Cascade of phase transitions in the vicinity of a quantum critical point

We study the timely issue of charge order checkerboard patterns observed in a variety of cuprate superconductors. We suggest a minimal model in which strong quantum fluctuations in the vicinity of a single antiferromagnetic quantum critical point generate the complexity seen in the phase diagram of cuprates superconductors and, in particular, the evidenced charge order. The Fermi surface is found to fractionalize into hot spots and antinodal regions, where physically different gaps are formed. In the phase diagram, this is reflected by three transition temperatures for the formation of pseudogap, charge density wave, and superconductivity (or quadrupole density wave if a sufficiently strong magnetic field is applied). The charge density wave is characterized by modulations along the bonds of the CuO lattice with wave vectors connecting points of the Fermi surface in the antinodal regions. These features, previously observed experimentally, are so far unique to the quantum critical point in two spatial dimensions and shed a different light on the interplay between strongly fluctuating critical modes and conduction electrons in high-temperature superconductors.