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

Published

May 3, 2021

Author(s)

Seth P. Whitsitt, Rhine Samajdar, Subir Sachdev

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 Z_N symmetry, to a gapped phase with the Z_N symmetry restored. The transition has dynamical critical exponent z≠1, 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 re-normalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in 2-d, with 4-N chosen to be of order 2-d. At two-loop order, we find a regime of parameters with a re-normalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix re-normalization 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 Ņ.

Citation

Physical Review B

Pub Type

Journals

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Citation

Whitsitt, S. , Samajdar, R. and Sachdev, S. (2021), Quantum field theory for the chiral clock transition in one spatial dimension, Physical Review B, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=926674 (Accessed May 4, 2026)

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