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

Journal Article · Fri Nov 09 00:00:00 UTC 2018 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.98.205118 · OSTI ID:1613073

Whitsitt, Seth ^[1]; Samajdar, Rhine ^[2]; Sachdev, Subir ^[3]

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1. Harvard Univ., Cambridge, MA (United States); National Inst. of Standards and Technology and the Univ. of Maryland, College Park, MD (United States); DOE/OSTI
2. Harvard Univ., Cambridge, MA (United States)
3. Harvard Univ., Cambridge, MA (United States); Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)

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. Here, we present a renormalization 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 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.

• Research Organization: Harvard Univ., Cambridge, MA (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC)
• Grant/Contract Number: SC0019030
• OSTI ID: 1613073
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 20 Vol. 98; ISSN 2469-9950
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English