Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets

By using the density matrix renormalization group, we study the spin-liquid phases of spin-$1/2$ XXZ kagome antiferromagnets. We find that the emergence of spin liquid phase does not depend on the anisotropy of the XXZ interaction. In particular, the two extreme limits---Ising (strong $S^z$ interaction) and XY (zero $S^z$ interaction)---host the same spin-liquid phases as the isotropic Heisenberg model. Both the time-reversal-invariant spin liquid and the chiral spin liquid with spontaneous time-reversal symmetry breaking are obtained. We show they evolve continuously into each other by tuning the second- and third-neighbor interactions. At last, we discuss the possible implication of our results on the nature of spin liquid in nearest neighbor XXZ kagome antiferromagnets, including the most studied nearest neighbor spin-$1/2$ kagome anti-ferromagnetic Heisenberg model

Increase of entanglement by local PT -symmetric operations

Entanglement plays a central role in the field of quantum information science. It is well known that the degree of entanglement cannot be increased under local operations. Here, we show that the concurrence of a bipartite entangled state can be increased under the local PT -symmetric operation. This violates the property of entanglement monotonicity. We also use the Bell-CHSH and steering inequalities to explore this phenomenon.Comment: 6 pages, 5 figures, to appear in PRA (2014

Uniqueness and Pseudolocality Theorems of the Mean Curvature Flow

Mean curvature flow evolves isometrically immersed base manifolds $M$ in the direction of their mean curvatures in an ambient manifold $\bar{M}$. If the base manifold $M$ is compact, the short time existence and uniqueness of the mean curvature flow are well-known. For complete isometrically immersed submanifolds of arbitrary codimensions, the existence and uniqueness are still unsettled even in the Euclidean space. In this paper, we solve the uniqueness problem affirmatively for the mean curvature flow of general codimensions and general ambient manifolds. In the second part of the paper, inspired by the Ricci flow, we prove a pseudolocality theorem of mean curvature flow. As a consequence, we obtain a strong uniqueness theorem, which removes the assumption on the boundedness of the second fundamental form of the solution.Comment: 40 page

Critical behavior of the QED3_3-Gross-Neveu model: Duality and deconfined criticality

We study the critical properties of the QED$_3$-Gross-Neveu model with $2N$ flavors of two-component Dirac fermions coupled to a massless scalar field and a U(1) gauge field. For $N=1$, this theory has recently been suggested to be dual to the SU(2) noncompact CP$^1$ model that describes the deconfined phase transition between the Neel antiferromagnet and the valence bond solid on the square lattice. For $N=2$, the theory has been proposed as an effective description of a deconfined critical point between chiral and Dirac spin liquid phases, and may potentially be realizable in spin-$1/2$ systems on the kagome lattice. We demonstrate the existence of a stable quantum critical point in the QED$_3$-Gross-Neveu model for all values of $N$. This quantum critical point is shown to escape the notorious fixed-point annihilation mechanism that renders plain QED$_3$ (without scalar-field coupling) unstable at low values of $N$. The theory exhibits an upper critical space-time dimension of four, enabling us to access the critical behavior in a controlled expansion in the small parameter $\epsilon = 4-D$. We compute the scalar-field anomalous dimension $\eta_\phi$, the correlation-length exponent $\nu$, as well as the scaling dimension of the flavor-symmetry-breaking bilinear $\bar\psi\sigma^z\psi$ at the critical point, and compare our leading-order estimates with predictions of the conjectured duality.Comment: 12 pages, 7 figures, 1 table; v2: loop diagrams added, additional comments and references, published versio