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



Seth P. Whitsitt, Rhine Samajdar, Subir Sachdev


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.
Physical Review B


Whitsitt, S. , Samajdar, R. and Sachdev, S. (2021), Quantum field theory for the chiral clock transition in one spatial dimension, Physical Review B, [online], (Accessed May 26, 2024)


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Created May 3, 2021, Updated November 29, 2022