Electronic Correlations and Beyond
- in Memory of Peter Fulde

Several Heavy Fermion systems (notably, CeCu6-xAux ) show SDW instability and exhibit various NFL behaviors such as sub T-linear resistivity and log(T)-divergence in specific heat, hence called quantum critical phase (QCP). Furthermore, spin-fluctuation dynamics measured by neutron scattering exhibit a scaling behavior with a non-integer critical exponent of 0.75 (WF fixed point) in contrast to the Hertz-Millis theory. In this talk, I propose a possible way to cure the Hertz-Millis theory to generate a Non-Gaussian fixed point and Non-Fermi liquid behaviors.

Yttrium Iron Garnet is a much studied and widely used crystalline ferrimagnet but belongs to a whole series, when the non-magnetic yttrium ion is substituted for the other rare earth ions bearing a magnetic moment. While many details of the magnetic structurse were recognised long ago by Neel and co-workers, there has been a substantial renewal of interest in recent years. This is because of the potential applications in spintronics applications, exploiting the large spin-orbit coupling in the rare-earth and the strong coupling of the iron moments. New insights can de found by the use of spectroscopic methods, particularly spin-polarised neutron and X-ray beams, applied to crystals and film samples. Novel experimental techniques look at special dynamic properties at compensation temperatures, where either the net magnetisation or the net total angular moment vanish because of the different temperature dependence of the angular momenta of the rare earth ions and the iron moments.I will discuss new ideas in the dynamics of non-collinear magnetic structures that arise, with the interplay of the crystal field and exchange effects and the relation to measurements of the spin-Seebeck effects.

Electronic correlations can lead to highly entangled states of quantum matter in which electrons and spins are fractionalized into nonlocal novel elementary excitations. Quantum spin liquids (QSLs) in frustrated magnets are among such states and represent a timely field of search for manifestations of fractional quasiparticles. Here we will report on some of their fingerprints in transport and spectroscopy in Kitaev magnets, which are among the QSLs of great current interest, comprising a compass Ising model on the honeycomb lattice, allowing for fractionalization of spins into mobile Majorana matter and gauge flux visons.

In this talk, we report the progress of predicting four different phases (Haldane, Dimerized, Ferromagnetic, and critical phases) of 1-D spin-1 Bilinear-Biquadratic models by using unsupervised learning. The difficulty of detecting a second-order phase transition point is overcome by using three spin-spin correlation functions.

Spintronics replaces electronics, by using both the charge and the spin of the electrons. Quantum information is contained in qubits (two-componennt spinors). Here we discuss mobile (flying) electrons, which can carry such quantum information. Tuning this information involves electric and magnetic fields, which vary geometrical and topological phases on the related spinors. Although the spin-orbit interaction (which determines the Aharonov-Casher phase) is a major tool for such tuning, it is often not sufficient, because it conserves time-reversal symmetry. The talk will describe several ways to break this symmetry, and allow spin selection, both for a mesoscopic interferometer and for helical molecules.

The pseudogap phase in cuprate superconductors is one of the most intriguing challenges in the theory of high temperature superconductivity. In this talk we elaborate on the idea that pseudogap phenomena are mostly due to strong magnetic fluctuations. Using the two-dimensional Hubbard model to describe the electrons in the copper-oxygen planes of the cuprates, a gauge theory of fluctuating magnetic order is formulated and analyzed [1]. The theory is based on a fractionalization of electrons in fermionic chargons with a pseudospin degree of freedom and bosonic spinons, which leads to a SU(2) gauge redundancy. The chargons undergo Neel, spiral, or stripe order below a density dependent transition temperature $T^*$. Fluctuations of the spin orientation are described by a non-linear sigma model obtained from a gradient expansion of the spinon action. The spin stiffnesses are computed from a renormalization group improved random phase approximation. The spinon fluctuations prevent magnetic long-range order of the electrons at any finite temperature. The phase with magnetic chargon order exhibits many features characterizing the pseudogap regime in high-Tc cuprates: a strong reduction of charge carrier density, a spin gap, and Fermi arcs. A substantial fraction of the pseudogap regime exhibits electronic nematicity. [1] P. M. Bonetti and W. Metzner, Phys. Rev. B 106, 205152 (2022).

We review our recent development of the Multiscale Functional Renormalization Group (MfRG) as an approach to the study of strongly correlated electronic materials in which both electron-electron (e-e) and electron-phonon (e-ph) interactions play important roles. Our MfRG method includes in a systematic manner the effects of the scattering processes involving electrons away from the Fermi surface and also permits proper inclusion of phonon retardation effects. After introducing the basic concepts, I will discuss in detail the application of this method to the 1D Extended Hubbard model and show that it correctly captures the subtle bond-order wave (BOW) phase in that model. We will then discuss additional applications of the MfRG method and show that it can be applied to multi-band models in higher dimensions, recovering previously known results and predicting novel behaviors that have been seen in experiment. Finally, we will discuss possible future applications of the MfRG approach.

