Pair density wave state in the square lattice t-J model

Accumulating experimental evidence supports the existence of the pair density wave (PDW) state in cuprate superconductors. In such states the singlet pairing order parameter varies periodically with zero spatial average. The square lattice t-J model, which is believed to capture the essential physics of cuprates, is studied in this work using the fermionic tensor network approach, with focus on the small doping region ($delta$ < 0.10) and uniform states with bipartite structure. Using the simple update algorithm to perform imaginary time evolution on PEPS states, in addition to the usual $d_{x^2 - y^2}$-wave superconducting states, we also obtain PDW states with comparable energy.