• Breakdown of self-averaging in the Bose glass,
  A. Hegg, F. Krüger, and P. Phillips,
  submitted to Phys. Rev. Lett. (arXiv:1303.4386).
  
  
  
  We study the square-lattice Bose-Hubbard model with bounded random on-site energies at zero temperature. Starting from a dual
  representation obtained from a strong-coupling expansion around the atomic limit, we employ a real-space block decimation scheme.
  This approach is non-perturbative in the disorder and enables us to study the renormalization-group flow of the induced random-mass
  distribution. In both insulating phases, the Mott-insulator and the Bose glass, the average mass diverges signaling short range
  superfluid correlations. The relative variance of the mass distribution distinguishes the two phases, renormalizing to zero in the Mott
  insulator and diverging in the Bose glass. Negative mass values in the tail of the distribution signal the presence of rare superfluid
  regions in the Bose glass. The breakdown of self-averaging is evidenced by the divergent relative variance, increasingly non-Gaussian
  distributions, and a correlation length exponent $\nu = 0.6 \pm 0.05$ that violates the Harris-criterion bound.
  
  
  
  
• Helical glasses near ferromagnetic quantum criticality,
  S. J. Thomson, F. Krüger, and A. G. Green,
  submitted to Phys. Rev. Lett. (arXiv:1303.4300).
  
  
  
  We study the effects of quenched charge disorder on the phase reconstruction near itinerant ferromagnetic quantum critical points in
  three spatial dimensions. Combining a replica disorder average with a fermionic version of the quantum-order-by disorder mechanism,
  we show that weak disorder destabilizes the ferromagnetic state and enhances the susceptibility towards incommensurate, spiral
  magnetic ordering. The Goldstone modes of the spiral phase are governed by a 3d-XY model. The induced disorder in the pitch of the
  spiral generates a random anisotropy for the Goldstone modes, inducing vortex lines in the phase of the helical order and rendering
  the magnetic correlations short ranged with a strongly anisotropic correlation length.
  
  
  
  
• Disordered driven coupled cavity arrays: Non-equilibrium stochastic mean-field theory,
  G. Kulaitis, F. Krüger, F. Nissen, and J. Keeling,
  Phys. Rev. A 87, 013840 (2013).
  
  
  
  We study the interplay of disorder with pumping and decay in coupled qubit-cavity arrays, the Jaynes-Cummings-Hubbard model. We
  find that relatively weak disorder can wash out the bistability present in the clean pumped system, and that moreover, the combination
  of disorder in on-site energies and decay can lead to effective phase disorder. To explore these questions, we present a non-equilibrium
  generalisation of Stochastic-Mean-Field theory, providing a simple tool to address such questions. This technique is developed for
  rather general forms of light-matter coupling, driving, dissipation, and on-site disorder, making it applicable to a wide range of systems.
  
  
  
  
• Quantum order-by-disorder driven phase reconstruction in the vicinity of ferromagnetic quantum critical points,
  U. Karahasanovic, F. Krüger, and A. G. Green,
  Phys. Rev. B 85, 165111 (2012).
  
  
  
  The formation of new phases close to itinerant electron quantum critical points has been observed experimentally in many
  compounds. We present a unified analytical model that explains the emergence of new types of order around itinerant ferromagnetic
  quantum critical points. The central idea of our analysis is that certain Fermi-surface deformations associated with the onset
  of the competing order enhance the phase-space available for low-energy quantum fluctuations and so self-consistently lower
  the free energy. We demonstrate that this quantum order-by-disorder mechanism leads to instabilities towards the formation
  of spiral and d-wave spin nematic phases close to itinerant ferromagnetic quantum critical points in three spatial dimensions.
  
  
  
  
• Quantum order-by-disorder near criticality and the secret of partial order in MnSi,
  F. Krüger, U. Karahasanovic, and A. G. Green,
  Phys. Rev. Lett. 108, 067003 (2012).
  