"Strange Metallicity", by now seen in a variety of correlated electronic systems that exhibit novel superconductivity, presents an enigma. The "normal" metals that turn into novel, non-BCS superconductors fall out of the purview of any traditional or modern Landau quasiparticle theory. Rather, in spite of very different chemistry, all these cases seem to exhibit anomalies resulting from infra-red singular long-time dynamical responses. These findings have spurred concepts like "Planckian dissipation" and universal scrambling in quantum matter. I will argue, using one single input from (cluster)-DMFT (CT-QQMC), that selective Mott localisation, either in orbital- or momentum space is a local mechanism, unrelated to consequent Landauesque symmetry-breaking, that can underlie the anomalous responses. Using an analytic framework with the above single numerical input, I will attempt to describe how this seems to capture a number of salient "strange metal" features. Using the same formulation, I will then seek to describe how the self-same mechanism (selective Mottness) that lead to normal state singular behavior also generates a singular pair glue that is not BCS-like and does not involve any well-defined or critical boson as the pair glue. An attempt to discuss the non-BCS ratio of the superconducting gap-to-T$_{c}$ in a wide variety of strange cases, like cuprates, Fe arsenides and f-electron systems in light of the present approach will be made.

Optically active polymers are intensively studied because of their optical properties, promising applications in light emitting and in energy harvesting. Still, there is no consensus on the very nature of the light emitting excitons. We develop an approach considering the polymers as generic one dimensional semiconductors with specific features of strongly correlated electronic systems. We demonstrate that optics of polymers can be understood within this combined frame of long range Coulomb interaction together with strong intra-monomer electronic correlations. Theory predicts different kinds of weakly and strongly bound excitons, in singlet and triplet states; all of them already show up in experiments. We shall mention also new polymers with a degenerate ground state which demonstrate solitons with expecting non-integer charge. These systems are promising in search of ferroelectricity in polymers.

The mean-field approximation provides a simple approach for many models of correlated particles on lattices. It replaces the original finite dimensional lattice with a generalized multidimensional version, in the infinite dimensional limit. The same approach sometimes works for zeta functions defined in terms of integers on lattices. We show how these zeta functions simplify in the infinite dimensional limit.

Experiments on the low temperature properties of multicomponent glasses revealed in 1998 evidence for a phase transition to a phase with strongly enhanced magnetosensitivity[1]. In the experimental paper [1] and in a theoretical investigation, initiated by Peter Fulde[2], it was suggested that this indicates a transition to a a coherent macroscopic quantum state of coupled tunneling systems. Here we review the status of the theory of quantum phase transitions in coupled tunneling systems, and whether the surprising transition to a phase with strongly enhanced magnetosensitivity discovered in the low temperature electric permittivity of multicomponent glasses can indeed be due to a quantum phase transition to a phase, where mesoscopically or even macroscopically large numbers of tunneling systems are coupled by the interaction and start tunneling in synchrony, yielding a strongly enhanced diamagnetic response as suggested in Ref. [2]. With the recent progress in understanding in long range interacting disordered quantum spin systems we aim to address this problem again, and review recent evidence for a Large Spin fixed point in such systems, which might provide the theoretical foundation for explaining the experimental results of Ref. [1], and thereby confirm the insightful intuition by Peter Fulde as revealed and developed in intensive discussions with the experimentalist Peter Strehlow and the author 25 years ago. [1] P. Strehlow, C. Enss, S. Hunklinger, Evidence for a phase transition in glasses at very low temperature: a macroscopic quantum state of tunneling systems?, Phys. Rev. Lett. 80, 5361 (1998). [2] S. Kettemann, P. Fulde, P. Strehlow, Correlated Persistent Tunneling Currents in Glasses, Phys. Rev. Lett. 83, 4325 (1999).

We all remember Peter's explanation of the correlation hole. I want to talk about the correlation hole that shows up in spatial patterns formed by correlated random walks [1]. I want to connect this to recent model calculations that help us to understand the spatial patterns formed by particles in turbulence [2]. I'll go rather quickly from $\hbar \neq 0$ to $\hbar = 0$. [1] Wilkinson & Mehlig, Phys. Rev. E 68 (2003) 040101 [2] Bec, Gustavsson & Mehlig, Annu. Rev. Fluid. Mech. 56 (2024) 189-213

We show that spontaneous time-reversal-symmetry (TRS) breaking can naturally arise from the interplay between pair density wave (PDW) ordering at multiple momenta and nesting of Fermi surfaces (FS). Concretely, we consider the PDW superconductivity on a hexagonal lattice with nested FS at 3/4 electron filling, which is related to a recently discovered superconductor CsV3Sb5. Because of nesting of the FS, each momentum on the FS has at least two counterparts on the FS to form finite momentum Cooper pairs, resulting in a TRS and inversion broken PDW state with stable Bogoliubov Fermi pockets. Possible implications to the Kagome superconductor CsV3Sb5 and future experiments will be discussed.

