论文标题
非相互作用费米子的非自动量子电路和张量网络中的临界和纠缠
Criticality and entanglement in non-unitary quantum circuits and tensor networks of non-interacting fermions
论文作者
论文摘要
已显示出非单生量子动力学的模型，例如包括投射测量的量子电路，已显示出表现出丰富的量子临界行为。关于这种行为有许多互补的观点。例如，在d =（d+1）维晶格上，d维局部非单身量子电路和张量网络之间存在已知的对应关系。在这里，我们表明，在非交互式费米子系统的情况下，在d空间维度中的非统一回路与D =（d+1）空间维度的静态遗传学汉密尔顿人的非统一回路与静态的遗传学汉密尔顿人之间的统一非相互作用的效费。这为理解纠缠阶段和非交互电路所表现出的批判行为提供了有力的新观点。对相应的非相互作用的哈密顿人的对称性进行分类，我们表明，一大批随机电路，包括时空和时间上具有随机性的最通用电路，与十个Altland-Zirnbauer对称类别中的静态空间疾病的汉密尔顿人对应。我们发现已知在所有这些类别中发生的关键性是相应的随机非单身电路的关键纠缠特性的起源。为了举例说明这一点，我们在数值上研究了尺寸d = 2和d = 3的Haar-random Gaussian fermionic Tensor网络的量子状态。我们表明，最通用的张量网络集成集合对应于Altland-Zirnbauer对称性类DIII中与静态疾病的非相互作用费米子的单一问题，该类别在d = 2和d = 3中都表现出稳定的关键金属相。在其他九个Altland-Zirnbauer对称类中，可以通过实现Clifford代数扩展来对其他九个Altland-Zirnbauer对称类别中的张量网络和相应的随机非单身电路进行分类。
Models for non-unitary quantum dynamics, such as quantum circuits that include projective measurements, have been shown to exhibit rich quantum critical behavior. There are many complementary perspectives on this behavior. For example, there is a known correspondence between d-dimensional local non-unitary quantum circuits and tensor networks on a D=(d+1)-dimensional lattice. Here, we show that in the case of systems of non-interacting fermions, there is furthermore a full correspondence between non-unitary circuits in d spatial dimensions and unitary non-interacting fermion problems with static Hermitian Hamiltonians in D=(d+1) spatial dimensions. This provides a powerful new perspective for understanding entanglement phases and critical behavior exhibited by non-interacting circuits. Classifying the symmetries of the corresponding non-interacting Hamiltonian, we show that a large class of random circuits, including the most generic circuits with randomness in space and time, are in correspondence with Hamiltonians with static spatial disorder in the ten Altland-Zirnbauer symmetry classes. We find the criticality that is known to occur in all of these classes to be the origin of the critical entanglement properties of the corresponding random non-unitary circuit. To exemplify this, we numerically study the quantum states at the boundary of Haar-random Gaussian fermionic tensor networks of dimension D=2 and D=3. We show that the most general such tensor network ensemble corresponds to a unitary problem of non-interacting fermions with static disorder in Altland-Zirnbauer symmetry class DIII, which for both D=2 and D=3 is known to exhibit a stable critical metallic phase. Tensor networks and corresponding random non-unitary circuits in the other nine Altland-Zirnbauer symmetry classes can be obtained from the DIII case by implementing Clifford algebra extensions for classifying spaces.
