Sabine Andergassen (TU Wien) | Silke Bühler-Paschen (TU Wien) | Karsten Held (TU Wien) | Alessandro Toschi (TU Wien)

Quantum phase transitions (QPTs) represent one of the most challenging topics for theoretical and experimental investigations of correlated quantum materials because they are found in extreme parameter regimes and because of the interplay between different degrees of freedom. Our results obtained in the 1st funding period within the P1 project outline a clear route towards a fundamental understanding of the underlying physics.

On the theoretical side, we plan to extend our investigations of quantum criticality to multi-orbital problems as well as to systems in the presence of magnetic fields. This will also allow us to study the pertinent effects of different Fermi surface geometries and of topology on quantum criticality in realistic many-body calculations that can be directly compared with experiments.

Experimentally, new information will be extracted from a combination of different spectroscopies, namely inelastic neutron scattering (INS), microwave (MW) conductivity, resonant inelastic x-ray scattering (RIXS), angle-resolved photoemission spectroscopy (ARPES), and shot noise, applied to both quantum critical (QC) (e.g. Ce₃Pd₂₀Si₆, YbRh₂Si₂) and topological (e.g. Ce₃Bi₄Pd₃) materials. The link between both will be studied using CeRu₄Sn₆ where, in the 1st funding period, we identified a topological phase emerging from quantum criticality.

A new focus of the 2nd funding period is the interplay between charge fluctuations and spin/orbital/lattice degrees of freedom. In the realm of QPTs, the link between the spin and charge sectors will be explicitly investigated by performing new MW-conductivity/shot-noise experiments—both sensitive to charge fluctuations—on YbRh₂Si₂. Theoretically, the interplay with charge fluctuations will also be considered beyond QPTs, both for unconventional superconductivity and for its possible impact on electron-phonon coupling. As a second step, we will investigate how such an interplay is modified by the inclusion of non-local interactions.

The quantum many-body calculations foreseen in the 2nd funding period will be mostly performed through dynamical mean-field theory (DMFT) and its diagrammatic extensions (such as the DΓA and the DMF²RG) in difficult but experimentally relevant parameter regimes (low temperatures, large interactions). This will require efficient algorithmic strategies for compressing and manipulating two-particle vertex functions such as the intermediate representation and quantic tensor trains. The corresponding methodological advances will benefit several theoretical projects (P4, P5, P7) of the QUAST Research Unit.

In addition, the following collaborations are planned: To advance the understanding across the various materials platforms, we will also study selected kagome and other frustrated lattice compounds (in collaboration with P3 and Mercator fellow Vergniory) and moiré heterostructures (P5 and Mercator fellow Bernevig). Further collaborations concern functional renormalization group (fRG) calculations P1 Research Unit Proposal QUAST (P3), configuration-interaction-enhanced exact diagonalization (P7), the diagnosis of correlated topological phases protected by space group symmetries and cluster-DMFT-based implementations (P4), calculations of current-current correlation functions and electron-phonon effects (P5), non-equilibrium responses at QPTs (P6) and real-frequency (P7) techniques on the one- and two-particle levels for correlated systems, and magnetic susceptibilities in Weyl-Kondo semimetals (P8).

Claudia Felser (MPI-CPfS Dresden) | Sushmita Chandra (MPI-CPfS Dresden) | Ronny Thomale (U Würzburg) | Titus Neupert (U Zürich)

P3 will continue as a tight-knit experiment-theory collaboration that pushes the boundaries of two contemporary QUAST material platforms which grew out of the research activity of the first funding period – kagome metals and transition-metal dichalcogenides (TMDs). Experimentally, the focus will be on expanding the range of materials in these classes and their new physical properties. Theoretically, we will concentrate on developing new methodology to meet the challenge of simulating electronically driven orders in these multi-band compounds, also accounting for mixed itinerant and localized degree of freedom.

Several families of kagome materials have been explored in recent years with a multitude of experimental techniques, demonstrating qualitatively new physics, such as giant anomalous Hall effects, emergent chirality in flux phases, an intricate interplay between superconductivity and such chiral charge orders as well as a delicate balance between electronic and phononic contributions to correlation phenomena. We expect that expanding the space of compounds will allow us to discern universal trends from the details of specific compounds.

