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Perturbative study of the one-dimensional quantum clock model.

Bingnan Zhang1

  • 1Department of Physics, Rutgers University, New Brunswick, New Jersey 08854, USA.

Physical Review. E
|November 20, 2020
PubMed
Summary
This summary is machine-generated.

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We calculated the quantum clock model

Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Condensed matter physics

Background:

  • The N-state quantum clock model is a key system for studying phase transitions.
  • Understanding its critical behavior is crucial for condensed matter physics.

Purpose of the Study:

  • To calculate the ground-state energy density of the 1D N-state quantum clock model.
  • To analyze the singular structure of the energy density and its relation to 2D classical models.
  • To investigate the nature of phase transitions for varying N.

Main Methods:

  • Padé approximation techniques were used to analyze the energy density up to order 18.
  • The singular structure of the energy density was extracted to identify critical points.
  • Heat capacity exponents were calculated for comparison with 2D classical models.

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Main Results:

  • For N=3 and N=4, a single critical point at g_c=1 was observed, with heat capacity exponents α=0.34±0.01 and α=-0.01±0.01, respectively.
  • For N>4, two critical points emerged, with the energy density exhibiting exponential singularities.
  • The exponent σ, characterizing these singularities, increased with N, stabilizing at 0.5 for N>9.

Conclusions:

  • The phase transitions in the N-state quantum clock model for N>4 appear to be generalizations of the Kosterlitz-Thouless transition.
  • The observed behavior suggests a rich phase diagram dependent on the number of states N.
  • The study provides insights into critical phenomena in quantum many-body systems.