Quantum Fluctuations of a Nearly Critical Heisenberg Spin Glass

We describe the interplay of quantum and thermal fluctuations in the infinite-range Heisenberg spin glass. This model is generalized to SU(N) symmetry, and we describe the phase diagram as a function of the spin S and the temperature T. The model is solved in the large N limit and certain universal critical properties are shown to hold to all orders in 1/N. For large S, the ground state is a spin glass, but quantum effects are crucial in determining the low T thermodynamics: we find a specific heat linear in T and a local spectral density of spin excitations linear in frequency for a spin glass state which is marginally stable to fluctuations in the replicon modes. For small S, the spin-glass order is fragile, and a spin-liquid state dominates the properties over a significant range of temperatures and frequencies. We argue that the latter state may be relevant in understanding the properties of strongly-disordered transition metal and rare earth compounds.Comment: 23 pages.Revtex

Width of the longitudinal magnon in the vicinity of the O(3) quantum critical point

We consider a three-dimensional quantum antiferromagnet in the vicinity of a quantum critical point separating the magnetically ordered and the magnetically disordered phases. A specific example is TlCuCl$_3$ where the quantum phase transition can be driven by hydrostatic pressure and/or by external magnetic field. As expected two transverse and one longitudinal magnetic excitation have been observed in the pressure driven magnetically ordered phase. According to the experimental data, the longitudinal magnon has a substantial width, which has not been understood and has remained a puzzle. In the present work, we explain the mechanism for the width, calculate the width and relate value of the width with parameters of the Bose condensate of magnons observed in the same compound. The method of an effective quantum field theory is employed in the work.Comment: 6 pages, 3 figure

Enhancement of Tc in the Superconductor-Insulator Phase Transition on Scale-Free Networks

A road map to understand the relation between the onset of the superconducting state with the particular optimum heterogeneity in granular superconductors is to study a Random Tranverse Ising Model on complex networks with a scale-free degree distribution regularized by and exponential cutoff p(k) \propto k^{-\gamma}\exp[-k/\xi]. In this paper we characterize in detail the phase diagram of this model and its critical indices both on annealed and quenched networks. To uncover the phase diagram of the model we use the tools of heterogeneous mean-field calculations for the annealed networks and the most advanced techniques of quantum cavity methods for the quenched networks. The phase diagram of the dynamical process depends on the temperature T, the coupling constant J and on the value of the branching ratio / where k is the degree of the nodes in the network. For fixed value of the coupling the critical temperature increases linearly with the branching ration which diverges with the increasing cutoff value \xi or value of the \gamma exponent \gamma< 3. This result suggests that the fractal disorder of the superconducting material can be responsible for an enhancement of the superconducting critical temperature. At low temperature and low couplings T<<1 and J<<1, instead, we observe a different behavior for annealed and quenched networks. In the annealed networks there is no phase transition at zero temperature while on quenched network we observe a Griffith phase dominated by extremely rare events and a phase transition at zero temperature. The Griffiths critical region, nevertheless, is decreasing in size with increasing value of the cutoff \xi of the degree distribution for values of the \gamma exponents \gamma< 3.Comment: (17 pages, 3 figures

Scattering and Pairing in Cuprate Superconductors

The origin of the exceptionally strong superconductivity of cuprates remains a subject of debate after more than two decades of investigation. Here we follow a new lead: The onset temperature for superconductivity scales with the strength of the anomalous normal-state scattering that makes the resistivity linear in temperature. The same correlation between linear resistivity and Tc is found in organic superconductors, for which pairing is known to come from fluctuations of a nearby antiferromagnetic phase, and in pnictide superconductors, for which an antiferromagnetic scenario is also likely. In the cuprates, the question is whether the pseudogap phase plays the corresponding role, with its fluctuations responsible for pairing and scattering. We review recent studies that shed light on this phase - its boundary, its quantum critical point, and its broken symmetries. The emerging picture is that of a phase with spin-density-wave order and fluctuations, in broad analogy with organic, pnictide, and heavy-fermion superconductors.Comment: To appear in Volume 1 of the Annual Review of Condensed Matter Physic

Extended dual description of Mott transition beyond two-dimensional space

Motivated by recent work of Mross and Senthil [Phys. Rev. B \textbf{84}, 165126 (2011)] which provides a dual description for Mott transition from Fermi liquid to quantum spin liquid in two space dimensions, we extend their approach to higher dimensional cases, and we provide explicit formalism in three space dimensions. Instead of the vortices driving conventional Fermi liquid into quantum spin liquid states in 2D, it is the vortex lines to lead to the instability of Fermi liquid in 3D. The extended formalism can result in rich consequences when the vortex lines condense in different degrees of freedom. For example, when the vortex lines condense in charge phase degrees of freedom, the resulting effective fermionic action is found to be equivalent to that obtained by well-studied slave-particle approaches for Hubbard and/or Anderson lattice models, which confirm the validity of the extended dual formalism in 3D. When the vortex lines condense in spin phase degrees of freedom, a doublon metal with a spin gap and an instability to the unconventional superconducting pairing can be obtained. In addition, when the vortex lines condense in both phase degrees, an exotic doubled U(1) gauge theory occurs which describes a separation of spin-opposite fermionic excitations. It is noted that the first two features have been discussed in a similar way in 2D, the last one has not been reported in the previous works. The present work is expected to be useful in understanding the Mott transition happening beyond two space dimensions.Comment: 7 pages, no figure

