysRevB.98.205118

©2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & ThermodynamicsAtomic, Molecular & Optical

Authors & Affiliations

Seth Whitsitt1,2, Rhine Samajdar1, and Subir Sachdev1,3

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
  • 2Joint Quantum Institute, National Institute of Standards and Technology and the University of Maryland, College Park, Maryland 20742, USA
  • 3Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5

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Issue

Vol. 98, Iss. 20 — 15 November 2018

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