  
  
  The vicinity of quantum phase transitions has proven fertile ground in the search for new quantum phases. We propose a physically
  motivated and unifying description of phase reconstruction near metallic quantum-critical points using the idea of quantum
  order-by-disorder. Certain deformations of the Fermi surface associated with the onset of competing order enhance the phase
  space available for low-energy, particle-hole fluctuations and self-consistently lower the free energy. Applying the notion of quantum
  order-by-disorder to the itinerant helimagnet MnSi, we show that near to the quantum critical point, fluctuations lead to an increase
  of the spiral ordering wave vector and a reorientation away from the lattice favored directions. The magnetic ordering pattern in this
  fluctuation-driven phase is found to be in excellent agreement with the neutron scattering data in the partially ordered phase of MnSi.
  
  
  
  
• Spin-wave excitations in the ferromagnetic-metallic and in the charge, orbital and spin ordered states in
  Nd(1-x)Sr(x)MnO(3)$ with x~0.5,
  H. Ulbrich, F. Krüger, A. A. Nugroho, D. Lamago, Y. Sidis, M. Braden,
  Phys. Rev. B 84, 094453 (2011).
  
  
  
  
  Inelastic neutron scattering experiments have been performed on single crystals of Nd(1-x)Sr(x)MnO(3) with x~0.5. Colossal
  magnetoresistance (CMR) in the manganites arises from the interplay between a ferromagnetic metallic and antiferromagnetic charge
  and orbital ordered insulating state. Therefore, it appears important to compare these phases concerning their underlying magnetic
  interaction parameters. Our investigations of the spin-wave disperion in the AFM ordered state of Nd(0.5)Sr(0.5)MnO(3) exhibits a
  strongly anisotropic stiffness. The sign of the anisotropy is characteristic for the site-centered model for charge and orbital ordering in
  half-doped manganites. Within this model, linear spin-wave theory yields a perfect description of the experimental dispersion.
  Furthermore, magnetic excitations in the ferromagnetic metallic state of Nd(1-x)Sr(x)MnO(3) with x=0.49 and x=0.50 exhibit
  nearly the same magnon dispersion which can be described with a Heisenberg model including nearest-neighbor interactions.
  
  
  
  
• Two distinct Mott-Insulator to Bose-glass transitions and breakdown of self averaging in the disordered
  Bose-Hubbard model,
  F. Krüger, Seungmin Hong, and P. Phillips,
  Phys. Rev. B 84, 115118 (2011).
  
  
  
  We investigate the instabilities of the Mott-insulating phase of the weakly disordered Bose-Hubbard model within a renormalization group
  analysis of the replica field theory obtained by a strong-coupling expansion around the atomic limit. We identify a new order parameter
  and associated correlation length scale that is capable of capturing the transition from a state with zero compressibility, the Mott insulator,
  to one in which the compressibility is finite, the Bose glass. The order parameter is the relative variance of the disorder-induced mass
  distribution. In the Mott insulator, the relative variance renormalizes to zero, whereas it diverges in the Bose glass. The divergence of
  the relative variance signals the breakdown of self-averaging. The length scale governing the breakdown of self-averaging is the distance
  between rare regions. This length scale is finite in the Bose glass but diverges at the transition to the Mott insulator with an exponent of
  $\nu=1/D$ for incommensurate fillings. Likewise, the compressibility vanishes with an exponent of $\gamma=4/D-1$ at the transition. At
  commensurate fillings, the transition is controlled by a different fixed point at which both the disorder and interaction vertices are relevant.
  
  
  
  
• Orbital Ordering and Unfrustrated (pi,0) Magnetism from Degenerate Double Exchange in the Pnictides,
  Weicheng Lv, F. Krüger, and P. Phillips,
  Phys. Rev. B 82, 045125 (2010).
  
