Transition from the Z_{2} spin liquid to antiferromagnetic order: Spectrum on the torus
Abstract
We describe the finitesize spectrum in the vicinity of the quantum critical point between a Z_{2} spin liquid and a coplanar antiferromagnet on the torus. We obtain the universal evolution of all lowlying states in an antiferromagnet with global SU(2) spin rotation symmetry, as it moves from the fourfold topological degeneracy in a gapped Z_{2} spin liquid to the Anderson "towerofstates" 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 LandauGinzburgWilson framework. Instead, it is described by a theory involving fractionalized degrees of freedom known as the O (4^{) *} 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 ) WilsonFisher 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 (2 N ) model is calculated directly at N =∞ , which then allows a reconstruction of the full spectrum of the O (2^{N ) *} 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 Z_{2} topological and antiferromagnetically ordered phases, and can be compared with numerical computations on quantum antiferromagnets on twodimensional lattices.
 Publication:

Physical Review B
 Pub Date:
 August 2016
 DOI:
 10.1103/PhysRevB.94.085134
 arXiv:
 arXiv:1603.05652
 Bibcode:
 2016PhRvB..94h5134W
 Keywords:

 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 34 pages, 6 figures. (v2) Minor corrections and added discussion on the triangular torus