Department of Physics, University of Portland, Portland, Oregon 97203, USA.
Departamento de Física, Universidade Federal Fluminense Av. Litorânea s/n, Niterói, 24210-340, RJ, Brazil.
Phys Rev E. 2019 Jan;99(1-1):012122. doi: 10.1103/PhysRevE.99.012122.
The critical properties of the one-dimensional spin-1/2 transverse Ising model in the presence of a longitudinal magnetic field were studied by the quantum fidelity method. We used exact diagonalization to obtain the ground-state energies and corresponding eigenvectors for lattice sizes up to 24 spins. The maximum of the fidelity susceptibility was used to locate the various phase boundaries present in the system. The type of dominant spin ordering for each phase was identified by examining the corresponding ground-state eigenvector. For a given antiferromagnetic nearest-neighbor interaction J_{2}, we calculated the fidelity susceptibility as a function of the transverse field B_{x} and the longitudinal field B_{z}. The phase diagram in the (B_{x},B_{z})-plane shows three phases. These findings are in contrast with the published literature that claims that the system has only two phases. For B_{x}<1, we observed an antiferromagnetic phase for small values of B_{z} and a paramagnetic phase for large values of B_{z}. For B_{x}>1 and low B_{z}, we found a disordered phase that undergoes a second-order phase transition to a paramagnetic phase for large values of B_{z}.
通过量子保真度方法研究了一维自旋 1/2 横向伊辛模型在存在纵向磁场时的临界性质。我们使用精确对角化方法获得了格点尺寸高达 24 个自旋的基态能量和相应的本征向量。最大保真度灵敏度用于定位系统中存在的各种相边界。通过检查相应的基态本征向量来确定每个相的主要自旋有序类型。对于给定的反铁磁近邻相互作用 J_2，我们计算了作为横向场 B_x 和纵向场 B_z 的函数的保真度灵敏度。(B_x, B_z) 平面中的相图显示了三个相。这些发现与发表的文献相矛盾，该文献声称系统只有两个相。对于 B_x<1，我们观察到 B_z 较小时为反铁磁相，B_z 较大时为顺磁相。对于 B_x>1 和低 B_z，我们发现了一个无序相，它经历了一个二级相变，对于大的 B_z，它会转变为顺磁相。
