Degenerate ground states and multiple bifurcations in a two-dimensional q-state quantum Potts model.
Degenerate ground states and multiple bifurcations in a two-dimensional q-state quantum Potts model.
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DOI：
10.1103/physreve.89.062142
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发表时间：
2014-03
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影响因子：
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通讯作者：
Yan-Wei Dai;Sam Young Cho;M. Batchelor;Huan-Qiang Zhou
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作者：
Yan-Wei Dai;Sam Young Cho;M. Batchelor;Huan-Qiang Zhou
利用无限投影纠缠对态(IPEPS)算法，数值研究了无限正方形晶格上的二维Q态量子Potts模型。我们证明了量子保真度，即系统的任意参考态和iPEPS基态之间的重叠测量，可以检测到Z{q}破缺对称相的q重简并基态。相应地，当横向磁场从对称相变化到破对称相时，量子基态保真度出现多重分叉，这意味着一个多分岔点对应于一个临界点。量子保真度在相变点的连续行为是(非)连续相变的特征。与量子保真度的特征行为类似，从简并基态得到的磁化强度作为序参数，在临界点上表现出多重分叉。每个序参数也被显式地证明在哈密顿量对称群的Z_{q}子群下变换。我们发现，正方形晶格上的Q态量子Potts模型在q=3和q=4时经历了不连续(一阶)相变，而在q=2时经历了连续相变(二维量子横向伊辛模型)。
We numerically investigate the two-dimensional q-state quantum Potts model on the infinite square lattice by using the infinite projected entangled-pair state (iPEPS) algorithm. We show that the quantum fidelity, defined as an overlap measurement between an arbitrary reference state and the iPEPS ground state of the system, can detect q-fold degenerate ground states for the Z_{q} broken-symmetry phase. Accordingly, a multiple bifurcation of the quantum ground-state fidelity is shown to occur as the transverse magnetic field varies from the symmetry phase to the broken-symmetry phase, which means that a multiple-bifurcation point corresponds to a critical point. A (dis)continuous behavior of quantum fidelity at phase transition points characterizes a (dis)continuous phase transition. Similar to the characteristic behavior of the quantum fidelity, the magnetizations, as order parameters, obtained from the degenerate ground states exhibit multiple bifurcation at critical points. Each order parameter is also explicitly demonstrated to transform under the Z_{q} subgroup of the symmetry group of the Hamiltonian. We find that the q-state quantum Potts model on the square lattice undergoes a discontinuous (first-order) phase transition for q=3 and q=4 and a continuous phase transition for q=2 (the two-dimensional quantum transverse Ising model).