Finding the ground states of symmetric infinite-dimensional Hamiltonians: explicit constrained optimizations of tensor networks

Abstract

Understanding extreme non-locality in many-body quantum systems can help resolve questions in thermostatistics and laser physics. The existence of symmetry selection rules for Hamiltonians with non-decaying terms on infinite-size lattices can lead to finite energies per site, which deserves attention. Here, we present a tensor network approach to construct the ground states of nontrivial symmetric infinite-dimensional spin Hamiltonians based on constrained optimizations of their infinite matrix product states description, which contains no truncation step (offering a very simple mathematical structure) at the cost of slightly higher polynomial complexity in comparison to existing methods. Our proposed algorithm is in part equivalent to the more generic and wellestablished solvers of infinite density-matrix renormalization-group and variational uniform matrix product states, which are, in principle, capable of precisely representing the ground states of such infinite-range-interacting many-body systems. However, we employ some mathematical simplifications that only allow for efficient brute-force optimizations of tensor-network matrices for the specific cases of highly-symmetric infinite-size infinite-range models. As a toy-model example, we showcase the effectiveness and explain some features of our method by finding the ground state of the U(1)-symmetric infinite-dimensional antiferromagnetic XX Heisenberg model. arXiv:1910.10370v2 [cond-mat.str-el]