



01937nas a2200157   4500008004100000245008200041210006900123260001500192300001200207490000700219520145800226100001901684700002001703700001901723856003701742       2018                        eng d00aQuantum field theory for the chiral clock transition in one spatial dimension0 aQuantum field theory for the chiral clock transition in one spat  c2018/11/09  a205118 0 vB 3 a<p>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 z&ne;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 renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in 2&minus;d, with 4&minus;N chosen to be of order 2&minus;d. 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.</p>1 aWhitsitt, Seth1 aSamajdar, Rhine1 aSachdev, Subir  uhttps://arxiv.org/abs/1808.07056