Quantum phase transitions in the triangular coupled-top model

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.Comment: 9 pages, 5 figure

Triple-product asymmetry in the radiative two-pion tau decay

In this work, we perform a detailed study of the $\tau^-\to\pi^-\pi^0\gamma\nu$ decay process within the resonance chiral theory. We pay special attention to the triple-product asymmetry in the $\tau^-\to\pi^-\pi^0\gamma\nu$ process. The minimal resonance chiral Lagrangian and the odd-intrinsic parity resonance operators are simultaneously included to calculate the decay amplitudes. Various invariant-mass distributions in the $\pi^-\pi^0$, $\pi^-\gamma$ and $\pi^0\gamma$ systems are studied and they reveal different resonance dynamics. We further predict the intriguing nonzero triple-product asymmetry distributions, which may provide useful guidelines for future experimental measurements conducted at the Belle-II and super tau-charm facilities.Comment: 32 pages, 9 figures. To match the published versio