
Hubbard Systems (chair: Johannes Knolle)

09:00  09:20

Michael Lang
(Johann Wolfgang GoetheUniversität Frankfurt)
Breakdown of Hooke’s law of elasticity at the Mott critical endpoint in an organic conductor
The Mott transition is a key phenomenon in strongly correlated electron systems. Despite its relevance for a wide range of materials, fundamental aspects of this transition are still unresolved. Of particular interest is the role of the lattice degrees of freedom in the Mott transition. In this talk, we will present results of the thermal expansion coefficient as a function of Heliumgas pressure around the Mott transition of the organic chargetransfer salt $\kappa$(BEDTTTF)$_2$Cu[N(CN)$_2$]Cl. The salient result of our study is the observation of a strong, highly nonlinear lattice response upon approaching the secondorder critical endpoint of the transition. This apparent breakdown of Hooke’s law of elasticity reflects an intimate, nonperturbative coupling of the critical electronic degrees of freedom to the crystal lattice. Our results are fully consistent with meanfield criticality, predicted theoretically for electrons coupled to a compressible lattice with finite shear modulus [2].
[1] E. Gati et al., Science Advances 2: e1601646 (2016)
[2] M. Zacharias et al., Phys. Rev. Lett. 109, 176401 (2012)
Work has been done in collaboration with E. Gati, M. Garst, R.S. Manna, U. Tutsch, B. Wolf, L. Bartosch, T. Sasaki, H. Schubert, and J.A. Schlueter

09:20  09:40

Walter Metzner
(MaxPlanckInstitut für Festkörperforschung)
Competition between magnetism and superconductivity in the Hubbard model and in the cuprates
We analyze the competition of magnetism and superconductivity in the twodimensional Hubbard model with a moderate interaction strength, including the possibility of incommensurate spiral magnetic order. Using an unbiased renormalization group approach, we compute magnetic and superconducting order parameters in the ground state. In addition to previously established regions of Neel order coexisting with dwave superconductivity, the calculations reveal further coexistence regions where superconductivity is accompanied by incommensurate magnetic order [1].
We show that a Fermi surface reconstruction due to spiral antiferromagnetic
order may explain the rapid change in the Hall number in a strong magnetic field as recently observed near optimal doping in cuprate superconductors. The singleparticle spectral function in the spiral state exhibits hole pockets which look like Fermi arcs due to a strong momentum dependence of the spectral weight [2].
[1] H. Yamase, A. Eberlein, and W. Metzner, Phys. Rev. Lett. 116, 096402 (2016).
[2] A. Eberlein, W. Metzner, S. Sachdev, and H. Yamase, Phys. Rev. Lett. 117, 187001 (2016).

09:40  10:00

Reinhard Noack
(PhilippsUniversität Marburg)
Application of the hybridspace DMRG to multichain and twodimensional Hubbard models
I describe the hybrid momentumrealspace DMRG method and discuss applications to multichain and twodimensional Hubbard models at and away from halffilling and with and without frustration.

10:00  10:20

Philippe Corboz
(University of Amsterdam)
Stripe order in the 2D Hubbard model
The discovery of hightemperature superconductivity in the cuprates has stimulated intense study of the Hubbard and tJ models on a square lattice. However, the accurate simulation of these models is one of the major challenges in computational physics. In this talk I report on recent progress in simulating the Hubbard model at a particularly challenging point in the phase diagram, $U/t=8$, and doping $\delta=1/8$, at which an extremely close competition between a uniform dwave superconducting state and different types of stripe states is found. Here I mostly focus on results obtained with infinite projectedentangled pair states (iPEPS)  a variational tensor network approach where the accuracy can be systematically controlled by the socalled bonddimension D. Systematic extrapolations to the exact, infinite D limit show that the fullyfilled stripe ordered state is the lowest energy state. Consistent results are obtained with density matrix embedding theory, the density matrix renormalization group, and constrainedpath auxiliary field quantum Monte Carlo, demonstrating the power of current stateoftheart numerical methods to solve challenging open problems.

