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Multi-orbital quantum materials with strong interactions can host a variety of novel phases. In this work we study the possibility of interaction-driven superconductivity in the iridate compound Sr$_2$IrO$_4$ under strain and doping. We find numerous regimes of strain-induced superconductivity in which the pairing structure depends on model parameters. Spin-fluctuation mediated superconductivity is modeled by a Hubbard-Kanamori model with an effective particle-particle interaction, calculated via the random phase approximation. Magnetic orders are found using the Stoner criterion. The most likely superconducting order we find has $d$-wave pairing, predominantly in the total angular momentum, $J=1/2$ states. Moreover, an $s_{\pm}$-order which mixes different bands is found at high Hund's coupling, and at high strain anisotropic $s$- and $d$-wave orders emerge. Finally, we show that in a fine-tuned region of parameters a spin-triplet $p$-wave order exists. The combination of strong spin-orbit coupling, interactions, and a sensitivity of the band structure to strain proves a fruitful avenue for engineering new quantum phases., Comment: 26 pages, 21 figures

We study two entanglement measures in a large family of systems including incompressible quantum Hall states: the logarithmic negativity (LN), and mutual information (MI). For pure states, obtained for example from a bipartition at zero temperature, these provide distinct characterizations of the entanglement present between two spatial subregions, while for mixed states (such as at finite temperature) only the LN remains a good entanglement measure. Our focus is on regions that have corners, either adjacent or tip-touching. We first obtain non-perturbative properties regarding the geometrical dependence of the LN and MI in a large family of isotropic states, including fractional quantum Hall states. A close similarity is observed with mutual charge fluctuations, where super-universal angle dependence holds. For the MI, we make stronger statements due to strong subadditivity. We also give ramifications of our general analysis to conformal field theories (CFTs) in two spatial dimensions. We then explicitly verify these properties with integer quantum Hall states. To do so we develop two independent approaches to obtain the fermionic LN, which takes into account Fermi statistics: an overlap-matrix method, and a real-space lattice discretization. At finite temperature, we find a rapid decrease of the LN well inside the cyclotron gap at integer fillings. We further show that the LN decays faster compared to the MI at high temperatures., Comment: 15+7 pages, 16+2 figures

Strange metals appear in a wide range of correlated materials. Electronic localization-delocalization and the expected loss of quasiparticles characterize beyond-Landau metallic quantum critical points and the associated strange metals. Typical settings involve local spins. Systems that contain entwined degrees of freedom offer new platforms to realize novel forms of quantum criticality. Here, we study the fate of an SU(4) spin-orbital Kondo state in a multipolar Bose-Fermi Kondo model, which provides an effective description of a multipolar Kondo lattice, using a renormalization-group method. We show that at zero temperature a generic trajectory in the model's parameter space contains two quantum critical points, which are associated with the destruction of Kondo entanglement in the orbital and spin channels respectively. Our asymptotically exact results reveal an overall phase diagram, provide the theoretical basis to understand puzzling recent experiments of a multipolar heavy fermion metal, and point to a means of designing new forms of quantum criticality and strange metallicity in a variety of strongly correlated systems., Comment: 43 pages, 9 figures. To appear in PNAS

Quantum criticality in iron pnictides involves both the nematic and antiferromagnetic degrees of freedom, but the relationship between the two types of fluctuations has yet to be clarified. Here we study this problem in the presence of a small external uniaxial potential, which breaks the $C_4$-symmetry in the B$_{1g}$ sector. We establish an identity that connects the spin excitation anisotropy, which is the difference of the dynamical spin susceptibilities at $\vec{Q}_1=\left(\pi,0\right)$ and $\vec{Q}_2=\left(0,\pi\right)$, with the dynamical magnetic susceptibility and static nematic susceptibility. Using this identity, we introduce a scaling procedure to determine the dynamical nematic susceptibility in the quantum critical regime, and illustrate the procedure for the case of the optimally Ni-doped BaFe$_2$As$_2$[Y. Song \textit{et al.}, Phys. Rev. B 92, 180504 (2015)]. The implications of our results for the overall physics of the iron-based superconductors are discussed., Comment: 8 pages, 5 figures

Due to the interaction between topological defects of an order parameter and underlying fermions, the defects can possess induced fermion numbers, leading to several exotic phenomena of fundamental importance to both condensed matter and high energy physics. One of the intriguing outcome of induced fermion number is the presence of fluctuating competing orders inside the core of topological defect. In this regard, the interaction between fermions and skyrmion excitations of antiferromagnetic phase can have important consequence for understanding the global phase diagrams of many condensed matter systems where antiferromagnetism and several singlet orders compete. We critically investigate the relation between fluctuating competing orders and skyrmion excitations of the antiferromagnetic insulating phase of a half-filled Kondo-Heisenberg model on honeycomb lattice. By combining analytical and numerical methods we obtain exact eigenstates of underlying Dirac fermions in the presence of a single skyrmion configuration, which are used for computing induced chiral charge. Additionally, by employing this nonperturbative eigenbasis we calculate the susceptibilities of different translational symmetry breaking charge, bond and current density wave orders and translational symmetry preserving Kondo singlet formation. Based on the computed susceptibilities we establish spin Peierls and Kondo singlets as dominant competing orders of antiferromagnetism. We show favorable agreement between our findings and field theoretic predictions based on perturbative gradient expansion scheme which crucially relies on adiabatic principle and plane wave eigenstates for Dirac fermions. The methodology developed here can be applied to many other correlated systems supporting competition between spin-triplet and spin-singlet orders in both lower and higher spatial dimensions., Comment: 15 pages, 11 figures