Quantum critical transport, duality, and M-theory

We consider charge transport properties of 2+1 dimensional conformal field theories at non-zero temperature. For theories with only Abelian U(1) charges, we describe the action of particle-vortex duality on the hydrodynamic-to-collisionless crossover function: this leads to powerful functional constraints for self-dual theories. For the n=8 supersymmetric, SU(N) Yang-Mills theory at the conformal fixed point, exact hydrodynamic-to-collisionless crossover functions of the SO(8) R-currents can be obtained in the large N limit by applying the AdS/CFT correspondence to M-theory. In the gravity theory, fluctuating currents are mapped to fluctuating gauge fields in the background of a black hole in 3+1 dimensional anti-de Sitter space. The electromagnetic self-duality of the 3+1 dimensional theory implies that the correlators of the R-currents obey a functional constraint similar to that found from particle-vortex duality in 2+1 dimensional Abelian theories. Thus the 2+1 dimensional, superconformal Yang Mills theory obeys a "holographic self duality" in the large N limit, and perhaps more generally.Comment: 35 pages, 4 figures; (v2) New appendix on CFT2, corrected normalization of gauge field action, added ref

Spin-stiffness of anisotropic Heisenberg model on square lattice and possible mechanism for pinning of the electronic liquid crystal direction in YBCO

Using series expansions and spin-wave theory we calculate the spin-stiffness anisotropy $\rho_{sx}/\rho_{sy}$ in Heisenberg models on the square lattice with anisotropic couplings $J_x,J_y$. We find that for the weakly anisotropic spin-half model ($J_x\approx J_y$), $\rho_{sx}/\rho_{sy}$ deviates substantially from the naive estimate $\rho_{sx}/\rho_{sy} \approx J_x/J_y$. We argue that this deviation can be responsible for pinning the electronic liquid crystal direction, a novel effect recently discovered in YBCO. For completeness, we also study the spin-stiffness for arbitrary anisotropy $J_x/J_y$ for spin-half and spin-one models. In the limit of $J_y/J_x\to 0$, when the model reduces to weakly coupled chains, the two show dramatically different behavior. In the spin-one model, the stiffness along the chains goes to zero, implying the onset of Haldane-gap phase, whereas for spin-half the stiffness along the chains increases monotonically from a value of $0.18 J_x$ for $J_y/J_x=1$ towards $0.25 J_x$ for $J_y/J_x\to 0$. Spin-wave theory is extremely accurate for spin-one but breaks down for spin-half presumably due to the onset of topological terms.Comment: 6 pages, 3 figure

U(1) spin liquids and valence bond solids in a large-N three-dimensional Heisenberg model

We study possible quantum ground states of the Sp(N) generalized Heisenberg model on a cubic lattice with nearest-neighbor and next-nearest-neighbor exchange interactions. The phase diagram is obtained in the large-N limit and fluctuation effects are considered via appropriate gauge theories. In particular, we find three U(1) spin liquid phases with different short-range magnetic correlations. These phases are characterized by deconfined gapped spinons, gapped monopoles, and gapless ``photons''. As N becomes smaller, a confinement transition from these phases to valence bond solids (VBS) may occur. This transition is studied by using duality and analyzing the resulting theory of monopoles coupled to a non-compact dual gauge field; the condensation of the monopoles leads to VBS phases. We determine the resulting VBS phases emerging from two of the three spin liquid states. On the other hand, the spin liquid state near J_1 \approx J_2 appears to be more stable against monopole condensation and could be a promising candidate for a spin liquid state in real systems.Comment: revtex file 12 pages, 17 figure

Heisenberg Uncertainty Principle as Probe of Entanglement Entropy: Application to Superradiant Quantum Phase Transitions

Quantum phase transitions are often embodied by the critical behavior of purely quantum quantities such as entanglement or quantum fluctuations. In critical regions, we underline a general scaling relation between the entanglement entropy and one of the most fundamental and simplest measure of the quantum fluctuations, the Heisenberg uncertainty principle. Then, we show that the latter represents a sensitive probe of superradiant quantum phase transitions in standard models of photons such as the Dicke Hamiltonian, which embodies an ensemble of two-level systems interacting with one quadrature of a single and uniform bosonic field. We derive exact results in the thermodynamic limit and for a finite number N of two-level systems: as a reminiscence of the entanglement properties between light and the two-level systems, the product $\Delta x\Delta p$ diverges at the quantum critical point as $N^{1/6}$. We generalize our results to the double quadrature Dicke model where the two quadratures of the bosonic field are now coupled to two independent sets of two level systems. Our findings, which show that the entanglement properties between light and matter can be accessed through the Heisenberg uncertainty principle, can be tested using Bose-Einstein condensates in optical cavities and circuit quantum electrodynamicsComment: 7 pages, 3 figures. Published Versio

Two-spin subsystem entanglement in spin 1/2 rings with long range interactions

We consider the two-spin subsystem entanglement for eigenstates of the Hamiltonian $$H= \sum_{1\leq j< k \leq N} (\frac{1}{r_{j,k}})^{\alpha} {\mathbf \sigma}_j\cdot {\mathbf \sigma}_k$$ for a ring of $N$ spins 1/2 with asssociated spin vector operator $(\hbar /2){\bf \sigma}_j$ for the $j$-th spin. Here $r_{j,k}$ is the chord-distance betwen sites $j$ and $k$. The case $\alpha =2$ corresponds to the solvable Haldane-Shastry model whose spectrum has very high degeneracies not present for $\alpha \neq 2$. Two spin subsystem entanglement shows high sensistivity and distinguishes $\alpha =2$ from $\alpha \neq 2$. There is no entanglement beyond nearest neighbors for all eigenstates when $\alpha =2$. Whereas for $\alpha \neq 2$ one has selective entanglement at any distance for eigenstates of sufficiently high energy in a certain interval of $\alpha$ which depends on the energy. The ground state (which is a singlet only for even $N$) does not have entanglement beyond nearest neighbors, and the nearest neighbor entanglement is virtually independent of the range of the interaction controlled by $\alpha$.Comment: 16 figure