Spontaneous symmetry breaking and bifurcations in ground-state fidelity for quantum lattice systems.
Spontaneous symmetry breaking and bifurcations in ground-state fidelity for quantum lattice systems.
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DOI：
10.1103/physreve.82.061127
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发表时间：
2009-02
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影响因子：
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通讯作者：
Jian-hui Zhao;Hong-Lei Wang;Bo Li;Huan-Qiang Zhou
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文献类型：
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作者：
Jian-hui Zhao;Hong-Lei Wang;Bo Li;Huan-Qiang Zhou
当一个系统的哈密顿量具有一定的对称性，而基态波函数不保持对称性时，系统就会发生自发对称性破缺，这就提供了这样一种情况：当某个控制参数超过临界值时，系统就会发生分叉，从而打破对称性。结果表明，在量子相变过程中，每个格点的基态保真度也会出现这种分叉。这一结果的意义在于这样一个事实，即每个晶格位置的基态保真度是普遍的，在这个意义上，它是模型无关的，相反（模型依赖）序参数。这个基本量可以通过利用开发的张量网络算法在无限大小的格子上计算。我们说明了该计划在横向磁场中的量子伊辛模型和自旋1/2 XYX模型在外部磁场中的无限大小的晶格在一个空间维度。
Spontaneous symmetry breaking occurs in a system when its Hamiltonian possesses a certain symmetry, whereas the ground-state wave functions do not preserve it. This provides such a scenario that a bifurcation, which breaks the symmetry, occurs when some control parameter crosses its critical value. It is unveiled that the ground-state fidelity per lattice site exhibits such a bifurcation for quantum lattice systems undergoing quantum phase transitions. The significance of this result lies in the fact that the ground-state fidelity per lattice site is universal, in the sense that it is model independent, in contrast to (model-dependent) order parameters. This fundamental quantity may be computed by exploiting the developed tensor network algorithms on infinite-size lattices. We illustrate the scheme in terms of the quantum Ising model in a transverse magnetic field and the spin-1/2 XYX model in an external magnetic field on an infinite-size lattice in one spatial dimension.