10:20  10:40

coffee break


Methods 2 (chair: Walter Metzner)

10:40  11:00

Karsten Held
(Technische Universität Wien)
Nonlocal correlations beyond DMFT: from quantum criticality to metal insulator transitions
Dynamical mean field theory (DMFT) has been a big step forward for our
understanding of electronic correlations. A major part of the electronic
correlations, the local ones, are included. On the other hand, DMFT
neglects nonlocal correlations that are at the origin of many physical
phenomena such as (quantum) criticality, highT superconductivity, weak
localization and other vertex corrections to transport in nanoscopic
systems. To address these topics the scientific frontier moved to
cluster and diagrammatic extensions of DMFT such as the dynamical vertex
approximation [1,2].
I will present an introduction to the diagramtic extensions of DMFT and
discuss selected applications: the calculation of quantum critical exponents rendering Kohn lines in the bandstructure [3], the fate of the MottHubbard metalinsulator tranistion in two dimensions [4], and the application to realisitc materials calcualtions [5].
[1] A. Toschi, A. A. Katanin, and K. Held, Phys. Rev. B 75, 045118 (2007).
[2] G. Rohringer et al., in preparation.
[3] T. Schäfer et al., arXiv:1605.06355.
[4] T. Schäfer et al., Phys. Rev. B 91, 125109 (2015).
[5] A. Galler et al., Phys. Rev. B 95, 115107 (2016).

11:00  11:20

Enrico Arrigoni
(Technische Universität Graz)
Correlated impurities and interfaces out of equilibrium: auxiliary master equation approach
I will present a numerical scheme to address correlated quantum
impurities out of equilibrium down to the Kondo scale. This Auxiliary
Master Equation Approach [1,2,3] is also suited to deal with transport
across correlated interfaces within nonequilibrium Dynamical Mean
Field Theory [5].
The method consists in mapping the original impurity problem onto an
auxiliary open quantum system including bath orbitals as well as a
coupling to a Markovian environment. The mapping becomes exponentially
exact upon increasing the number of bath orbitals. The intervening
auxiliary orbitals allow for a treatment of nonMarkovian dynamics at
the impurity.
The time dependence of the auxiliary system is controlled by a
Lindblad master equation whose parameters are determined via an
optimization scheme. Green's functions are evaluated via
(nonhermitian) Lanczos exact diagonalisation [2] or by matrixproduct
states (MPS) [3]. In particular, the MPS implementation produces
highly accurate spectral functions for the Anderson impurity model in
the Kondo regime. The approach can be also used in equilibrium, where
we obtain a remarkably close agreement to numerical renormalization
group.
I will present results for electric and thermal transport across an
Anderson impurity [2,3,4] and across correlated interfaces [5]. An
implementation within Floquet theory for periodic driving [6] will be
discussed as well.
[1] E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013)
[2] A. Dorda et al., Phys. Rev. B 89 165105 (2014)
[3] A. Dorda et al., Phys. Rev. B 92, 125145 (2015)
[4] A. Dorda et al., Phys. Rev. B 94, 245125 (2016)
[5] I. Titvinidze et al., Phys. Rev. B 92, 245125 (2015)
[6] M. Sorantin et al., in preparation.

11:20  11:40

Hans Gerd Evertz
(Technische Universität Graz)
Multiorbital real time impurity solver with matrix product states
A multiorbital impurity solver for dynamical mean field theory (DMFT) is presented, which employs a tensor network similar to Matrix Product States. It yields high spectral resolution at all frequencies. The solver works directly on the realtime / realfrequency axis and yields high spectral resolution at all frequencies. We use a large number (O(100)) of bath sites, and therefore achieve an accurate representation of the bath. The solver can treat full rotationally invariant interactions with reasonable numerical eﬀort. We first show the eﬃciency and accuracy of the method by a benchmark for the threeorbital testbed material SrVO3, where we observe multiplet structures in the highenergy spectrum which are almost impossible to resolve by other multiorbital methods. Finally we will present new results for fiveorbital models.