  
  
  The magnetic excitations of the iron pnictides are explained within a degenerate double-exchange model. The local-moment spins are
  coupled by superexchanges J1 and J2 between nearest and next-nearest neighbors, respectively, and interact with the itinerant electrons
  of the degenerate d(xz) and d(yz) orbitals via a ferromagnetic Hund exchange. The latter stabilizes (pi,0) stripe antiferromagnetism due to
  emergent ferro-orbital order and the resulting kinetic energy gain by hopping preferably along the ferromagnetic spin direction. Taking the
  quantum nature of the spins into account, we calculate the magnetic excitation spectra in the presence of both, super- and double-
  exchange. A dramatic increase of the spin-wave energies at the competing Néel ordering wave vector is found, in agreement with recent
  neutron scattering data. The spectra are fitted to a spin-only model with a strong spatial anisotropy and additional longer ranged couplings
  along the ferromagnetic chains. Over a realistic parameter range, the effective couplings along the chains are negative corresponding to
  unfrustrated stripe antiferromagnetism.
  
  
  
  
• Anomalous suppression of the Bose glass at commensurate fillings in the disordered Bose-Hubbard model,
  F. Krüger, Jiansheng Wu, and P. Phillips,
  Phys. Rev. B 80, 094526 (2009),
  Virtual Journal of Atomic Quantum Fluids 1, (4) (2009).
  
  
  
  We study the weakly disordered Bose-Hubbard model on a cubic lattice through a one-loop renormalization group analysis of the
  corresponding effective field theory which is explicitly derived by combining a strong-coupling expansion with a replica average over
  the disorder. The method is applied not only to generic uncorrelated on-site disorder but also to simultaneous hopping disorder
  correlated with the differences of adjacent disorder potentials. Such correlations are inherent in fine-grained optical speckle potentials
  used as a source of disorder in optical lattice experiments. As a result of strong coupling, the strength of the replica mixing disorder
  vertex, responsible for the emergence of a Bose glass, crucially depends on the chemical potential and the Hubbard repulsion and
  vanishes to leading order in the disorder at commensurate boson fillings. As a consequence, at such fillings a direct transition
  between the Mott-insulator and the superfluid in the presence of disorder cannot be excluded on the basis of a one-loop
  calculation. At incommensurate fillings, at a certain length scale, the Mott insulator will eventually become unstable towards
  the formation of a Bose glass. Phase diagrams as a function of the microscopic parameters are presented and the finite-size
  crossover between the Mott-insulating state and the Bose glass is analyzed.
  
  
  
  
• Phase diagram of the frustrated, spatially anisotropic S=1 antiferromagnet on a square lattice,
  H. C. Jiang, F. Krüger, J. E. Moore, D. N. Sheng, J. Zaanen, and Z. Y. Weng,
  Phys. Rev. B 79, 174409 (2009).
  
  
  
  We study the S=1 square lattice Heisenberg antiferromagnet with spatially anisotropic nearest neighbor couplings J1x, J1y
  frustrated by a next-nearest neighbor coupling J2 numerically using the density-matrix renormalization group (DMRG) method and
  analytically employing the Schwinger-Boson mean-field theory (SBMFT). Up to relatively strong values of the anisotropy, within both
  methods we find quantum fluctuations to stabilize the Neel ordered state above the classically stable region. Whereas SBMFT
  suggests a fluctuation-induced first order transition between the Néel state and a stripe antiferromagnet for 1/3<J1x/J1y<1
  and an intermediate paramagnetic region opening only for very strong anisotropy, the DMRG results clearly demonstrate that the two
  magnetically ordered phases are separated by a quantum disordered region for all values of the anisotropy with the remarkable implication
  that the quantum paramagnetic phase of the spatially isotropic J1-J2 model is continuously connected to the limit of decoupled
  Haldane spin chains. Our findings indicate that for S=1 quantum fluctuations in strongly frustrated antiferromagnets are crucial and
  not correctly treated on the semiclassical level.
  