Early proposals for creating Majorana zero modes involve spin triplet superconductivity while almost all known superconductors belong to the spin singlet class with a few possible exceptions. As a result, various ingenious heterostructures of superconducting nano-wires have been proposed to generate the required p-wave pairing component. In this presentation, I will review the recent findings of two-component superconductivity with a dominant p-wave part in CoSi2/TiSi2 heterostructures In particular, I will review the effect of interface-induced Rashba spin orbit coupling on the conductance of a three terminal ``T" shape superconducting device and present our calculations for the differential conductance for this device within the quasi-classical formalism that includes the mixing of triplet-singlet pairing due to the Rashba spin orbit coupling.

The low energy crystalline electric field states and heavy electron bands in strongly correlated 4f- and 5f electron compounds exhibit possibilities of broken symmetry states and collective excitations at low temperatures as well as distinct interaction effects with the lattice. Characteristic examples such as charge ordering, multipolar order and coexistence of magnetism and unconventional superconductivity is presented, focusing on the Ce- Yb- and U- based compounds, including the most prominent heavy fermmion materials. Emphasis is also placed on the methods to investigate order parameter symmetries and the associated collective excitations.

It will describe how the diffusion process is used in generative AI model and a new physics-based AI model.

Wavefunctions can tell everything. The computation of many-electron wavefunctions from first principles in solid-state context is one of the long-term projects set up by Peter Fulde. A few illustrative examples are reviewed in this contribution, ranging from the calculation of quasiparticle bands in either weakly [1] or strongly [2] correlated electronic systems to the nature of ground-state wavefunctions across group-5 mixed-valent 'breathing' pyrochlores [3] and in alkaline-earth hexaborides [4]. [1] L Hozoi, U Birkenheuer, P Fulde, A Mitrushchenkov, and H Stoll, Ab initio wavefunction-based methods for excited states in solids: correlation corrections to the band structure of ionic oxides, Phys. Rev. B 76, 085109 (2007). [2] L Hozoi, M S Laad, and P Fulde, Fermiology of cuprates from first principles: from small pockets to the Luttinger Fermi surface, Phys. Rev. B 78, 165107 (2008). [3] T Petersen, P Bhattacharyya, U K Roessler, and L Hozoi, Resonating holes vs molecular spin-orbit coupled states in group-5 lacunar spinels, Nat. Commun. 14, 5218 (2023). [4] T Petersen, U K Roessler, and L Hozoi, Quantum chemical insights into hexaboride electronic structures: correlations within the boron p-orbital subsystem, Commun. Phys. 5, 214 (2022).

Peter Fulde's early work on the so-called "local ansatz" for a wavefunction in extended systems provided the basis for the application of correlation methods, developed mainly in Theoretical Chemistry for finite systems, to extended systems namely solids. Within this contributions I will focus on the method of increments and its application to different kind of solids, from insulators to metals, from van der Waals bound rare gas crystals to metallic binding in mercury.

