We study the competition between stripe states with different periods and a uniform d-wave superconducting state in the extended 2D Hubbard model at 1/8 hole doping using infinite projected entangled-pair states (iPEPS). With increasing strength of negative next-nearest neighbor hopping t , the preferred period of the stripe decreases. For the values of t predicted for cuprate high-Tc superconductors, we find stripes with a period 4 in the charge order, in agreement with experiments. Superconductivity in the period 4 stripe is suppressed at 1/8 doping. Only at larger doping, 0.18 δ < 0.25, the period 4 stripe exhibits coexisting d-wave superconducting order. The uniform d-wave state is only favored for sufficiently large positive t .

We present an extension of a framework for simulating single quasiparticle or collective excitations on top of strongly correlated quantum many-body ground states using infinite projected entangled pair states, a tensor network ansatz for two-dimensional wave functions in the thermodynamic limit. Our approach performs a systematic summation of locally perturbed states in order to obtain excited eigenstates localized in momentum space, using the corner transfer matrix method, and generalizes the framework to arbitrary unit cell sizes, the implementation of global Abelian symmetries and fermionic systems. Results for several test cases are presented, including the transverse Ising model, the spin-1 /2 Heisenberg model, and a free fermionic model, to demonstrate the capability of the method to accurately capture dispersions. We also provide insight into the nature of excitations at the k = (π, 0) point of the Heisenberg model.

The excitation ansatz for tensor networks is a powerful tool for simulating the low-lying quasiparticle excitations above ground states of strongly correlated quantum many-body systems. Recently, the two-dimensional tensor network class of infinite projected entangled-pair states gained new ground state optimization methods based on automatic differentiation, which are at the same time highly accurate and simple to implement. Naturally, the question arises whether these new ideas can also be used to optimize the excitation ansatz, which has recently been implemented in two dimensions as well. In this paper, we describe a straightforward way to reimplement the framework for excitations using automatic differentiation, and demonstrate its performance for the Hubbard model at half filling.