Quantum phase transitions in the triangular coupled-top model
- URL: http://arxiv.org/abs/2211.03008v1
- Date: Sun, 6 Nov 2022 02:24:37 GMT
- Title: Quantum phase transitions in the triangular coupled-top model
- Authors: Liwei Duan, Yan-Zhi Wang, Qing-Hu Chen
- Abstract summary: We study the coupled-top model with three large spins located on a triangle.
Depending on the coupling strength, there exist three phases: disordered paramagnetic phase, geometricmagnetic phase, and frustrated antiferromagnetic phase.
- Score: 23.303857456199328
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We study the coupled-top model with three large spins located on a triangle.
Depending on the coupling strength, there exist three phases: disordered
paramagnetic phase, ferromagnetic phase, and frustrated antiferromagnetic
phase, which can be distinguished by the mean-field approach. The
paramagnetic-ferromagnetic phase transition is accompanied by the breaking of
the global $Z_2$ symmetry, whereas the paramagnetic-antiferromagnetic phase
transition is accompanied by the breaking of both the global $Z_2$ symmetry and
the translational symmetry. Exact analytical results of higher-order quantum
effects beyond the mean-field contribution, such as the excitation energy,
quantum fluctuation and von Neumann entropy, can be achieved by the
Holstein-Primakoff transformation and symplectic transformation in the
thermodynamic limit. Near the quantum critical point, the energy gap closes,
along with the divergence of the quantum fluctuation in certain quadrature and
von Neumann entropy. Particular attention should be paid to the
antiferromagnetic phase, where the geometric frustration takes effect. The
critical behaviors in the antiferromagnetic phase are quite different from
those in the paramagnetic and ferromagnetic phases, which highlights the
importance of the geometric frustration. The triangular coupled-top model
provides a simple and feasible platform to study the quantum phase transition
and the novel critical behaviors induced by the geometric frustration.
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