11:40  12:00

Rainer Härtle
(GeorgAugustUniversität Göttingen)
Transport through strongly correlated materials: a hierarchical quantum master equation approach
We investigate the transport properties of strongly correlated materials in the framework of nonequilibrium dynamical mean field theory, where we use the hierarchical quantum master equation approach to solve the respective impurity problem [1,2]. The approach employs a hybridization expansion which can be converged if the temperature of the environment is not too low [3]. It is timelocal and can, therefore, be used to study the longlived dynamics inherent to this problem, including the nonequilibrium steady states. Different truncation levels allow for a systematic analysis of the relevant physical processes. Our results elucidate, in particular, the role of inelastic processes for the transport properties of materials that can be described by the Hubbard model.
[1] Jin et al., JCP 128, 234703 (2008);
[2] Härtle et al., PRB 88, 235426 (2013);
[3] Härtle et al., PRB 92, 085430 (2015).

12:00  12:20

Simone Montangero
(Universität Ulm)
Recent advancements in tensor network methods
We review some recent advancements in tensor network
algorithms and their application to the study of correlated matter.
We present novel approaches to study abelian and nonabelian lattice
gauge theories, open manybody quantum systems and systems with
longrange interactions or periodic boundary conditions.
These novel approaches allowed us to obtain results on
a variety of phenomena hardly accessible before,
such as the KibbleZurek mechanism in Wigner
crystals, the outofequilibrium dynamics of the Schwinger model
and the phase diagram of the disordered BoseHubbard model.

12:20  13:20

lunch

13:20  14:00

discussion


Excitations (chair: Roser Valenti)

14:00  14:20

Christian Jooß
(GeorgAugustUniversität Göttingen)
Tuning of hot polaron states with a nanosecond lifetime in a manganite perovskite via correlations
Understanding and controlling the relaxation process of optically excited charge carriers in solids with strong correlations is of great interest in the quest for new strategies to exploit solar energy. Usually, optically excited electrons in a solid thermalize rapidly on a femtosecond to picosecond timescale due to interactions with other electrons and phonons. New mechanisms to slow down thermalization would thus be of great significance for efficient light energy conversion, e.g. in photovoltaic devices. Ultrafast optical pump probe experiments in the manganite Pr$_0.65$Ca$_0.35$MnO$_3$, a photovoltaic, thermoelectric and electrocatalytic material with strong polaronic correlations, reveal an ultraslow recombination dynamics on a nanosecondtime scale [1]. The nature of long living excitations is further elucidated by photovoltaic measurements, showing the presence of photodiffusion of excited electronhole polaron pairs [1,2]. Theoretical considerations suggest that the excited charge carriers are trapped in a hot polaron state. The dependence of the lifetime on charge order implies that strong correlation between the excited polaron and the octahedral dynamics of its environment appears to be substantial for stabilizing the hot polaron [3]. Furthermore, modification of the interfacial atomic and electronic structure of the manganitetitanite junctions gives insights into the processes underlying the transfer of a small polaron between materials with different correlations [4].
[1] Evolution of hot polaron states with a nanosecond lifetime in a manganite, D. Raiser, S. Mildner, B. Ifland, M. Sotoudeh, P. Blöchl, S. Techert, C. Jooss, Advanced Energy Materials, 2017, 1602174, DOI: 10.1002/aenm.201602174.
[2] Polaron absorption for photovoltaic energy conversion in a manganitetitanate pnheterojunction, G. Saucke, J. Norpoth, D. Su, Y. Zhu and Ch. Jooss, Phys. Rev. B 85, 165315 (2012).
[3] Contribution of JahnTeller and charge transfer excitations to the photovoltaic effect of manganite/titanite heterojunctions, B. Ifland, J. Hoffmann, B. Kressdorf, V. Roddatis, M. Seibt and Ch. Jooss, New Journal of Physics, accepted for publication.
[4] Current–voltage characteristics of manganite–titanite perovskite junctions, B. Ifland, P. Peretzki, B. Kressdorf, Ph. Saring, A. Kelling, M. Seibt and Ch. Jooss, Beilstein Journal of Nanotechnology, 2015, 6, 1467–1484