TMDs have driven several of the breakthrough findings in condensed matter physics in recent years (type-II Weyl semimetals, high-temperature quantum spin Hall effect, Wigner crystals, fractional Chern insulators) as a very versatile family offering both topological and correlated physics. We will focus on exploring layered bulk materials for supporting a 3D quantum Hall effect (both integer and fractional) and, once successful, attempt to exfoliate them down to monolayers. This will be accompanied by theoretical simulations similar to our past work on 1T′-Wse₂ and twisted MoTe₂. The exploration of 3D quantum Hall effects is a high-risk/high-gain aspect of this proposal and will be accompanied by a multi-pronged theory effort.

To be able to analyze symmetry-breaking electronic instabilities in both of these families of (quasi-)two-dimensional compounds, we rely on our established methodological toolkit. As a key theory method development in P3 to address the strongly correlated regime of systems with localized magnetic moment in either a Mott- or Kondo-insulating environment, we will focus on the methodological refinement of slave-boson mean-field theory and fluctuations.

P3 has strong ties with several other QUAST projects. We will provide crystals to P1 and P6 and collaborate on theoretical modeling. For device fabrication and transport measurements, we will collaborate with P5 and P1 and also collaborate with P6 and P7 on DMRG-calculations. Furthermore, the already established collaborations with P4 and P5 will be continued and strengthened.

Roser Valentí (GU Frankfurt) | Thomas Schäfer (MPI-FKF Stuttgart)

Disorder is ubiquitous to many correlated materials. While in the past it has been considered as an aspect to be avoided in materials’ design, it is often of central importance for the manifestation of some of the notable properties of the systems. Gaining a microscopic understanding of the influence of disorder on the electronic, magnetic and topological properties of correlated materials is, however, a challenging task due to the many-body character of correlations.

Our goal for the second funding period is to explore correlated phases of matter by addressing the interplay of correlations, non-locality, topology and – as a further aspect – disorder, through microscopic modeling. To address this interplay we will consider and further develop a combination of ab initio density functional theory (DFT), projective Wannier functions and many-body methods such as dynamical mean-field theory (DMFT), the two-particle self-consistent approach (TPSC), the triply irreducible local expansion (TRILEX), cellular DMFT (CDMFT), a Blackman-Esterling-Berk molecular potential extension of CDMFT (C-CDMFT), and machine learning techniques, as specified in the Research Methods section. Our focus will be on moiré, triangular-, and kagome-lattice platforms in collaboration with P1, P3, and P5-P8. We will proceed along three lines:

(i) We will investigate exemplary many-body models containing onsite potential disorder and disorder in hopping parameters to test and further develop our methods. A choice of models are: topological heavy-fermion models, relevant for moiré systems, multi-orbital (extended) Hubbard models on the kagome and triangular lattice (with longer-range interactions), relevant for organic charge transfer salts and moiré transition-metal dichalcogenides (TMDs), as well as Haldane-Hubbard, Kane-Mele-Hubbard models and extensions.

(ii) We will perform microscopic modeling from first principles of a choice of materials relevant in QUAST where the concepts and methods developed and applied to simple models in (i) will now be used for more realistic calculations. These are, in particular, moiré systems in collaboration with P5, Cr-based kagome systems with filling near the flat band in collaboration with P3 and P5, (doped) transition-metal dichalcogenides (TMDs) in collaboration with P6, and charge-transfer salts.

(iii) We will continue our efforts to scan and diagnose topologically non-trivial phases in interacting systems in collaboration with P3, P5, and P8.

Tim Wehling (U Hamburg) | Giorgio Sangiovanni (U Würzburg) | Dmitri Efetov (LMU München)

The interplay of phonons, electron correlations, and topology is an outstanding challenge in condensed matter physics. It determines phase diagrams, transport properties, and the response of quantum phases to external stimuli. Very often, however, there is no clear link between simple models and the physics taking place in actual materials, and the complexity of quantum materials evades a clear understanding, let alone a theory-guided optimization of their functional properties.

The theme of P5 is to facilitate a quantitative understanding and modeling of quantum materials featuring an interplay of phonons, electron correlations, and topology.

With the exemplary platforms of topological heavy fermions (THF) in twisted moiré materials, of kagome metals and TaS₂, we aim to understand how this interplay influences the emergence of phases, including charge ordered, time-reversal broken and superconducting states, how it affects phase-coexistence and metastability, and how it controls the coupling to strain and to electromagnetic fields. We aim at explaining the impact of phonons, correlations, and topology on electronic excitations, collective modes, and transport properties including the enigmatic strange-metallicity seen in correlated electron systems.

