A theory of deconfined pseudo-criticality

TL;DR

This paper proposes a theoretical model using a Wess-Zumino-Witten nonlinear sigma model to explain the pseudo-criticality observed in deconfined quantum critical points, aligning with numerical results.

Contribution

It introduces a controlled field theory framework for deconfined pseudo-criticality, incorporating emergent symmetries and fixed point annihilation in a $2+oldsymbol{ extit{ extepsilon}}$-dimensional setting.

Findings

Fixed point annihilation at $d^\ast\approx2.77$

Complex fixed points in $d=3$ consistent with pseudo-criticality

Qualitative agreement with numerical results on correlation length and scaling dimensions

Abstract

It has been proposed that the deconfined criticality in $(2+1)d$ -- the quantum phase transition between a Neel anti-ferromagnet and a valence-bond-solid (VBS) -- may actually be pseudo-critical, 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 (non-unitary) 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 conformal bootstrap. However, an actual theory of such 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 $2+\epsilon$ dimensions, with target space $S^{3+\epsilon}$ and global symmetry $SO(4+\epsilon)$. This gives a formal interpolation between the deconfined criticality at $d=3$ and the $SU(2)_1$ 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 $d^*\approx2.77$, with complex fixed points above this dimension including the physical $d=3$ case. The pseudo-critical 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.