14:20  14:40

Achim Rosch
(Universität zu Köln)
Pumping correlated materials with approximate conservation laws
Weak perturbations can drive an interacting manyparticle system far from its initial equilibrium state if one is able to pump into degrees of freedom approximately protected by conservation laws. This concept has for example been used to realize BoseEinstein condensates of photons, magnons, and excitons. Integrable quantum system like the onedimensional Heisenberg model are characterized by an infinite set of conservation laws. Here we develop a theory of weakly driven integrable systems and show that pumping can induce huge spin or heat currents even in the presence of integrability breaking perturbations, since it activates local and quasilocal approximate conserved quantities. The resulting steady state is approximately, though efficiently, described by a generalized Gibbs ensemble, which depends sensitively on the structure but not on the overall amplitude of perturbations or on the initial state. We suggest to realize novel heat or spin pumps using spinchain materials driven by THz radiation.

14:40  15:00

Frank Pollmann
(Technische Universität München)
Dynamical signatures of quantum spin liquids
Condensed matter is found in a variety of phases, the vast majority of which are characterized in terms of symmetry breaking. However, the last few decades have yielded a plethora of theoretically proposed quantum phases of matter which fall outside this paradigm. Recent focus lies on the search for concrete realizations of quantum spin liquids. These are notoriously difficult to identify experimentally because of the lack of local order parameters. In my talk, I will discuss universal properties found in dynamical response functions that are useful to characterize these exotic states of matter.
First, we show that the anyonic statistics of fractionalized excitations display characteristic signatures in threshold spectroscopic measurements. The low energy onset of associated correlation functions near the threshold show universal behavior depending on the statistics of the anyons. This explains some recent theoretical results in spin systems and also provides a route towards detecting statistics in experiments such as neutron scattering and tunneling spectroscopy [1].
Second, we introduce a matrixproduct state based method to efficiently obtain dynamical response functions for twodimensional microscopic Hamiltonians, which we apply to different phases of the KitaevHeisenberg model. We find significant broad high energy features beyond spinwave theory even in the ordered phases proximate to spin liquids. This includes the phase with zigzag order of the type observed in αRuCl3, where we find high energy features like those seen in inelastic neutron scattering experiments.
[1] S. C. Morampudi, A. M. Turner, F. Pollmann, and F. Wilczek, arXiv:1608.05700.
[2] M. Gohlke, R. Verresen, R. Moessner, and and F. Pollmann, arXiv:1701.04678.

15:00  15:20

Michael Bonitz
(ChristianAlbrechtsUniversität zu Kiel)
Dynamics of highly excited strongly correlated fermions  a nonequilibrium Green functions approach
Strongly correlated quantum particles with halfinteger spin are of growing interest in many fields, including condensed matter, dense plasmas and ultracold atoms. From a theory point of view these systems are very challenging. Also, ab initio quantum simulations such as DMRG are essentially limited to the 1D case. Here, I will present an example of recent breakthroughs we could achieve using
a Nonequilibrium Green functions approach [1] that has recently allowed us to simulate the nonequilibrium transport in 2D and 3D fully including strong correlation effects. We achieve, for the first time, excellent agreement with ultracold atom experiments [2]. Our results are close to DMRG results where they are available but, in many cases, allow for much longer simulations [3]. I will close by discussing prospects of using NEGF for transport and optics of solids as well as solids in contact with a plasma [4].
[1] Michael Bonitz, "Quantum Kinetic Theory", 2nd edition, Springer 2016.
[2] Niclas Schlünzen, Sebastian Hermanns, Michael Bonitz, and Claudio Verdozzi, Phys. Rev. B 93, 035107 (2016).
[3] Niclas Schlünzen, JanPhilip Joost, Fabian HeidrichMeisner, and Michael Bonitz, Phys. Rev. B (2017)
[4] Karsten Balzer, Niclas Schlünzen, JanPhilip Joost, and Michael Bonitz, Phys. Rev. B 94, 245118(2016).

