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

Journal Article · · Physical Review. B
 [1];  [2];  [3]
  1. Harvard Univ., Cambridge, MA (United States); National Inst. of Standards and Technology and the Univ. of Maryland, College Park, MD (United States)
  2. Harvard Univ., Cambridge, MA (United States)
  3. Harvard Univ., Cambridge, MA (United States); Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
+ Show Author Affiliations

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.

Research Organization:
Harvard Univ., Cambridge, MA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
SC0019030
OSTI ID:
1613073
Alternate ID(s):
OSTI ID: 1481455
Journal Information:
Physical Review. B, Vol. 98, Issue 20; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 24 works
Citation information provided by
Web of Science

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Cited By (10)

Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator journal April 2019
Diagnosing Potts criticality and two-stage melting in one-dimensional hard-core boson models journal March 2019
Nonequilibrium critical dynamics in the quantum chiral clock model journal May 2019
Floating Phase versus Chiral Transition in a 1D Hard-Boson Model journal January 2019
Systematic Construction of Scarred Many-Body Dynamics in 1D Lattice Models journal July 2019
Diagnosing Potts criticality and two-stage melting in one-dimensional hard-boson models text January 2019
Floating Phases in One-Dimensional Rydberg Ising Chains preprint January 2019
Quantum clock models with infinite-range interactions text January 2020
Quantum phases of Rydberg atoms on a kagome lattice text January 2020
Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array text January 2021

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Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Materials Science
Physics
Quantum phase transitions
Renormalization group
Ultracold gases