We study, for the first time, the effects of strong short-range electron-electron interactions in generic Rarita-Schwinger-Weyl semimetals hosting spin-3/2\ electrons with linear dispersion at a fourfold band crossing point. The emergence of this novel quasiparticle, which is absent in high-energy physics, has recently been confirmed experimentally in the solid state. We combine symmetry considerations and a perturbative renormalization group analysis to discern three interacting phases that are prone to emerge in the strongly correlated regime: The chiral topological semimetal breaks a\ Z2\ symmetry and features four Weyl nodes of monopole charge\ +1\ located at vertices of a tetrahedron in momentum space. The\ s-wave superconducting state opens a Majorana mass gap for the fermions and is the leading superconducting instability. The Weyl semimetal phase removes the fourfold degeneracy and creates two Weyl nodes with either equal or opposite chirality depending on the anisotropy of the band structure. We find that symmetry breaking occurs at weaker coupling if the total monopole charge remains constant across the transition.

}, doi = {10.1103/PhysRevLett.124.127602}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.124.127602}, author = {Boettcher, Igor} } @article {17096, title = {Quantum simulation of hyperbolic space with circuit quantum electrodynamics: From graphs to geometry}, journal = {Phys. Rev. A}, volume = {102}, year = {2020}, month = {Sep}, pages = {032208}, abstract = {We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. The underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a table-top quantum simulation of quantum physics in curved background. Our mapping provides a computational tool to determine observables of the discrete system even for large lattices, where exact diagonalization fails. As an application and proof of principle we quantitatively reproduce the ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincar{\'e} disk, and show how conformal symmetry emerges for large lattices. This sets the stage for studying interactions and disorder on hyperbolic graphs in the future. Importantly, our analysis reveals that even relatively small discrete hyperbolic lattices emulate the continuous geometry of negatively curved space, and thus can be used to experimentally resolve fundamental open problems at the interface of interacting many-body systems, quantum field theory in curved space, and quantum gravity.

}, keywords = {hyperbolic geometry, quantum simulation}, doi = {10.1103/PhysRevA.102.032208}, url = {https://link.aps.org/doi/10.1103/PhysRevA.102.032208}, author = {Boettcher, Igor and Bienias, Przemyslaw and Belyansky, Ron and Kollar, Alicia J. and Gorshkov, Alexey V.} } @article {ISI:000483803100006, title = {Ground state of the three-dimensional BCS d-wave superconductor}, journal = {Phys. Rev. B}, volume = {100}, number = {10}, year = {2019}, month = {SEP 4}, pages = {104503}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We determine the mean-field ground state of the three-dimensional rotationally symmetric d-wave (l = 2) superconductor at weak coupling. It is a noninert state, invariant under the symmetry C-2 only, which breaks time-reversal symmetry almost maximally, and features a high but again less-than-maximal average magnetization. The state obtained by minimization of the expanded sixth-order Ginzburg-Landau free energy is found to be an excellent approximation to the true ground state. The coupling to a parasitic s-wave component has only a minuscule quantitative and no qualitative effect on the ground state.}, issn = {2469-9950}, doi = {10.1103/PhysRevB.100.104503}, author = {Herbut, Igor F. and Boettcher, Igor and Mandal, Subrata} } @article {ISI:000462898900011, title = {Optical response of Luttinger semimetals in the normal and superconducting states}, journal = {Phys. Rev. B}, volume = {99}, number = {12}, year = {2019}, month = {MAR 25}, pages = {125146}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We investigate the optical response properties of three-dimensional Luttinger semimetals with the Fermi energy close to a quadratic band touching point. In particular, in order to address recent experiments on the spectroscopy of pyrochlore iridates and half-Heusler superconductors, we derive expressions for the optical conductivity in both the normal and general superconducting states in the linear response regime within the random phase approximation. The response functions can be decomposed into contributions from intraband and interband transitions, the latter comprising a genuine signature of the quadratic band touching point. We demonstrate the importance of interband transitions in the optical response in the normal state both in the homogeneous and quasistatic limit. Our analysis reveals a factorization property of the homogeneous conductivity in the spatially anisotropic case and the divergence of the conductivity for strong spatial anisotropy. In the quasistatic limit, the response is dominated by interband transitions and significantly different from systems with a single parabolic band. As an applications of the formalism in the superconducting state we compute the optical conductivity and superfluid density for the s-wave singlet superconducting case for both finite and vanishing chemical potential.}, issn = {2469-9950}, doi = {10.1103/PhysRevB.99.125146}, author = {Boettcher, Igor} }