Publications

The Bloch electron energy spectrum of a crystalline solid is determined by the underlying lattice structure at the atomic level. In a 2-dimensional (2d) crystal it is possible to impose a superlattice with nanometer-scale periodicity, allowing to tune the fundamental Bloch electron spectrum, and enabling novel physical properties which are not accessible in the original crystal. In recent years, a top-down approach for creating 2d superlattices on monolayer graphene by means of nanopatterned electric gates has been studied, which allows the formation of isolated energy bands and Hofstadter Butterfly physics in quantizing magnetic fields. Within this approach, however, evidence of electron correlations which drive many problems at the forefront of physics research remains to be uncovered. In this work we demonstrate signatures of a correlated insulator phase in Bernal-stacked bilayer graphene (BLG) modulated by a gate-defined superlattice potential, manifested as a set of resistance peaks centered at carrier densities of integer multiples of a single electron per unit cell of the superlattice potential. We associate the correlated insulator phase to the formation of flat energy bands due to the superlattice potential combined with inversion symmetry breaking. Inducing correlated electron phases with nanopatterning defined electric gates paves the way to custom-designed superlattices with arbitrary geometries and symmetries for studying band structure engineering and strongly correlated electrons in 2d materials.

The simulation of quantum Hall physics with rotating quantum gases is witnessing a revival due to recent experimental advances that enabled the observation of a Bose-Einstein condensate entirely contained in its lowest kinetic energy state, i.e. the lowest Landau level. We theoretically describe this experimental result, and show that it can be interpreted as a squeezing of the geometric degree of freedom of the problem, the guiding center metric. This "geometric squeezing" offers an unprecedented experimental control over the quantum geometry in Landau-level analogues, and at the same time opens a realistic path towards achieving correlated quantum phases akin to quantum Hall states with neutral atoms.

Strange metals arise in a variety of platforms for strongly correlated electrons, ranging from the cuprates, heavy fermions to flat band systems. Motivated by recent experiments in kagome metals, we study a Hubbard model on a kagome lattice whose noninteracting limit contains flat bands. A Kondo lattice description is constructed, in which the degrees of freedom are exponentially localized molecular orbitals. We identify an orbital-selective Mott transition through an extended dynamical mean field theory of the effective model. The transition describes a quantum critical point at which quasiparticles are lost and strange metallicity emerges. Our theoretical work opens up a new route for realizing beyond-Landau quantum criticality and emergent quantum phases that it nucleates.

Lattice symmetries are central to the characterization of electronic topology. Recently, it was shown that Green's function eigenvectors form a representation of the space group. This formulation has allowed the identification of gapless topological states even when quasiparticles are absent. Here we demonstrate the profundity of the framework in the extreme case, when interactions lead to a Mott insulator, through a solvable model with long-range interactions. We find that both Mott poles and zeros are subject to the symmetry constraints, and relate the symmetry-enforced spectral crossings to degeneracies of the original non-interacting eigenstates. Our results lead to new understandings of topological quantum materials and highlight the utility of interacting Green's functions toward their symmetry-based design.

Model Hamiltonians are regularly derived from first-principles data to describe correlated matter. However, the standard methods for this contain a number of largely unexplored approximations. For a strongly correlated impurity model system, here we carefully compare standard downfolding techniques with the best-possible ground-truth estimates for charge-neutral excited state energies and charge densities using state-of-the-art first-principles many-body wave function approaches. To this end, we use the vanadocene molecule and analyze all downfolding aspects, including the Hamiltonian form, target basis, double counting correction, and Coulomb interaction screening models. We find that the choice of target-space basis functions emerges as a key factor for the quality of the downfolded results, while orbital-dependent double counting correction diminishes the quality. Background screening to the Coulomb interaction matrix elements primarily affects crystal-field excitations. Our benchmark uncovers the relative importance of each downfolding step and offers insights into the potential accuracy of minimal downfolded model Hamiltonians.

The Hund-metal route to strong correlations continues to attract large interest in the condensed-matter community. The question arose to what extent it applies to the infinite-layer nickelates and, as a related question, to two-orbital systems in general. Here, we provide a low-energy perspective on this topic through a dynamical mean-field study using the numerical renormalization group (NRG) as a real-frequency impurity solver. We find that the RG flow from high to low energy is a uniquely adequate tool to reveal two-stage Kondo screening (2SKS), a fascinating mechanism for Hund physics. Further, we show that 2SKS takes place in a quarter-filled two-orbital system, but can be easily suppressed by a sufficiently large crystal-field splitting. We apply these insights to LaNiO2 using a recently proposed two-orbital model and show that it is indeed the crystal-field splitting that suppresses multiorbital phenomena in this scenario. Our general findings open the way for further explorations of 2SKS, and we propose a way of reviving low-energy Hund physics in LaNiO2 by counteracting the crystal field.

Conceptually, the Matsubara formalism (MF), using imaginary frequencies, and the Keldysh formalism (KF), formulated in real frequencies, give equivalent results for systems in thermal equilibrium. The MF has less complexity and is thus more convenient than the KF. However, computing dynamical observables in the MF requires the analytic continuation from imaginary to real frequencies. The analytic continuation is well-known for two-point correlation functions (having one frequency argument), but, for multipoint correlators, a straightforward recipe for deducing all Keldysh components from the MF correlator had not been formulated yet. Recently, a representation of MF and KF correlators in terms of formalism-independent partial spectral functions and formalism-specific kernels was introduced by Kugler, Lee, and von Delft [Phys. Rev. X 11, 041006 (2021)]. We use this representation to formally elucidate the connection between both formalisms. We show how a multipoint MF correlator can be analytically continued to recover all partial spectral functions and yield all Keldysh components of its KF counterpart. The procedure is illustrated for various correlators of the Hubbard atom.

Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief propagation, a method that was originally formulated for performing statistical inference on graphical models and has recently found applications in tensor network algorithms. We show that this method is closely related to known tensor network gauging methods. It has the practical advantage, however, that existing belief propagation implementations can be repurposed for tensor network gauging, and that belief propagation is a very simple algorithm based on just tensor contractions so it can be easier to implement, optimize, and generalize. We present numerical evidence and scaling arguments that this algorithm is faster than existing gauging algorithms, demonstrating its usage on structured, unstructured, and infinite tensor networks. Additionally, we apply this method to improve the accuracy of the widely used simple update gate evolution algorithm.

We explore all the chiral limits of perturbed Dirac field theories applicable to C

The phenomena of superconductivity and charge density waves are observed in close vicinity in many strongly correlated materials. Increasing evidence from experiments and numerical simulations suggests both phenomena can also occur in an intertwined manner, where the superconducting order parameter is coupled to the electronic density. Employing density matrix renormalization group simulations, we investigate the nature of such an intertwined state of matter stabilized in the phase diagram of the elementary t-t-U Hubbard model in the strong coupling regime. Remarkably, the condensate of Cooper pairs is shown to be fragmented in the presence of a charge density wave where more than one pairing wave function is macroscopically occupied. Moreover, we provide conclusive evidence that the macroscopic wave functions of the superconducting fragments are well-described by soliton solutions of a Ginzburg-Landau equation in a periodic potential constituted by the charge density wave. In the presence of an orbital magnetic field, the order parameters are gauge invariant, and superconducting vortices are pinned between the stripes. This intertwined Ginzburg-Landau theory is proposed as an effective low-energy description of the stripe fragmented superconductor.