Quantum field theory for the chiral clock transition in one spatial dimension
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 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 pointmore »
- Authors:
-
- Harvard Univ., Cambridge, MA (United States); National Inst. of Standards and Technology and the Univ. of Maryland, College Park, MD (United States)
- Harvard Univ., Cambridge, MA (United States)
- Harvard Univ., Cambridge, MA (United States); Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
- Publication Date:
- Research Org.:
- Harvard Univ., Cambridge, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1613073
- Alternate Identifier(s):
- OSTI ID: 1481455
- Grant/Contract Number:
- SC0019030
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 98; Journal Issue: 20; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics; Quantum phase transitions; Renormalization group; Ultracold gases
Citation Formats
Whitsitt, Seth, Samajdar, Rhine, and Sachdev, Subir. Quantum field theory for the chiral clock transition in one spatial dimension. United States: N. p., 2018.
Web. doi:10.1103/physrevb.98.205118.
Whitsitt, Seth, Samajdar, Rhine, & Sachdev, Subir. Quantum field theory for the chiral clock transition in one spatial dimension. United States. https://doi.org/10.1103/physrevb.98.205118
Whitsitt, Seth, Samajdar, Rhine, and Sachdev, Subir. Fri .
"Quantum field theory for the chiral clock transition in one spatial dimension". United States. https://doi.org/10.1103/physrevb.98.205118. https://www.osti.gov/servlets/purl/1613073.
@article{osti_1613073,
title = {Quantum field theory for the chiral clock transition in one spatial dimension},
author = {Whitsitt, Seth and Samajdar, Rhine and Sachdev, Subir},
abstractNote = {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 ≠ 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.},
doi = {10.1103/physrevb.98.205118},
journal = {Physical Review. B},
number = 20,
volume = 98,
place = {United States},
year = {Fri Nov 09 00:00:00 EST 2018},
month = {Fri Nov 09 00:00:00 EST 2018}
}
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