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Register a new userTransition from the $mathbb{Z}_2$ spin liquid to antiferromagnetic order: spectrum on the torus
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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.
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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 distinct sectors in the space of dimer coverings, which is a signature of the topological nature of the RVB wave function. Furthermore, by calculating the reduced density matrix of a bipartition of the RVB state on an infinite cylinder and exploring its entanglement entropy, we confirm the topological nature of the RVB wave function by obtaining non-zero topological contribution, $gamma=-rm{ln} 2$, consistent with that of a $mathbb{Z}_2$ topological quantum spin liquid. We also calculate the ground-state energy of the spin-$frac{1}{2}$ antiferromagnetic Heisenberg model on the ruby lattice and compare it with the RVB energy. Finally, we construct a quantum-dimer model for the ruby lattice and discuss it as a possible parent Hamiltonian for the RVB wave function.
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 phase by interpolating between the exactly solvable parent Hamiltonian of the topological phase and an effective low-energy description of the Heisenberg model in terms of a quantum-dimer Hamiltonian. Therefore, we perform a perturbative treatment of the low-energy excitations in the topological phase including free and interacting quasi-particles. We find a phase transition out of the topological phase far from the Heisenberg point. The resulting phase is characterized by a spontaneously broken rotational symmetry and a unit cell involving six sites.
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 to be free of the sign-problem of quantum Monte Carlo. In our numerical analysis, we find as a function of $N$ a quadrupolar magnetic state and a wide range of a quantum spin liquid. A solvable large-$N$ generalization suggests that the quantum spin liquid in our original model is a gapped ${mathbb Z}_2$ topological phase. Supporting this assertion, a numerical study of the entanglement entropy in the sign free model shows a quantized topological contribution.
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, including the 12 fully symmetric nearest-neighbor $mathbb{Z}_2$ spin liquids that have been classified by Liu et al. [https://journals.aps.org/prb/abstract/10.1103/PhysRevB.100.075125]. For each class we specify the most general symmetry-allowed mean-field Hamiltonian. Additionally, we test the properties of a subset of the spin liquid ansatze by solving the mean-field equations for the spin-$1/2$ XXZ model near the antiferromagnetic Heisenberg point. We find that the ansatz with the lowest energy at mean-field level is a chiral spin liquid that breaks the screw symmetry of the lattice modulo time reversal symmetry. This state has a different symmetry than the previously studied monopole flux state. Moreover, this chiral spin liquid state has a substantially lower energy than all other symmetric spin liquid states, suggesting that it could be a stable ground state beyond the mean-field approximation employed in this work.
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 interactions. Here we report on a new frustrated member to the family, SrTb$_2$O$_4$ with a record $T_{rm N}$ = 4.28(2) K, and an experimental study of the magnetic interacting and frustrating mechanisms by polarized and unpolarized neutron scattering. The compound SrTb$_2$O$_4$ displays an incommensurate antiferromagnetic (AFM) order with a transverse wave vector textbf{Q}$^{rm 0.5 K}_{rm AFM}$ = (0.5924(1), 0.0059(1), 0) albeit with partially-ordered moments, 1.92(6) $mu_{rm B}$ at 0.5 K, stemming from only one of the two inequivalent Tb sites mainly by virtue of their different octahedral distortions. The localized moments are confined to the emph{bc} plane, 11.9(66)$^circ$ away from the emph{b} axis probably by single-ion anisotropy. We reveal that this AFM order is dominated mainly by dipole-dipole interactions and disclose that the octahedral distortion, nearest-neighbour (NN) ferromagnetic (FM) arrangement, different next NN FM and AFM configurations, and in-plane anisotropic spin correlations are vital to the magnetic structure and associated multiple frustrations. The discovery of the thus far highest AFM transition temperature renders SrTb$_2$O$_4$ a new friendly frustrated platform in the family for exploring the nature of magnetic interactions and frustrations.
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