The concept of electron correlation has long been a cornerstone of modern condensed matter physics and quantum chemistry. Traditionally, correlation effects are quantified solely by a real-valued magnitude that measures the strength of inter-electronic interactions beyond mean-field approximations. In this work we propose a generalized framework that incorporates not only the amplitude of correlation but also a phase factor, denoted as φ_C. The combined entity, referred to as the Electron Correlation Phase Spectrum (ECPS), provides a richer description of correlated electronic systems. By formulating the ECPS in terms of many-body wavefunctions and Green's functions, we demonstrate that the phase component encodes information about collective excitations, topological characteristics, and symmetry-breaking phenomena. The ECPS offers a unified language for interpreting spectroscopic data from angle-resolved photoemission spectroscopy, scanning tunneling microscopy, and resonant inelastic x-ray scattering, thereby opening new avenues for discovering hidden electronic orders and potentially guiding the next generation of Nobel-prize-worthy discoveries in quantum materials.
The concept of electron correlation has long been a cornerstone of modern condensed matter physics and quantum chemistry. Traditionally, correlation effects are quantified solely by a real-valued magnitude that measures the strength of inter-electronic interactions beyond mean-field approximations. In this work we propose a generalized framework that incorporates not only the amplitude of correlation but also a phase factor, denoted as φ_C. The combined entity, referred to as the Electron Correlation Phase Spectrum (ECPS), provides a richer description of correlated electronic systems. By formulating the ECPS in terms of many-body wavefunctions and Green's functions, we demonstrate that the phase component encodes information about collective excitations, topological characteristics, and symmetry-breaking phenomena. The ECPS offers a unified language for interpreting spectroscopic data from angle-resolved photoemission spectroscopy, scanning tunneling microscopy, and resonant inelastic x-ray scattering, thereby opening new avenues for discovering hidden electronic orders and potentially guiding the next generation of Nobel-prize-worthy discoveries in quantum materials.
Electron correlation is a cornerstone of modern condensed matter physics, traditionally quantified by the magnitude of the two‑particle correlation function. In this work we introduce the concept of the Electron Correlation Phase Spectrum (ECPS), which records not only the amplitude but also the phase of the correlation function. The phase of a correlation function contains information about the relative timing and spatial ordering of electronic excitations, and its spectral decomposition provides a new observable for quantum materials spectroscopy. We formulate a rigorous definition of the ECPS, derive its properties from many‑body theory, and demonstrate how it can be computed from first‑principles wavefunctions. The ECPS is shown to be sensitive to hidden orders, fractionalization, and topological invariants that are invisible to conventional amplitude‑only probes. This work lays the theoretical foundation for future experimental realizations of phase‑sensitive correlation spectroscopy, with potential applications to high‑temperature superconductors, quantum spin liquids, and engineered quantum devices.
The study of electron correlation has traditionally focused on static measures of interaction strength, such as the on‑site Coulomb repulsion U or the exchange integral J. However, the dynamical aspect of correlations—how perturbations propagate through an electronic system—has received comparatively little attention. In this work we introduce the concept of the Electron Correlation Velocity Spectrum (ECVS), which assigns a propagation speed v_c(ω) to correlation effects at a given frequency ω. This framework treats correlation as a wave‑like entity whose velocity depends on the energy scale, offering a new lens through which to examine many‑body dynamics. We derive the formalism starting from the time‑dependent two‑particle correlation function, transform to the frequency domain, and extract v_c(ω) by analyzing the spatial phase delay of correlation signals. A simplified lattice model demonstrates that v_c(ω) can vary dramatically across the spectrum, even changing sign in strongly interacting regimes. The implications of a frequency‑dependent correlation velocity are profound: they provide a natural explanation for disparate relaxation times in pump‑probe experiments, predict novel regimes of non‑local entanglement propagation, and suggest new experimental observables in ultrafast electron microscopy and time‑resolved spectroscopy. The ECVS framework opens a pathway to quantify dynamical correlation in complex systems, bridging the gap between static many‑body theory and real‑time electronic motion.