Having a pioneer in graphene moiré experiments, Dmitri Efetov, joining P5 as a new PI enables a unique synergy between theory and experiment, bridging the gap between theoretical modeling and the rapidly advancing experimental characterization of transport properties. Addressing transport in correlated systems remains a major challenge, as the accuracy of current-current response functions does not yet measure up to that of single-particle spectral functions, the natural output of most Green function-based many-body approaches. Efetov’s group will provide direct experimental access to both electronic spectra and transport measurements, allowing us to implement a unique double handshake approach connecting theoretical predictions and experiments on both kinds of observables.

We will closely collaborate among the three groups of P5 and with our QUAST partners, to investigate topology in many-electron systems together with P3 and P4, explore electron-phonon-induced metastability and dynamics in cooperation with experiments and theory in P6, and study non-local correlations and electron-phonon interaction effects using diagrammatic extensions of the dynamical mean-field theory (DMFT) in collaboration with P1, P4, P6, and P8. Transport phenomena in topological systems will be addressed by joining forces with theoretical developments of real-frequency impurity solvers from P7 and with P1 and P3 on low-temperature magnetotransport experiments.

Methodologically, we will advance the ab initio model-building of electron-phonon-coupled correlated quantum matter, bring phase-space-extension methods for metastable states in DMFT to a next level, advance the modeling of charge- and current-response functions as well as electron-phonon (EPH) vertices, include dispersive phonons, and address spatial correlation effects through diagrammatic extensions of DMFT as well as slave-rotor approaches.

Uwe Bovensiepen (U Duisburg-Essen) | Martin Eckstein (Uni Hamburg) | Philipp Werner (U Fribourg)

Correlated materials exhibit complex free energy landscapes with competing low-energy states, resulting in intricate phase diagrams and pronounced responses to external stimuli. Driving these systems out of equilibrium using ultrashort laser pulses offers a novel perspective on correlation phenomena, providing insights into electron-electron, electron-phonon, and electron-spin interactions. By studying non-equilibrium states and the relaxation dynamics of photo-excited charge carriers, we seek to uncover pathways to induce and stabilize non-trivial long-lived or metastable states that are not accessible by slow thermodynamic pathways. To investigate the dynamics of strongly correlated electron systems, the project combines time-and angle-resolved photoemission spectroscopy (ARPES) to probe the transient electronic structure and femtosecond x-ray absorption spectroscopy (XAS) to explore multiplet dynamics, alongside simulations that use non-equilibrium dynamical mean-field theory (DMFT) and its extensions. We focus on transient non-equilibrium states in bulk- and surface-doped 1T-TaS₂, adatom systems on Si(111) surfaces, and charge transfer insulators, which can reveal non-equilibrium phenomena involving the interplay between local Mott physics and non-local effects.

In the previous funding period, two key advancements on the theoretical side were made to achieve a better understanding of the non-equilibrium dynamics of Mott systems over extended timescales: (i) Development of improved steady-state methodologies, including the use of numerically exact quantum Monte Carlo solvers for photo-doped Mott states, and (ii), extended time-domain simulations, incorporating memory truncation methods for multi-orbital Mott systems. The latter approach was used to simulate multilayer models of 1T-TaS₂ and to clarify the important role of the stacking arrangement in the photo-induced, ultrafast dynamics. Experimentally, the effects of bulk doping on dynamics in 1T-TaS₂ have been investigated. We find doping-induced long-lived non-thermal states and changes of the amplitude mode spectral response linked to changes in the bi- and monolayer stacking. Furthermore, time-resolved x-ray spectroscopy supported by DMFT simulations revealed transient population of local multiplets in CT insulators.

In the second funding period, we would like to step from understanding dynamics that is governed by local correlations to the key question how non-local effects influence the dynamics of correlated systems, thus linking two main threads of QUAST (Fig. 49). We will explore the possibility of controlling long-range interactions in adatom systems and investigate the role of dynamically emergent spatial inhomogeneities in photo-induced phase transitions, as observed in doped 1T-TaS₂. A second main development that is envisioned for the next funding period will be the implementation of efficient higher-order or exact impurity solvers for non-equilibrium DMFT. This will enable more accurate descriptions of multiplet structures, which is relevant for the interpretation of time-resolved XAS measurements, and also aid in the search for non-thermal states in Mott systems with multiple active orbitals.

Maurits W. Haverkort (U Heidelberg) | Fabian Kugler (Uni Köln) | Jan von Delft (LMU München)

Project P7 focuses on developing real-frequency, real-time quantum impurity solvers with capabilities well beyond the current state of the art, and on applying them to several interesting and challenging physical systems.

