Competing pair density wave orders in the square lattice t-J model

Competing orders in high-Tc cuprates have been intensively studied in the past two decades. The competition among stripe, charge density wave (CDW) and pair density wave (PDW) orders is closely related to the key mechanism of high temperature superconductivity. As the simplest model for high-Tc cuprates, we numerically investigate the t-J model on a square lattice using the fermionic infinite projected entangled pair state (iPEPS) method. We discover several new types of PDW states in the low energy subspace of the t-J model, in addition to the well known d-wave state, stripe states and the recently discovered fluctuating diagonal PDW state (arXiv 2404.16770). Their complex competition in underdoped region suggests the possibility of a highly fluctuating Cooper-pairs quantum liquid state arising from their mixing and superposition, which may provide new insights into the pseudogap phenomenon.