publications

• The order parameter of the Bose glass,
S. J. Thomson and F. Krüger,
submitted to Phys. Rev. Lett., arXiv:1312.0515.

We investigate the nature of the Bose glass phase of the disordered Bose-Hubbard model and demonstrate the existence of a glass-like
replica symmetry breaking (RSB) order parameter in terms of particle number fluctuations. Starting from a strong-coupling expansion
around the atomic limit, we study the instability of the Mott insulator towards the formation of a Bose glass. We add some infinitesimal
RSB, following the Parisi hierarchical approach in the most general form, and observe its flow under the momentum-shell renormalization
group scheme. We find a new fixed point with one-step RSB, corresponding to the transition between the Mott insulator and a Bose-glass
phase with hitherto unseen RSB. This finding is consistent with the expectation of glassy behavior and previous results showing the
breakdown of self-averaging. We discuss the possibility of measuring the glass-like order parameter in optical lattice experiments.

• Resummation of fluctuations near ferromagnetic quantum critical points,
C. J. Pedder, F. Krüger, and A. G. Green,
Phys. Rev. B 88, 165109 (2013).

We present a detailed analysis of the non-analytic structure of the free energy for the itinerant ferromagnet near the quantum
critical point in two and three dimensions. We analyze a model of electrons with an isotropic dispersion interacting through a contact
repulsion. A fermionic version of the quantum order-by-disorder mechanism allows us to calculate the free energy as a functional of
the dispersion in the presence of homogeneous and spiralling magnetic order. We re-sum the leading divergent contributions, to derive
an algebraic expression for the non-analytic contribution to free energy from quantum fluctuations. Using a recursion which relates
sub-leading divergences to the leading term, we calculate the full T=0 contribution in d=3. We propose an interpolating functional form,
which allows us to track phase transition lines at temperatures far below the tricritical point and down to T=0. In d=2, quantum
fluctuations are stronger and non-analyticities more severe. Using a similar re-summation approach, we find that despite the different
non-analytic structures, the phase diagrams in two and three dimensions are remarkably similar, exhibiting an incommensurate spiral
phase near to the avoided quantum critical point.

• Breakdown of self-averaging in the Bose glass,
A. Hegg, F. Krüger, and P. Phillips,
Phys. Rev. B 88, 134206 (2013).

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 and increasingly
non-Gaussian distributions. We determine an explicit phase boundary between the Mott insulator and Bose glass.

• Helical glasses near ferromagnetic quantum criticality,
S. J. Thomson, F. Krüger, and A. G. Green,
Phys. Rev. B 87, 224203 (2013).

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).