Gradient-Based Algorithms for Infinite Strip Tensor Network States

Matrix-product state (MPS) methods have proven to be successful numerical and analytical tools for studying one-dimensional (1D) quantum many-body systems. MPS methods are also used extensively for systems on quasi-two-dimensional (2D) geometries, e.g., infinite cylinder, despite the exponential scaling in the computational complexity in system width. In this work, we consider the setup of 2D tensor network states (TNS) on finite by infinite lattices, which differs from the typical setup of finite by finite or infinite by infinite geometries. We develop gradient-based algorithms with both 2D TNS and 2D isometric TNS (isoTNS) for finding the ground states of the given Hamiltonian and finding the state with the maximum overlap with the given state. The latter algorithm leads to the applications including (i) quantum state compression, (ii) transforming TNS into isoTNS, and (iii) time evolution algorithm. We benchmark the aforementioned algorithms on the transverse field Ising model and compare the result with the MPS-based algorithm and the isoTNS-based algorithm.