Study of the 1D anisotropic Kondo necklace model at criticality via an entanglement entropy estimator

We use an estimator of quantum criticality based on the entanglement entropy to discuss the ground state properties of the 1D anisotropic Kondo necklace model. We found that the T=0 phase diagram of the model is described by a critical line separating an antiferromagnetic phase from a Kondo singlet state. Moreover we calculate the conformal anomaly on the critical line and obtained that c tends to 0.5 as the thermodynamic limit is reached. We conclude that these transitions belong to Ising universality class being, therefore, second order transitions instead of infinite order as claimed before.Comment: 11 pages, 5 figure

Spin-3/2 random quantum antiferromagnetic chains

We use a modified perturbative renormalization group approach to study the random quantum antiferromagnetic spin-3/2 chain. We find that in the case of rectangular distributions there is a quantum Griffiths phase and we obtain the dynamical critical exponent $Z$ as a function of disorder. Only in the case of extreme disorder, characterized by a power law distribution of exchange couplings, we find evidence that a random singlet phase could be reached. We discuss the differences between our results and those obtained by other approaches.Comment: 4 page

Nonviolation of Bell's Inequality in Translation Invariant Systems

The nature of quantum correlations in strongly correlated systems has been a subject of intense research. In particular, it has been realized that entanglement and quantum discord are present at quantum phase transitions and able to characterize it. Surprisingly, it has been shown for a number of different systems that qubit pairwise states, even when highly entangled, do not violate Bell's inequalities, being in this sense local. Here we show that such a local character of quantum correlations is in fact general for translation invariant systems and has its origins in the monogamy trade-off obeyed by tripartite Bell correlations. We illustrate this result in a quantum spin chain with a soft breaking of translation symmetry. In addition, we extend the monogamy inequality to the $N$-qubit scenario, showing that the bound increases with $N$ and providing examples of its saturation through uniformly generated random pure states.Comment: Published erratum added at the en

Griffiths phases in the strongly disordered Kondo necklace model

The effect of strong disorder on the one-dimensional Kondo necklace model is studied using a perturbative real-space renormalization group approach which becomes asymptotically exact in the low energy limit. The phase diagram of the model presents a random quantum critical point separating two phases; the {\em random singlet phase} of a quantum disordered XY chain and the random Kondo phase. We also consider an anisotropic version of the model and show that it maps on the strongly disordered transverse Ising model. The present results provide a rigorous microscopic basis for non-Fermi liquid behavior in disordered heavy fermions due to Griffiths phases.Comment: 4 pages, 4 figure

Nonadditive entropy for random quantum spin-S chains

We investigate the scaling of Tsallis entropy in disordered quantum spin-S chains. We show that an extensive scaling occurs for specific values of the entropic index. Those values depend only on the magnitude S of the spins, being directly related with the effective central charge associated with the model.Comment: 5 pages, 7 figures. v3: Minor corrections and references updated. Published versio

Breakdown of the perturbative renormalization group for S >= 1 random antiferromagnetic spin chains

We investigate the application of a perturbative renormalization group (RG) method to random antiferromagnetic Heisenberg chains with arbitrary spin size. At zero temperature we observe that initial arbitrary probability distributions develop a singularity at J=0, for all values of spin S. When the RG method is extended to finite temperatures, without any additional assumptions, we find anomalous results for S >= 1. These results lead us to conclude that the perturbative scheme is not adequate to study random chains with S >= 1. Therefore a random singlet phase in its more restrictive definition is only assured for spin-1/2 chains.Comment: 5 pages, 3 figures. To appear in Physical Review

Phase diagram of the random Heisenberg antiferromagnetic spin-1 chain

We present a new perturbative real space renormalization group (RG) to study random quantum spin chains and other one-dimensional disordered quantum systems. The method overcomes problems of the original approach which fails for quantum random chains with spins larger than S=1/2. Since it works even for weak disorder we are able to obtain the zero temperature phase diagram of the random antiferromagnetic Heisenberg spin-1 chain as a function of disorder. We find a random singlet phase for strong disorder and as disorder decreases, the system shows a crossover from a Griffiths to a disordered Haldane phase.Comment: 4 pages, 10 figure

Random Antiferromagnetic SU(N) Spin Chains

We analyze random isotropic antiferromagnetic SU(N) spin chains using the real space renormalization group. We find that they are governed at low energies by a universal infinite randomness fixed point different from the one of random spin-1/2 chains. We determine analytically the important exponents: the energy-length scale relation is $\Omega\sim\exp(-L^{\psi})$, where $\psi=1/N$, and the mean correlation function is given by $\bar{C_{ij}}\sim(-1)^{i-j}/|i-j|^{\phi}$, where $\phi=4/N$. Our analysis shows that the infinite-N limit is unable to capture the behavior obtained at any finite N.Comment: 4 pages, 3 figure

Phase transitions in the two-dimensional super-antiferromagnetic Ising model with next-nearest-neighbor interactions

We use Monte Carlo and Transfer Matrix methods in combination with extrapolation schemes to determine the phase diagram of the 2D super-antiferromagnetic (SAF) Ising model with next-nearest-neighbor (nnn) interactions in a magnetic field. The interactions between nearest-neighbor (nn) spins are ferromagnetic along x, and antiferromagnetic along y. We find that for sufficiently low temperatures and fields, there exists a region limited by a critical line of 2nd-order transitions separating a SAF phase from a magnetically induced paramagnetic phase. We did not find any region with either first-order transition or with re-entrant behavior. The nnn couplings produce either an expansion or a contraction of the SAF phase. Expansion occurs when the interactions are antiferromagnetic, and contraction when they are ferromagnetic. There is a critical ratio R_c = 1/2 between nnn- and nn-couplings, beyond which the SAF phase no longer exists.Comment: 12 pages, 10 figure