In cerium oxide-based catalysis, surface structure plays a crucial role in the catalyst's reactivity. The vibrational frequency of surface-adsorbed carbon monoxide (CO) surface serves as a precise marker for identifying active defect sites and determining the exposed crystal facets. To analyze spectroscopic data accurately, reference data for well-characterized single crystal surfaces and a precise theoretical assignment of the vibrations are essential. Significant efforts have been made to gather comprehensive IRRAS (infrared reflection absorption spectroscopy) data for CO adsorption on all three low-index single-crystal ceria surfaces, both in their oxidized and reduced forms, at saturation coverage.$^{1-3}$ However, applying theoretical methods, many of which rely on density functional theory (DFT) with the generalized gradient approximation (GGA) for exchange and correlation, has encountered significant challenges in accurately describing CO adsorption on oxides. Recently, there has been a growing interest in combining machine learning (ML) techniques with DFT calculations for interpreting spectroscopic data. In this study, we demonstrate that by employing DFT with the HSE06 hybrid functional yields excellent agreement with experimental data. Achieving this high level of consistency, requires meticulously adjustment of the model to closely align with experimental conditions. These conditions encompass factors such as surface orientation, the presence of oxygen vacancies, and the extent of CO coverage. Our study reveals that CO is highly sensitive to the precise structure of ceria surfaces. We also explain the limitations of conventional DFT by highlighting its inability to accurately capture facet- and configuration-specific donation and backdonation effects, which control the changes in the C$─$O bond length upon CO adsorption and the CO force constant.$^{4,5}$ Our findings establish a robust theoretical foundation for the accurate interpretation of experimental results. Furthermore, we emphasize the importance of understanding the origin of DFT data before blindly incorporating them into ML models.$^{6}$ [1] C. Yang, X. Yu, S. Heisler, A. Nefedov, S. Colussi, J. Llorca, A. Trovarelli, Y.Wang, C. Wöll, Angew. Chem., Int. Ed. 56 (2017) 375. [2] C. Yang, L.-L. Yin, F. Bebensee, M. Buchholz, H. Sezen, S. Heissler, J. Chen, A. Nefedov, H. Idriss, X.-Q. Gong, C. Wöll, Phys. Chem. Chem. Phys. 16 (2014) 24165. [3] C. Yang, M. Capdevila-Cortada, C. Dong, Y. Zhou, J. Wang, X. Yu, A. Nefedov, S. Heissler, N. López, W. Shen, C. Wöll, Y. Wang, J. Phys. Chem. Lett. 11 (2020) 7925. [4] P. G. Lustemberg, P. N. Plessow, Y. Wang, C. Yang, A. Nefedov, F. Studt, C. Wöll, M. V. Ganduglia-Pirovano, Phys. Rev. Lett. 125 (2020) 256101. [5] P. G. Lustemberg, C. Yang, Y. Wang, C. Wöll, M. V. Ganduglia-Pirovano, J. Chem. Phys. 159 (2023) 034704. [6] M. V. Ganduglia-Pirovano, A. Martínez-Arias, S. Chen, Y. Wang, Pablo G. Lustemberg, Mater. Today Sustain. 26 (2024) 100783.

Biological sensory systems exhibit remarkable power efficiency, largely due to their capacity to store and recall learned solutions. Emulating this efficiency in artificial sensory systems necessitates adaptability and analog functionality. One promising approach involves computing based on the complex dynamics of interacting oscillators, particularly when these oscillators serve as the building blocks of artificial intelligence. This talk explores how the Coulomb blockade effect in single molecule transistors can form the foundation of the smallest conceivable oscillators. We will discuss a potential pathway from utilizing Coulomb blockade to developing oscillatory neural networks capable of executing complex tasks such as image recognition and tackling computationally intensive problems like vertex coloring.

“Nonreciprocity” means “not going the same way backward as forward”. The well-known is the rectification by using PN junctions in electronics where electrons flow in one direction but not the other. The spin Hall effect and its inverse are the interconversion mechanism between electron current and spin current. It has been shown that the interconversion is reciprocal and described by the Onsager reciprocal relation [1]. On the contrary, many of the spin transport phenomena are nonreciprocal. Here, the nonreciprocity in spin transport is discussed together with various examples. The key is that the spin current is a flow of spin angular momentum, in contrast to the electric current. A flow of electrons can have the orbital angular momentum , which is called “vorticity”, and may be interconverted with spin current [2]. However, since the vorticity of electron flow is highly nonlinear, the conservation mechanism, i.e., the spin-vorticity coupling, is also nonlinear and, in general, nonreciprocal[1]. As a result, we find a variety of nonreciprocal phenomena in spin transport. The nonreciprocity of surface acoustic waves in magnetic films [3], the magnetic skyrmion generation and annihilation by electric current in magnetic films with notch structure [4], and the spin current generation in the graded materials [5] will be discussed. [1] T. Kimura, Y. Otani, T. Sato, S. Takahashi and S. Maekawa: Phys. Rev. Lett. 98, 156601 (2007), [2] M.Matsuo, E.Saitoh and S.Maekawa, Chapter 25 in “Spin Current” ed. S.Maekawa et al. (Oxford University Press, 2017). [3] M. Xu, K. Yamamoto, J. Puebla, K. Baungaert, B. Rana, K. Miura, H. Takahashi, D. Grundler, A. Maekawa and Y. Otani: Sci. Adv. 6, eabb1724 (2020), [4] J.Fujimoto, W.Koshibae, M.Matsuo and S.Maekawa, Phys. Rev. B103, L220404 (2021). [5] G.Okano, M.Matsuo, Y.Ohnuma, S.Maekawa, and Y.Nozaki, Phys. Rev. Lett. 122, 217701 (2019).

Recent discovery of high temperature superconductivity La3Ni2O7 under high pressure has attracted a lot of attention. In this talk, I shall present our theory for electronic structure of the compound and address the similarity and difference of this newly discovered bilayer nickelate superconductor in comparison with high temperature superconducting cuprates and with infinite layer nickelate superconductor Nd_(1-x)Sr_xNiO2. I shall propose that La3Ni2O7 is a self-doped molecule Mott insulator, where molecule stands for the strongly coupled nickel ions on the top and bottom layers.