Cooperative Secret Communication with Artificial Noise in Symmetric Interference Channel

We consider the symmetric Gaussian interference channel where two users try to enhance their secrecy rates in a cooperative manner. Artificial noise is introduced along with useful information. We derive the power control and artificial noise parameter for two kinds of optimal points, max-min point and single user point. It is shown that there exists a critical value $P_c$ of the power constraint, below which the max-min point is an optimal point on the secrecy rate region, and above which time-sharing between single user points achieves larger secrecy rate pairs. It is also shown that artificial noise can help to enlarge the secrecy rate region, in particular on the single user point.Comment: 3 pages, 3 figures, to appear in IEEE Communications Letter

Can Hubbard model resist electric current?

It is claimed by a recent quantum Monte Carlo simulation that the linear-in-temperature DC resistivity observed in the high-$T_{c}$ cuprate superconductors can be reproduced in the pure two dimensional Hubbard model\cite{Huang}. Here we show perturbatively that such a translational invariant electronic model can not support a steady state current in the presence of a uniform electric field at any finite temperature. Instead, the Hubbard model is perfectly conducting in the linear response regime and will undergo Bloch oscillation at finite electric field for any finite temperature. Nevertheless, the quantum Monte Carlo simulation can provide us the key information on the temperature dependence of the Drude weight, a quantity of central importance in the holographic description of the transport properties of the strange metal phase.Comment: 5 pages, 0 figures, new arguments based on emergent symmetry and related anomaly adde

Instability of the U(1)U(1) spin liquid with a large spinon Fermi surface in the Heisenberg-ring exchange model on the triangular lattice

It is widely believed that the $U(1)$ spin liquid with a large spinon Fermi surface(SFS state) can be realized in the spin-$\frac{1}{2}$ $J_{1}-J_{4}$ model on the triangular lattice, when the ring exchange coupling $J_{4}$ is sufficiently strong to suppress the 120 degree magnetic ordered state. This belief is supported by many variational studies on this model and seems to be consistent with observations on the organic spin liquid materials such as $\kappa$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$, a system that is close to Mott transition and thus has large ring exchange coupling. Here we show through a systematic variational search that such a state is never favored in the $J_{1}-J_{4}$ model on the triangular lattice. Instead, a state with broken spatial symmetry is favored in the most probable parameter regime for the SFS state, with an energy much lower than that of the SFS state and other previously proposed variational states. More specifically, we find that for $J_{4}\ge 0.09J_{1}$, the system favors a valence bond solid state with a $4\times6$ period in its local spin correlation pattern, with a variational energy that is about $5\%$ lower than that of the SFS state. This state is separated form the $\pi$-flux state for $J_{4}\le 0.045J_{1}$ by an intermediate valence bond solid state with a zigzag pattern in its local spin correlation. We find that the variational phase digram is in qualitative agreement with that obtained from exact diagonalization on a $6\times6$ cluster.Comment: 16 pages, 17 figure

Strong relevance of Zinc impurity in the spin-12\frac{1}{2} Kagome quantum antiferromagnets: a variational study

Copper hydroxyhalide materials herbertsmithite ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$ and Zn-barlowite ZnCu$_{3}$(OH)$_{6}$FrBr are thought to be the best realizations of the spin-$\frac{1}{2}$ Kagome quantum antiferromagnetic Heisenberg model and are widely believed to host a spin liquid ground state. However, the exact nature of such a novel state of matter is still under strong debate, partly due to the complication related to the occupation disorder between the Zinc and the Copper ions in these systems. In particular, recent nuclear magnetic resonance measurements indicate that the magnetic response of the Kagome plane is significantly spatial inhomogeneous, even though the content of the misplaced Zinc or Copper ions is believed to be very small. Here we use extensive variational optimization to show that the well known $U(1)$-Dirac spin liquid state is extremely sensitive to the introduction of the nonmagnetic Zinc impurity in the Kagome plane. More specifically, we find that the Zinc impurities can significantly reorganize the local spin correlation pattern around them and induce strong spatial oscillation in the magnetic response of the system. We argue that this is a general trend in highly frustrated quantum magnet systems, in which the nonmagnetic impurity may act as strongly relevant perturbation on the emergent resonating valence bond structure in their spin liquid ground state. We also argue that the strong spatial oscillation in the magnetic response should be attributed to the free moment released by the doped Zinc ions and may serve as the smoking gun evidence for the Dirac node in the $U(1)$ Dirac spin liquid state on the Kagome lattice.Comment: 12 pages, 10 figure

Secure Beamforming for MIMO Two-Way Communications with an Untrusted Relay

This paper studies the secure beamforming design in a multiple-antenna three-node system where two source nodes exchange messages with the help of an untrusted relay node. The relay acts as both an essential signal forwarder and a potential eavesdropper. Both two-phase and three-phase two-way relay strategies are considered. Our goal is to jointly optimize the source and relay beamformers for maximizing the secrecy sum rate of the two-way communications. We first derive the optimal relay beamformer structures. Then, iterative algorithms are proposed to find source and relay beamformers jointly based on alternating optimization. Furthermore, we conduct asymptotic analysis on the maximum secrecy sum-rate. Our analysis shows that when all transmit powers approach infinity, the two-phase two-way relay scheme achieves the maximum secrecy sum rate if the source beamformers are designed such that the received signals at the relay align in the same direction. This reveals an important advantage of signal alignment technique in against eavesdropping. It is also shown that if the source powers approach zero the three-phase scheme performs the best while the two-phase scheme is even worse than direct transmission. Simulation results have verified the efficiency of the secure beamforming algorithms as well as the analytical findings.Comment: 10 figures, Submitted to IEEE Transactions on Signal Processin