Quantum impurity solvers are key ingredients of dynamical mean-field theory (DMFT) and its extensions, used in several QUAST projects (P1, P3, P4, P5, P6, P8). DMFT treats the interplay between a given lattice site or cluster of sites (the “impurity”) and the rest of the lattice (the “bath”) as a quantum impurity model with a self-consistently determined bath. Many popular quantum impurity solvers employ imaginary times or frequencies. However, obtaining real-time or -frequency response functions, as observed in experiment, then requires analytic continuation of numerical data. This is a mathematically ill-posed problem, so that achieving very high real-frequency resolution is challenging.

In project P7, we therefore focus on impurity solvers employing real frequencies or real times from the outset. We will employ three types of solvers: (1) The QUANTY package developed by MWH, which can handle open d or f valence shells with arbitrary interactions hybridizing with a few hundred non-interacting bath sites. (2) The MUNRG package developed by current and former members (including FK) of JvD’s group in Munich, based on the numerical renormalization group (NRG), which achieves unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures, but is currently limited to models with at most 4 (spinful) bands. (3) A new tangent-space Krylov solver (TANKS) developed in JvD’s group, which achieves high resolution at both low and high energies and holds promise for handling models with more than 4 (spinful) bands.

Our long-term goal, reaching beyond the next funding period, is to extend the capabilities of these impurity solvers such that they can calculate n-particle correlation functions in the time and frequency domain for open d or f shell elements with arbitrary material-realistic interactions, a Rydberg bandwidth, and 0.1 meV (1K) resolution. This will enable us to solve numerous important problems. Within the next funding period, we will take significant steps towards achieving this ambitious goal. We will develop methodological improvements of our three methods, benchmark them against each other, and, where possible, combine their strengths to boost performance. Within QUAST, these methods will be applied, for example, to Ce Heavy fermion problems with flat bands, magnetic interactions, and possible Kondo ground states (P1), electronic transport in moiré systems (P5), and electron dynamics studied with pump-probe spectroscopy (P6).

Michael Potthoff (U Hamburg) | Alexander I. Lichtenstein (U Hamburg)

This project explores novel physics at the intersection of topologically non-trivial electronic structure, quantum geometry, electron correlations, and slow real-time dynamics in condensed-matter systems. We consider systems with local magnetic moments (LMMs) exchange-coupled to various lattice-electron models. The state of the LMMs is represented by a point in the space of classical spin configurations (“S-space”), the dynamical, topological and geometrical properties of which will be studied in detail. In addition this provides us with new perspectives on the non-local magnetic response of prototypical models for QUAST materials: flat-band systems (studied experimentally in P5), transition-metal dichalcogenides (P6), or Weyl-Kondo semimetals (P1), along with disordered and correlated Chern insulators (with P4) and topological Mott insulators (with P5).

More specifically, we will extend the adiabatic spin-dynamics theory by combining non-linear response theory in the local exchange coupling J and an expansion in the retardation time, quantifying deviations from the adiabatic limit. This allows us to access shorter time scales, as addressed in P6, and provides a “geometrization” of close-to-adiabatic spin dynamics, where the geometric spin torque, spin friction and quantum metric are seen as aspects of the quantum-geometrical tensor (QGT) on S-space. In addition, novel geometrical interactions from terms quadratic in time derivatives Ṡ_i find their interpretation in the geodesics equation.

New ways to topologically characterize correlated electron systems with LMMs are explored in cooperation with P4. Here, we focus on the impact of electron correlations on the topological structure of S-space, characterized by spin-Chern numbers, and deduce the implications of local S-space topology on the correlated electronic structure of gapped systems, including k-space Z and Z₂ topological and disordered systems. With P4 and P5, we will apply this dual, S- and k-space topological characterization to Mott and Anderson insulators.

Systems with a few quantum-spin impurities coupled to Z and Z₂ insulators or BCS superconductors will be studied with quantum-chemistry methods from P7 to find remnants of a finite spin-Chern number in the quantum-spin case and thereby to characterize the J-spectral flow of one-particle Green’s function poles and zeros, and of the two-particle excitations.

Electron correlations will significantly impact the quantum geometry of S-space. This offers the exciting perspective of correlation-driven singularities in the geometry and related feedback on the electronic structure. Together with P4, P1, we aim for methodical extensions of TPSC, D-TRILEX and DΓA approaches to compute the QGT and derived differential-geometrical quantities for gapped correlated systems.