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We describe the finite-size spectrum in the vicinity of the quantum critical point between a $mathbb{Z}_2$ spin liquid and a coplanar antiferromagnet on the torus. We obtain the universal evolution of all low-lying states in an antiferromagnet with global SU(2) spin rotation symmetry, as it moves from the 4-fold topological degeneracy in a gapped $mathbb{Z}_2$ spin liquid to the Anderson tower-of-states in the ordered antiferromagnet. Due to the existence of nontrivial order on either side of this transition, this critical point cannot be described in a conventional Landau-Ginzburg-Wilson framework. Instead it is described by a theory involving fractionalized degrees of freedom known as the O$(4)^ast$ model, whose spectrum is altered in a significant way by its proximity to a topologically ordered phase. We compute the spectrum by relating it to the spectrum of the O$(4)$ Wilson-Fisher fixed point on the torus, modified with a selection rule on the states, and with nontrivial boundary conditions corresponding to topological sectors in the spin liquid. The spectrum of the critical O($2N$) model is calculated directly at $N=infty$, which then allows a reconstruction of the full spectrum of the O($2N)^ast$ model at leading order in 1/N. This spectrum is a unique characteristic of the vicinity of a fractionalized quantum critical point, as well as a universal signature of the existence of proximate $mathbb{Z}_2$ topological and antiferromagnetically-ordered phases, and can be compared with numerical computations on quantum antiferromagnets on two dimensional lattices.
We construct a short-range resonating valence-bond state (RVB) on the ruby lattice, using projected entangled-pair states (PEPS) with bond dimension $D=3$. By introducing non-local moves to the dimer patterns on the torus, we distinguish four distinc
The $mathbb{Z}_2$ topological phase in the quantum dimer model on the Kagome-lattice is a candidate for the description of the low-energy physics of the anti-ferromagnetic Heisenberg model on the same lattice. We study the extend of the topological p
We present a study of a simple model antiferromagnet consisting of a sum of nearest neighbor SO($N$) singlet projectors on the Kagome lattice. Our model shares some features with the popular $S=1/2$ Kagome antiferromagnet but is specifically designed
We give a complete classification of fully symmetric as well as chiral $mathbb{Z}_2$ quantum spin liquids on the pyrochlore lattice using a projective symmetry group analysis of Schwinger boson mean-field states. We find 50 independent ansatze, inclu
The N$acute{rm e}$el temperature of the new frustrated family of Sremph{RE}$_2$O$_4$ (emph{RE} = rare earth) compounds is yet limited to $sim$ 0.9 K, which more or less hampers a complete understanding of the relevant magnetic frustrations and spin i