15:20  15:40

Martin Eckstein
(FriedrichAlexanderUniversität ErlangenNürnberg)
Manipulating correlated electron systems with short electric field transients
Femtosecond laser technology has opened the possibility to probe and control the dynamics of complex condensed matter phases on microscopic timescales. In this talk, I will focus on various proposals to manipulate complex states with spin and orbital order, using the electric field of the laser. This can be done both in the transient regime, where one can use short field transients to switch between different polarizations of a composite orbital order, and for periodic driving, where the laserdriven system effectively evolves with a FloquetHamiltonian with lightinduced spin and orbital exchange interactions.

15:40  16:00

discussion

16:00  16:20

coffee break


Impurity & Kondo Systems (chair: Markus Garst)

16:20  16:40

Johannes Knolle
(University of Cambridge)
Disorderfree localization: absence of ergodicity without quenched disorder
The venerable phenomena of Anderson localization, along with the much more recent manybody localization, both depend crucially on the presence of disorder. The latter enters either in the form of quenched disorder in the parameters of the Hamiltonian, or through a special choice of a disordered initial state. Here, we present a model with localization arising in a very simple, completely translationally invariant quantum model, with only local interactions between spins and fermions. By identifying an extensive set of conserved quantities, we show that the system generates purely dynamically its own disorder, which gives rise to localization of fermionic degrees of freedom. Our work gives an answer to a decades old question whether quenched disorder is a necessary condition for localization. It also offers new insights into the physics of manybody localization, lattice gauge theories, and quantum disentangled liquids.

16:40  17:00

Theo Costi
(Forschungszentrum Jülich)
Time evolution of the Kondo resonance in response to a quench
We investigate the time evolution of the Kondo resonance in response to a quench by applying the
timedependent numerical renormalization group (TDNRG) approach to the Anderson impurity model in the strong correlation limit [1]. For this purpose, we derive within TDNRG a numerically tractable expression for the retarded twotime nonequilibrium Green function $G(t+t',t)$, and its associated timedependent spectral function, $A(\omega,t)$, for times $t$ both before and after the quench. Quenches from both mixed valence and Kondo correlated initial states to Kondo correlated final states are considered. For both cases, we find that the Kondo resonance in the zero temperature spectral function only fully develops at very long times $t\gtrsim 1/T_{\rm K}$, where $T_{\rm K}$ is the Kondo temperature of the final state. In contrast, the final state satellite peaks develop on a fast time scale $1/\Gamma$ during the time interval $1/\Gamma \lesssim t \lesssim +1/\Gamma$, where $\Gamma$ is the hybridization strength. Initial and final state spectral functions are recovered in the limits $t\rightarrow \infty$ and $t\rightarrow +\infty$, respectively.
Our formulation of twotime nonequilibrium Green functions within TDNRG provides a first step towards using this method as an impurity solver within nonequilibrium dynamical mean field theory. Finally, we show how to improve the calculation of spectral functions in the long time limit within a new multiple quench TDNRG approach with potential application to precise steady state transport calculations for quantum dots [2].
[1] H. T. M. Nghiem and T. A. Costi, arXiv:1701.07558
[2]F. B. Anders, Phys. Rev. Lett. {\bf 101}, 66804 (2008)

