Dynamical quantum phase transitions and broken-symmetry edges in the many-body eigenvalue spectrum
Dynamical quantum phase transitions and broken-symmetry edges in the many-body eigenvalue spectrum
复制标题
多体特征值谱中的动态量子相变和对称破缺边
DOI：
--
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
M. Fabrizio
中科院分区：
文献类型：
--
作者：
G. Mazza;M. Fabrizio
多体模型经历量子相变到破对称相并能存活到临界温度时，在有序相中必须具有对称和非对称本征态。我们预测，并在横向场的全连通Ising模型中明确表明，这两类本征态在能量上不重叠，因此存在一条能量边将低能对称破缺本征态与高能对称不变本征态分开。正如我们所展示的，这个能量实际上是在横向场突然大幅增加的情况下，这个模型所显示的动态相变的原因。我们考虑的第二种情况是相反的，其中对称破缺的本征态是那些在光谱的高能部分，而低能本征态是对称的。在这种情况下，也必须存在一种特殊的能量，标志着边界并导致意外的非平衡动力学行为。一个例子是哈密顿的哈密顿数学模型{H}。利用$mathcal{H}$的高能谱也是$ensuremath{-}mathcal{H}$的低能谱这一简单事实，我们得出Hubbard模型的高能本征态是超流体的结论。在一个时间依赖的Gutzwiller近似中模拟了一个高能类bcs的试波函数的时间演化，我们表明，尽管相互作用具有排斥性，但一个小的超导序参数实际上会增长。
Many-body models undergoing a quantum phase transition to a broken-symmetry phase that survives up to a critical temperature must possess, in the ordered phase, symmetric as well as nonsymmetric eigenstates. We predict, and explicitly show in the fully connected Ising model in a transverse field, that these two classes of eigenstates do not overlap in energy, and therefore that an energy edge exists separating low-energy symmetry-breaking eigenstates from high-energy symmetry-invariant ones. This energy is actually responsible, as we show, for the dynamical phase transition displayed by this model under a sudden large increase of the transverse field. A second situation we consider is the opposite, where the symmetry-breaking eigenstates are those in the high-energy sector of the spectrum, whereas the low-energy eigenstates are symmetric. In that case too a special energy must exist marking the boundary and leading to unexpected out-of-equilibrium dynamical behavior. An example is the fermonic repulsive Hubbard model Hamiltonian $mathcal{H}$. Exploiting the trivial fact that the high-energy spectrum of $mathcal{H}$ is also the low-energy one of $ensuremath{-}mathcal{H}$, we conclude that the high-energy eigenstates of the Hubbard model are superfluid. Simulating in a time-dependent Gutzwiller approximation the time evolution of a high-energy BCS-like trial wave function, we show that a small superconducting order parameter will actually grow in spite of the repulsive nature of the interaction.