  
  
  
• Spin-orbital frustrations and anomalous metallic state in iron-pnictide superconductors,
  F. Krüger, S. Kumar, J. Zaanen, and J. van den Brink,
  Phys. Rev. B 79, 054504 (2009),
  Virtual Journal of Applications of Superconductivity 16, (4) (2009).
  
  
  
  We develop an understanding of the anomalous metal state of the parent compounds of recently discovered iron based superconductors
  starting from a strong coupling viewpoint, including orbital degrees of freedom. On the basis of an intermediate-spin (S=1) state for the
  Fe(2+) ions, we derive a Kugel-Khomskii spin-orbital Hamiltonian for the active t(2g) orbitals. It turns out to be a highly complex
  model with frustrated spin and orbital interactions. We compute its classical phase diagrams and provide an understanding for the stability
  of the various phases by investigating its spin-only and orbital-only limits. The experimentally observed spin-stripe state is found to be
  stable over a wide regime of physical parameters and can be accompanied by three different types of orbital orders. Of these the orbital-
  ferro and orbital-stripe orders are particularly interesting since they break the in-plane lattice symmetry --a robust feature of the undoped
  compounds. We compute the magnetic excitation spectra for the effective spin Hamiltonian, observing a strong reduction of the ordered
  moment, and point out that the proposed orbital ordering pattern can be measured in resonant X-ray diffraction.
  
  
  
  
• Fermionic quantum criticality and the fractal nodal surface,
  F. Krüger and J. Zaanen,
  Phys. Rev. B 78, 035104 (2008).
  
  
  
  The complete lack of theoretical understanding of the quantum critical states found in the heavy fermion metals and the normal states
  of the high-Tc superconductors is routed in deep fundamental problem of condensed matter physics: the infamous minus signs
  associated with Fermi-Dirac statistics render the path integral non-probabilistic and do not allow to establish a connection with critical
  phenomena in classical systems. Using Ceperley's constrained path-integral formalism we demonstrate that the workings of scale
  invariance and Fermi-Dirac statistics can be reconciled. The latter is self-consistently translated into a geometrical constraint structure.
  We prove that this "nodal hypersurface" encodes the scales of the Fermi liquid and turns fractal when the system becomes quantum
  critical. To illustrate this we calculate nodal surfaces and electron momentum distributions of Feynman backflow wave functions and indeed
  find that with increasing backflow strength the quasiparticle mass gradually increases, to diverge when the nodal structure becomes fractal.
  Such a collapse of a Fermi liquid at a critical point has been observed in the heavy-fermion intermetallics in a spectacular fashion.
  
  
  
  
  Triggered by our paper, the visualization of nodal surfaces of backflow
  wavefunctions has been implemented as a
  MATHEMATICA demonstration project.
  
  
  
  
  
  
  
  
  
  Synopsis: "Fractals and quantum criticality" by Sarma Kancharla
  
  
  
  
  
  
• Pacifying the Fermi-liquid: battling the devious fermion signs,
  J. Zaanen, F. Krüger, J.-H. She, D. Sadri, S. I. Mukhin,
  Iranian Journal of Physics Research, Vol. 8, No. 2, 39 (2008).
  
  
  
  The fermion sign problem is studied in the path integral formalism. The standard picture of Fermi liquids is first critically analyzed, pointing
  out some of its rather peculiar properties. The insightful work of Ceperley in constructing fermionic path integrals in terms of constrained
  worldlines is then reviewed. In this representation, the minus signs associated with Fermi-Dirac statistics are self consistently translated
  into a geometrical constraint structure (the nodal hypersurface) acting on an effective bosonic dynamics. As an illustrative example we use
  this formalism to study 1+1-dimensional systems, where statistics are irrelevant, and hence the sign problem can be circumvented. In this
  low-dimensional example, the structure of the nodal constraints leads to a lucid picture of the entropic interaction essential to one-
  dimensional physics. Working with the path integral in momentum space, we then show that the Fermi gas can be understood by analogy
  to a Mott insulator in a harmonic trap. Going back to real space, we discuss the topological properties of the nodal cells, and suggest
  a new holographic conjecture relating Fermi liquids in higher dimensions to soft-core bosons in one dimension. We also discuss some
  possible connections between mixed Bose/Fermi systems and supersymmetry.
  