17:00  17:20

Johann Kroha
(Universität Bonn)
Kondo breakdown in Kondo lattices: RKKY coupling and nonequilibrium THz spectroscopy
The fate of the fermionic quasiparticles near a quantum phase transition (QPT) in certain heavyfermion compounds where the HertzMoriyaMillis scenario does not apply has been subject of intense debate for many years. It is generally believed that this Kondo destruction is driven by the critical fluctuations near the QPT.
Here we show that the heavyfermion quasiparticles can be destroyed by the RKKY interaction even without critical fluctuations [1]. This is due to a hitherto unrecognized interference of Kondo screening and the RKKY interaction beyond the Doniach scenario: In a Kondo lattice, the spin exchange coupling between a local spin and the conduction electrons acquires nonlocal contributions due to conduction electron scattering from surrounding local spins and subsequent RKKY interaction. We develop a novel type of renormalization group theory for this RKKYmodified Kondo vertex [1]. The Kondo temperature, $T_K(y)$, is suppressed in a universal way, controlled by the dimensionless RKKY
coupling parameter y. Complete spin screening ceases to exist beyond a critical RKKY strength $y_c$ even in the absence of magnetic ordering. At this breakdown point, $T_K(y)$ remains nonzero and is not defined for larger RKKY couplings, $y>y_c$. These results agree
quantitatively with STM spectroscopy experiments on continuously tunable twoimpurity Kondo systems [2] and on twosite Kondo systems on a metallic surface [3].
We discuss in detail most recent timeresolved THz reflectometry experiments on the heavyfermion compound $CeCu_{6x}Au_x$ at the quantum critical concentration x=0.1 [4]. In
these experiments, the spectral weight as well as the energy scale $T_{K}^*$ for the formation of
the heavyfermion quasiparticles can be extracted from the intensity and the delay time, respectively, of a Kondoinduced, THz reflex. THz artifacts, e.g., reflexes from the optical components, are carefully excluded. Both experiment and theory support a quantum critical scenario in $CeCu_{6x}Au_x$ where the heavyfermion quasiparticles disintegrate near the QPT in
that their spectral weight collapses, but their resonance width (the lattice Kondo
temperature $T_K^*$) remains finite. This is consistent with $\omega/T$ scaling as an indicator for critical Kondo destruction.
[1] A. Nejati, K. Ballmann, and J. Kroha, Phys. Rev. Lett. 118, 117204 (2017).
[2] J. Bork, Y.H. Zhang, L. Diekhöhner L. Borda, P. Simon, J. Kroha, P. Wahl, and K. Kern,
Nature Physics 7, 901 (2011).
[3] N. Neel, R. Berndt, J. Kröger, T. O. Wehling, A. I. Lichtenstein, and M. I. Katsnelson, Phys.
Rev. Lett. 107, 106804 (2011): A. Nejati and J. Kroha, arXiv:1612.06620 (2016).
[4] Ch. Wetli, J. Kroha, K. Kliemt, C. Krellner, O. Stockert, H. von Löhneysen, and M. Fiebig,
arXiv:1703.04443.

17:20  17:40

Frithjof Anders
(Technische Universität Dortmund)
Nonequilibrium dynamics in a twoimpurity model close to quantum phase transition
We show that the two impurity Anderson model exhibit an additional quantum critical point at infinitely many specific distances between both impurities for an inversion symmetric 1D dispersion. Unlike the quantum critical point previously established by Jones and Varma, it is robust against particlehole or parity symmetry breaking. The quantum critical point separates a spin doublet from a spin singlet ground state and is, therefore, protected by symmetry. A finite single particle tunneling t or an applied uniform gate voltages will drive the system across the quantum critical point. The discriminative magnetic properties of the different phases cause a jump in the spectral functions at low temperature which might be useful for future spintronics devices. A local parity conservation will prevent the spinspin correlation function to decay to its equilibrium value after spinmanipulations.

17:40  18:00

discussion

18:00  19:30

dinner

19:30  21:00

poster session (focus on odd poster numbers)
