Transition from the Z(2) spin liquid to antiferromagnetic order: Spectrum on the torus

Article

关键词: QUANTUM ANTIFERROMAGNETS;    SYMMETRY-BREAKING;    PHASE;    LATTICE;    STATES;   

DOI  :  10.1103/PhysRevB.94.085134

来源: SCIE

【 摘 要 】

We describe the finite-size 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 low-lying 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 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)* 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 = infinity, which then allows a reconstruction of the full spectrum of the O(2N)* 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 two-dimensional lattices.

【 授权许可】

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