  
  
  
• Magnetic fluctuations in n-type high-Tc superconductors reveal breakdown of fermiology: Experiments and Fermi-liquid/
  RPA calculations,
  F. Krüger, S. D. Wilson, L. Shan, S. Li, Y. Huang, H. H. Wen, S. C. Zhang, Pengcheng Dai, J. Zaanen,
  Phys. Rev. B 76, 094506 (2007).
  
  
  
  By combining experimental measurements of the quasiparticle and dynamical magnetic properties of optimally electron-doped
  Pr(0.88)LaCe(0.12)CuO4 with theoretical calculations we demonstrate that the conventional fermiology approach cannot possibly account
  for the magnetic fluctuations in these materials. In particular, we perform tunneling experiments on the very same sample for which a
  dynamical magnetic resonance has been reported recently and use photoemission data by others on a similar sample to characterize the
  fermionic quasi-particle excitations in great detail. We subsequently use this information to calculate the magnetic response within the
  conventional fermiology framework as applied in a large body of work for the hole-doped superconductors to find a profound disagreement
  between the theoretical expectations and the measurements: this approach predicts a step-like feature rather than a sharp resonance
  peak, it underestimates the intensity of the resonance by an order of magnitude, it suggests an unreasonable temperature dependence
  of the resonance, and most severely, it predicts that most of the spectral weight resides in incommensurate wings which are a key
  feature of the hole-doped cuprates but have never been observed in the electron-doped counterparts. Our findings strongly suggest that
  the magnetic fluctuations reflect the quantum-mechanical competition between antiferromagnetic and superconducting orders.
  
  
  
  
• Is deconfined quantum criticality in frustrated antiferromagnets ruled out by generic fluctuation induced
  first-order behavior?
  F. Krüger,
  J. Supercond. Nov. Magn. 20, 575 (2007).
  
  Proceeding for International Conference Stripes2006, Rome, Italy.
  
  
  
  
• Frustrated Heisenberg antiferromagnets: fluctuation induced first order vs deconfined quantum criticality,
  F. Krüger and S. Scheidl,
  Europhys. Lett. 74, 896 (2006).
  
  
  
  Recently it was argued that quantum phase transitions can be radically different from classical phase transitions with as a highlight the
  'deconfined critical points' exhibiting fractionalization of quantum numbers due to Berry phase effects. Such transitions are supposed to
  occur in frustrated ('J1-J2') quantum magnets. We have developed a novel renormalization approach for such systems which is
  fully respecting the underlying lattice structure. According to our findings, another profound phenomenon is around the corner:
  a fluctuation induced (order-out-of-disorder) first order transition. This has to occur for large spin and we conjecture that it is responsible
  for the weakly first order behavior recently observed in numerical simulations for frustrated S=1/2 systems.
  
  
  
  
• Spin-wave dispersion in orbitally ordered La$_{1/2}$Sr$_{3/2}$MnO$_4$,
  D. Senff, F. Krüger, S. Scheidl, M. Benomar, Y. Sidis, S. Demmel, and M. Braden,
  Phys. Rev. Lett. 96, 257201 (2006).
  
  
  
  The magnon dispersion in the charge, orbital and spin ordered phase in La(1/2)Sr(3/2)MnO4 has been studied by means of
  inelastic neutron scattering. We find an excellent agreement with a magnetic interaction model basing on the CE-type superstructure.
  The magnetic excitations are dominated by ferromagnetic exchange parameters revealing a nearly-one dimensional character at high
  energies. The nearest neighbor ferromagnetic interaction in La(1/2)Sr(3/2)MnO4 is significantly larger than the one in the
  metallic ferromagnetically ordered manganites. The large ferromagneticinteraction in the charge/orbital ordered phase appears to be
  essential for the capability of manganites to switch between metallic and insulating phases.
  
