Theory of deconfined pseudocriticality
Ruochen Ma, Chong Wang
Abstract
It has been proposed that the deconfined criticality in $(2+1)d$---the quantum phase transition between a N\'eel antiferromagnet and a valence-bond solid (VBS)---may actually be pseudocritical, in the sense that it is a weakly first-order transition with a generically long correlation length. The underlying field theory of the transition would be a slightly complex (nonunitary) fixed point as a result of fixed points annihilation. This proposal was motivated by existing numerical results from large scale Monte Carlo simulations as well as a conformal bootstrap. However, an actual theory of such a complex fixed point, incorporating key features of the transition such as the emergent SO(5) symmetry, is so far absent. Here we propose a Wess-Zumino-Witten (WZW) nonlinear sigma model with level $k=1$, defined in $2+\ensuremath{\epsilon}$ dimensions, with target space ${S}^{3+\ensuremath{\epsilon}}$ and global symmetry $\text{SO}(4+\ensuremath{\epsilon})$. This gives a formal interpolation between the deconfined criticality at $d=3$ and the $\text{SU}{(2)}_{1}$ WZW theory at $d=2$ describing the spin-$1/2$ Heisenberg chain. The theory can be formally controlled, at least to leading order, in terms of the inverse of the WZW level $1/k$. We show that at leading order there is a fixed point annihilation at ${d}^{*}\ensuremath{\approx}2.77$, with complex fixed points above this dimension including the physical $d=3$ case. The pseudocritical properties such as correlation length, scaling dimensions, and the drifts of scaling dimensions as the system size increases, calculated crudely to leading order, are qualitatively consistent with existing numerics.