Continuous phase transitions exhibit richer critical phenomena on the surface
than in the bulk, because distinct surface universality classes can be realized
at the same bulk critical point by tuning the surface interactions. The
exploration of surface critical behavior provides a window looking into
higher-dimensional boundary conformal field theories. In this work, we study
the surface critical behavior of a two-dimensional (2D) quantum critical
Heisenberg model by tuning the surface coupling strength, and discover a direct
special transition on the surface from the ordinary phase into an extraordinary
phase. The extraordinary phase has a long-range antiferromagnetic order on the
surface, in sharp contrast to the logarithmically decaying spin correlations in
the 3D classical O(3) model. The special transition point has a new set of
critical exponents, ysβ=0.86(4) and Ξ·β₯β=β0.32(1), which are
distinct from the special transition of the classical O(3) model and indicate a
new surface universality class of the 3D O(3) Wilson-Fisher theory.Comment: 5 pages, 3 figures; v2: substantially revised, new fitting form in
extraordinary phas