  
  
  
• The spin excitation spectrum in striped bilayer compounds,
  F. Krüger and S. Scheidl,
  Phys. Rev. B 70, 064421 (2004),
  Virtual Journal of Applications of Superconductivity 7, (5) (2004).
  
  
  
  The spin dynamics of bilayer cuprate compounds are studied in a basic model. The magnetic spectral properties are calculated in linear
  spin-wave theory for several stripe configurations which differ by the relative location of the stripes in the layers. We focus on the bilayer
  splitting of the magnon bands near the incommensurate low energy peaks as well as near the pi resonance, distinguishing between the
  odd and even channel. We find that a x-shaped dispersion near the pi resonance is generic for stripes. By comparison of our results to
  neutron scattering data for YBa(2)Cu(3)O(6+x) we conclude that the stripe model is consistent with characteristic features of
  bilayer high-Tc compounds.
  
  
  
  
• Spin dynamics of stripes,
  F. Krüger and S. Scheidl,
  Phys. Rev. B. 67, 134512 (2003).
  
  
  
  The spin dynamics of stripes in high-temperature superconductors and related compounds is studied in the framework of a spin-wave
  theory for a simple spin-only model. The magnon dispersion relation and the magnetic structure factor are calculated for diagonal and
  vertical stripes. Acoustical as well as optical bands are included in the analysis. The incommensurability and the pi resonance
  appear as complementary features of the band structure at different energy scales. The dependence of spin-wave velocities and
  resonance frequencies on the stripe spacing and coupling is calculated. At low doping, the resonance frequency is found to scale
  roughly inversely proportional to the stripe spacing. The favorable comparison of the results with experimental data suggests
  that the spin-only model provides a suitable and simple basis for calculating and understanding the spin dynamics of stripes.
  
  
  
  
• Spin and charge ordering transitions in stripes,
  F. Krüger and S. Scheidl,
  J. Phys. IV France 12, Pr9-259 (2002).
  
  Proceeding for International Workshop on Electronic Crystal (ECRYS), St. Flour, France.
  
  
  
  
• Non-universal ordering of spin and charge in stripe phases,
  F. Krüger and S. Scheidl,
  Phys. Rev. Lett. 89, 095701 (2002).
  
  
  
  We study the interplay of topological excitations in stripe phases: charge dislocations, charge loops, and spin vortices. In two dimensions
  these defects interact logarithmically on large distances. Using a renormalization-group analysis in the Coulomb gas representation of
  these defects, we calculate the phase diagram and the critical properties of the transitions. Depending on the interaction parameters,
  spin and charge order can disappear at a single transition or in a sequence of two transitions (spin-charge separation). These transitions
  are non-universal with continuously varying critical exponents. We also determine the nature of the points where three phases coexist.
  
  
  
  
• Bond-disordered spin systems: Theory and application to doped high-$T_\textrm{c}$ compounds,
  F. Krüger and S. Scheidl,
  Phys. Rev. B 65, 224502 (2002).
  
  
  
  We examine the stability of magnetic order in a classical Heisenberg model with quenched random exchange couplings. This system
  represents the spin degrees of freedom in high-Tc compounds with immobile dopants. Starting from a replica representation
  of the nonlinear sigma model, we perform a renormalization-group analysis. The importance of cumulants of the disorder distribution
  to arbitrarily high orders necessitates a functional renormalization scheme. From the renormalization flow equations we determine the
  magnetic correlation length numerically as a function of the impurity concentration and of temperature. From our analysis follows that
  two-dimensional layers can be magnetically ordered for arbitrarily strong but sufficiently diluted defects. We further consider the
  dimensional crossover in a stack of weakly coupled layers. The resulting phase diagram is compared with experimental data for
  La(2-x)Sr(x)CuO(4).