Modeling the pseudogap metallic state in Cuprates: quantum disordered pair density wave and hidden bosonic Mott insulator

We present a way to quantum-disorder a pair density wave, and propose it to be a candidate of the effective low-energy description of the pseudogap metal which may reveal itself in a sufficiently high magnetic field to suppress the d-wave pairing. The ground state we construct is a small-pocket Fermi liquid with a hidden bosonic Mott insulator in the density-wave-enlarged unit cell. At low energy, the charge density is mainly carried by charge $2e$ bosons, which develop a small insulating gap. We discuss a number of experimental consequences. Optical excitation across the boson gap can explain the onset of mid infra-red absorption reported long ago. The interplay between the electron and the small-gap boson results in a characteristic electron spectral function consistent with ARPES. We also postulate a secondary magnetization density wave along (1,1) direction which breaks time-reversal symmetry, mirror symmetry, and $C_4$ rotation. Our treatment of fluctuating pair density wave provides a non-perturbative mechanism of gap generation on part of the Fermi surface, which can be generalized to other fluctuating orders.