Using the tensor renormalization group method based on the higher-order singular value decomposition, we have studied the phase transitions of the five-state clock model on the square lattice. The temperature dependen...Using the tensor renormalization group method based on the higher-order singular value decomposition, we have studied the phase transitions of the five-state clock model on the square lattice. The temperature dependence of the specific heat indicates the system has two phase transitions, as verified clearly by the correlation function at three representative tem- peratures. By calculating the magnetic susceptibility, we obtained only the upper critical temperature as To2 = 0.9565（7）. Investigating the fixed-point tensor, we precisely locate the transition temperatures at Tcl = 0.9029（1） and Tc2 = 0.9520（1）, consistent well with the Monte Carlo and the density matrix renormalization group results.展开更多
The similarity renormalization group is used to transform the Dirac Hamiltonian with tensor coupling into a diagonal form. The upper(lower) diagonal element becomes a Schr¨odinger-like operator with the tensor co...The similarity renormalization group is used to transform the Dirac Hamiltonian with tensor coupling into a diagonal form. The upper(lower) diagonal element becomes a Schr¨odinger-like operator with the tensor component separated from the original Hamiltonian.Based on the operator, the tensor effect of the relativistic symmetries is explored with a focus on the single-particle energy contributed by the tensor coupling. The results show that the tensor coupling destroying(improving) the spin(pseudospin) symmetry is mainly attributed to the coupling of the spin-orbit and the tensor term, which plays an opposite role in the single-particle energy for the(pseudo-) spin-aligned and spin-unaligned states and has an important influence on the shell structure and its evolution.展开更多
基金Project supported by the Fundamental Research Funds for the Central Universities,China(Grant No.531107040857)the Natural Science Foundation of Hunan Province,China(Grant No.851204035)the National Natural Science Foundation of China(Grant No.11774420)
文摘Using the tensor renormalization group method based on the higher-order singular value decomposition, we have studied the phase transitions of the five-state clock model on the square lattice. The temperature dependence of the specific heat indicates the system has two phase transitions, as verified clearly by the correlation function at three representative tem- peratures. By calculating the magnetic susceptibility, we obtained only the upper critical temperature as To2 = 0.9565（7）. Investigating the fixed-point tensor, we precisely locate the transition temperatures at Tcl = 0.9029（1） and Tc2 = 0.9520（1）, consistent well with the Monte Carlo and the density matrix renormalization group results.
基金supported by the National Natural Science Foundation of China(Grant Nos.11175001,11405040,11575002 and 11205004)the Program for New Century Excellent Talents in University of China(Grant No.NCET-05-0558)+2 种基金the Excellent Talents Cultivation Foundation of Anhui Province(Grant No.2007Z018)the Natural Science Foundation of Anhui Province(Grant No.11040606M07)the 211 Project of Anhui University
文摘The similarity renormalization group is used to transform the Dirac Hamiltonian with tensor coupling into a diagonal form. The upper(lower) diagonal element becomes a Schr¨odinger-like operator with the tensor component separated from the original Hamiltonian.Based on the operator, the tensor effect of the relativistic symmetries is explored with a focus on the single-particle energy contributed by the tensor coupling. The results show that the tensor coupling destroying(improving) the spin(pseudospin) symmetry is mainly attributed to the coupling of the spin-orbit and the tensor term, which plays an opposite role in the single-particle energy for the(pseudo-) spin-aligned and spin-unaligned states and has an important influence on the shell structure and its evolution.
