Technical University of Munich, School of CIT, Department of Informatics, Boltzmannstraße 3, 85748 Garching, Germany.
Technical University of Munich, Institute for Advanced Study, Lichtenbergstraße 2a, 85748 Garching, Germany.
Phys Rev Lett. 2023 Mar 3;130(9):090601. doi: 10.1103/PhysRevLett.130.090601.
We extend the concept of dual unitary quantum gates introduced in Phys. Rev. Lett. 123, 210601 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.210601 to quantum lattice models in 2+1 dimensions, by introducing and studying ternary unitary four-particle gates, which are unitary in time and both spatial dimensions. When used as building blocks of lattice models with periodic boundary conditions in time and space (corresponding to infinite temperature states), dynamical correlation functions exhibit a light ray structure. We also generalize solvable matrix product states introduced in Phys. Rev. B 101, 094304 (2020)PRBMDO2469-995010.1103/PhysRevB.101.094304 to two spatial dimensions with cylindrical boundary conditions, by showing that the analogous solvable projected entangled pair states can be identified with matrix product unitaries. In the resulting tensor network for evaluating equal-time correlation functions, the bulk ternary unitary gates cancel out. We delineate and implement a numerical algorithm for computing such correlations by contracting the remaining tensors.
我们将 Phys. Rev. Lett. 123, 210601 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.210601 中引入的双幺正量子门的概念扩展到 2+1 维的量子格点模型中，通过引入和研究三进制幺正四粒子门，该门在时间和两个空间维度上都是幺正的。当作为具有时间和空间周期性边界条件的格点模型的构建块（对应于无限温度状态）时，动力学相关函数表现出光线结构。我们还将 Phys. Rev. B 101, 094304 (2020)PRBMDO2469-995010.1103/PhysRevB.101.094304 中的可解矩阵乘积态推广到具有圆柱边界条件的两个空间维度，通过证明类似的可解投影纠缠对态可以与矩阵乘积幺正态相匹配。在评估等时相关函数的张量网络中，体三进制幺正门相互抵消。我们通过收缩剩余张量来阐明并实现计算这些相关性的数值算法。