Correlated electron systems present a profound challenge in condensed matter physics due to the intricate interplay between charge, spin, orbital, and lattice degrees of freedom. Understanding their rich macroscopic phase diagrams, which include phenomena like high-temperature superconductivity, colossal magnetoresistance, and Mott insulation, necessitates a bridge between the microscopic quantum interactions and emergent collective behavior. This paper introduces and formalizes the concept of quantum fugacity as a critical thermodynamic parameter capable of establishing this connection. Extending the classical notion of fugacity—a measure of a real gas's effective partial pressure—to the quantum many-body realm, quantum fugacity accounts for both particle density and the profound influence of quantum statistics and strong electron correlations. We develop a theoretical framework to calculate quantum fugacity from microscopic Hamiltonians, demonstrating its utility in mapping quantum phase transitions and discerning the driving forces behind symmetry-breaking phases. Through this approach, we show how variations in quantum fugacity serve as indicators for the onset of novel phases, providing a unified perspective on the phase behavior of diverse correlated electron materials. This concept offers a powerful new tool for designing and predicting materials with desired quantum functionalities.
The discovery of high-Tc superconductivity in cuprates in 1986 moved strongly correlated systems from exotic worlds interesting only for pure theorists to the focus of solid-state research. In recent decades, the majority of hot topics in condensed matter physics (high-Tc superconductivity, colossal magnetoresistance, multiferroicity, ferromagnetism in diluted magnetic semiconductors, etc.) have been related to strongly correlated transition metal compounds. The highly successful electronic structure calculations based on density functional theory lose their predictive power when applied to such compounds. It is necessary to go beyond the mean field approximation and use the many-body theory. The methods and models that were developed for the description of strongly correlated systems are reviewed together with the examples of response function calculations that are needed for the interpretation of experimental information (inelastic neutron scattering, optical conductivity, resonant inelastic X-ray scattering, electron energy loss spectroscopy, angle-resolved photoemission, electron spin resonance, and magnetic and magnetoelectric properties). The peculiarities of (quasi-) 0-, 1-, 2-, and 3- dimensional systems are discussed.
The exploration of quantum phases in strongly correlated electron systems represents a frontier in condensed matter physics, offering insights into phenomena such as high-temperature superconductivity, Mott insulation, and quantum spin liquids. Traditional theoretical approaches, relying on perturbative or mean-field approximations, often fall short in capturing the intricate interplay of electron correlations that drive these exotic phases. This paper delves into the critical role of exact and highly accurate diagrammatic expansions as powerful, non-perturbative tools for unraveling the emergence and characterization of quantum phases. We review the theoretical foundations of these methods, including advanced techniques like Dynamical Mean-Field Theory extensions and the Functional Renormalization Group, and discuss their ability to systematically incorporate non-local correlations. By examining their application to canonical models, we illustrate how these expansions provide a robust framework for constructing phase diagrams, predicting novel quantum states, and discerning the mechanisms underlying quantum phase transitions. We highlight the computational advancements, such as diagrammatic Monte Carlo, that enable the practical implementation of these complex theories. Finally, we discuss current challenges and future prospects, emphasizing the potential of exact diagrammatic expansions to deepen our understanding of quantum matter and guide the discovery of new materials with tailored functionalities.
The calculation of a wavefunction took about two afternoons, and five wavefunctions were calculated in the whole …. Wigner and Seitz, 1933 Summary In order to explain many important properties of materials and phenomena, it is necessary to go beyond independent-particle approximations and directly account for many-body effects that result from electronic interaction. The many-body problem is a major scientific challenge, but there has been great progress resulting from theoretical developments and advances in computation. This chapter is a short introduction to the interacting-electron problem, with some of the history that has led up to the concepts and methods described in this book. The many-body interacting-electron problem ranks among the most fascinating and fruitful areas of research in physics and chemistry. It has a rich history, starting from the early days of quantum mechanics and continuing with new intellectual challenges and opportunities. The vitality of electronic structure theory arises in large part from the close connection with experiment and applications. It is spurred on by new discoveries and advances in techniques that probe the behavior of electrons in depth. In turn, theoretical concepts and calculations can now make predictions that suggest new experiments, as well as provide quantitative information that is difficult or not yet possible to measure experimentally. This book is concerned with the effects of interactions between electrons beyond independent-particle approximations. Some phenomena cannot be explained by any independent-electron method, such as broadening and lifetime of excited states and two-particle bound states (excitons) that are crucial for optical properties of materials. There are many other examples, such as the van derWaals interaction between neutral molecules that arises from the dipole–induced dipole interaction. This force, which is entirely due to correlation between electrons, is an essential mechanism determining the functions of biological systems. Other properties, such as thermodynamically stable magnetic phases, would not exist if there were no interactions between electrons; even though mean-field approximations can describe average effects, they do not account for fluctuations around the average. Ground-state properties, such as the equilibrium structures of molecules and solids, can be described by density functional theory (DFT) and the Kohn–Sham independent-particle equations. However, present approximations are often not sufficient, and for many properties the equations, when used in a straightforward way, do not give a proper description, even in principle.