格点规范理论哈密顿表述中（3+1）维拓扑$θ$项的量子和经典模拟研究
Investigating a (3+1)D Topological $θ$-Term in the Hamiltonian Formulation of Lattice Gauge Theories for Quantum and Classical Simulations
摘要：
量子技术提供了有效地模拟格点场论中受符号问题困扰的机制的前景，例如拓扑项、化学势和非平衡动力学的存在。在这项工作中，我们推导出（3+1）D拓扑$θ$项的阿贝尔和非阿贝尔格点规范理论的哈密顿公式，铺平了道路，这些条款的量子和经典计算机上的哈密顿模拟。通过对单个周期立方体的精确对角化，我们进一步数值研究了具有$θ$项的（3+1）D U（1）格点规范理论的零温相结构.在强耦合制度，我们的研究结果表明发生相变在恒定值的$θ$，所示的避免水平交叉和突变的元格期望值，电能量密度，和拓扑电荷密度。一旦有足够的资源可用，这些结果原则上可以通过最近开发的（3+1）D张量网络方法和量子模拟进行交叉检查。
英文摘要：
Quantum technologies offer the prospect to efficiently simulate sign-problem afflicted regimes in lattice field theory, such as the presence of topological terms, chemical potentials, and out-of-equilibrium dynamics. In this work, we derive the (3+1)D topological $θ$-term for Abelian and non-Abelian lattice gauge theories in the Hamiltonian formulation, paving the way towards Hamiltonian-based simulations of such terms on quantum and classical computers. We further study numerically the zero-temperature phase structure of a (3+1)D U(1) lattice gauge theory with the $θ$-term via exact diagonalization for a single periodic cube. In the strong coupling regime, our results suggest the occurrence of a phase transition at constant values of $θ$, as indicated by an avoided level-crossing and abrupt changes in the plaquette expectation value, the electric energy density, and the topological charge density. These results could in principle be cross-checked by the recently developed (3+1)D tensor network methods and quantum simulations, once sufficient resources become available.
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