Holes in Heisenberg antiferromagnets

In this Brief Report we show that a recent model proposed by Shankar [Phys. Rev. Lett. 63, 203 (1989)], describing the motion of holes in quantum antiferromagnets is equivalent to the Schwinger model [Phys. Rev. 128, 2425 (1962)] in 1+1 dimensions. Some exact results are deduced. In addition to the superconducting long-range order found by Shankar, it is shown that there is a 2${\mathit{p}}_{\mathit{F}}$ hole density wave existing with the superconducting pairing instability.