Welcome! Our group is carrying out research at the interface of Quantum Information Theory, Quantum Computing and Quantum Many-Body Physics, particularly Quantum Chemistry. We resort to analytic approaches complemented and guided by computational studies to gain universal insights into interacting quantum many-body systems. A particular emphasis lies on the concept of reduced density matrices and the ground state problem.
Entanglement is one of the most fascinating concepts in modern physics. Its importance in physics and chemistry stems from three distinct reasons.
(i) It provides deep insights into the properties and behavior of physical and chemical systems. Notable examples include the formation and breaking of chemical bonds, as well as quantum phase transitions.
(ii) It serves as a diagnostic tool for describing many-body quantum states. Quantifying entanglement in a precise way has led to the development of more efficient numerical methods, for example for computing ground state energies in strongly interacting quantum systems.
(iii) It is a fundamental resource in quantum information science, where it plays a central role in enabling quantum information processing tasks.
A large part of quantum information theory has focused on entanglement between distinguishable subsystems ("Alice versus Bob"). However, in view of points (i) and (ii), entanglement in systems of identical particles — such as electrons — is at least equally relevant. The indistinguishability of fermions, though, introduces several conceptual difficulties. Entanglement is usually defined in terms of correlations between subsystems. But what is the appropriate notion of subsystems in the Hilbert space of antisymmetric N-electron wave functions? Even if such a structure can be introduced, it is not uniquely defined.
Drawing on ideas from resource theory, we examine two natural ways of defining entanglement and correlation in fermionic systems. The first approach measures how close a given N-electron state is to the set of uncorrelated Slater determinant states. The second is based on second quantization and describes the extent to which orbitals, rather than particles, are entangled and correlated. As explained in detail in, we construct corresponding measures by using a geometric picture of quantum states. We believe that these notions of particle and orbital correlation provide a concise and operationally meaningful alternative to the commonly used concepts of static and dynamic correlation in chemistry and materials science.
We are also developing protocols to extract entanglement from specific chemical systems. In particular, we are interested in how much physical work is required to extract this entanglement, and how this relates to the individual binding energies that must be overcome.
One of the central challenges in physics, chemistry, and materials science is the description of interacting quantum many-body systems, particularly in their ground states at zero temperature. This problem spans all length scales — from atoms and molecules at the microscopic scale to solids and neutron stars at the macroscopic and astronomical scale.
Building on our interdisciplinary background in quantum many-body physics, quantum information theory, and mathematical physics, we are developing a more systematic and effective approach to this notoriously difficult ground state problem. To clarify the scope, note that in realistic quantum many-body systems, electrons interact only via two-body forces, and these interactions typically display some form of spatial locality. We aim to explore, quantify, and make use of the implications of these two fundamental features.
In particular, we plan to show — from a general perspective — that the universal tension between energy minimization and fermionic exchange symmetry, when combined with the structure imposed by two-body interactions and locality, leads to a substantial reduction of particle and orbital correlations in ground states compared to generic quantum states.
It is also noteworthy that all major numerical methods developed over the past 90 years across physics, chemistry, and materials science can, in essence, be grouped into two broad categories, each with distinct strengths and limitations. The first includes methods such as density functional theory and coupled cluster theory, which are well suited for capturing strong particle correlations but largely overlook important orbital correlations. The second category includes methods such as the density matrix renormalization group, which can accurately describe strong orbital correlations but fail to capture key particle correlations.
One of our main research goals is to develop a combined approach that can describe both types of correlation — particle and orbital — in an efficient and unified framework.
One of the most refined ways to exploit spatial locality in one-dimensional lattice models is provided by the well-known density matrix renormalization group (DMRG) approach. Its remarkable success is largely due to the reduced spatial correlations, as described by the area law for entanglement entropy: the spatial entanglement S between the left and right halves of the lattice is significantly lower than in generic quantum states.
In contrast, the recent success of DMRG in quantum chemistry (QC-DMRG) is more surprising. Why should molecular Hamiltonians, written in second quantization with respect to a set of D orbitals, display any kind of locality on the artificial one-dimensional lattice defined by these orbitals?
One of our main goals is to explain the emergence of such effective locality in QC-DMRG by tracing it to a more fundamental origin — the universal tension between energy minimization and fermionic exchange symmetry in systems of confined fermions. Building on this understanding, we aim to use tools from quantum information theory to propose a scheme for optimizing the artificial orbital ordering, so as to localize the interaction as much as possible. This scheme is expected to be particularly effective in systems where the fermions are confined by a strong external potential.
Despite the notable success of QC-DMRG in treating atoms and molecules with up to fourty electrons, several important limitations remain, which we intend to address. For example, to recover the missing dynamic correlations, we are developing hybrid approaches that combine QC-DMRG with ground-state methods suited for capturing such effects, such as density functional theory or coupled cluster theory. In addition, to avoid the growth of effective correlation lengths in large virtual orbital spaces, we are exploring more general ansatz classes beyond matrix product states.
Density functional theory (DFT) is the workhorse of modern electronic structure theory in physics, chemistry, and materials science. Its widespread use is largely due to its low computational cost, which allows the treatment of even macroscopically large systems. However, DFT also has well-known fundamental limitations. The most prominent is its inability to describe strongly correlated systems, especially those dominated by static correlations. This shortcoming is not surprising, as the standard Kohn–Sham implementation relates the density to a single Slater determinant.
To better describe strongly correlated systems, it has been proposed to extend DFT by using the full one-particle reduced density matrix (1RDM) instead of just the spatial density. By allowing for fractional occupation numbers, this 1RDM functional theory (1RDMFT) offers a more natural and flexible framework for treating strong correlations.
One of our central goals is to establish a solid theoretical foundation for 1RDMFT. Drawing on methods from quantum information theory and mathematical physics, we are identifying universal features of the exact but unknown 1RDM functional. For example, a general relation between 1RDMs and their corresponding N-fermion quantum states allowed us to prove that the gradient of the universal functional diverges repulsively whenever an occupation number approaches its extremal values, n= 0 or n=1. In other words, we have shown that the fermionic exchange symmetry manifests itself in all fermionic systems in the form of a diverging “exchange force”. A similar feature arises in bosonic systems, where the corresponding theory predicts a so-called Bose–Einstein force, offering a concise and universal explanation for the absence of complete Bose–Einstein condensation in nature (i.e., the phenomenon of quantum depletion).
Another important open question concerns the role of the generalized Pauli constraints (GPCs) in 1RDMFT. In recent analytical work, we found strong evidence that the influence of GPCs has been underestimated so far, and that they may play a significant role in shaping the form of the universal functional.
In solid-state systems, 1RDMFT takes a particularly simple form. For example, in translationally invariant one-band lattice models, the natural orbitals are known from the outset, and the theory effectively reduces to a functional of the momentum occupation numbers. In this context, we recently proposed a systematic approach to constructing a hierarchy of functional approximations, based on different levels of irreducible fermionic particle entanglement. A key objective of our research is to develop and test such approximations for strongly correlated systems, including, for instance, the two-dimensional Hubbard model.
Finally, by generalizing the Rayleigh–Ritz variational principle to mixed states, we have introduced a version of 1RDMFT that allows for the computation of selected excited state energies. These developments also illustrate the power of tools from convex analysis in advancing functional theories. In particular, they enabled us to solve the underlying one-body N-representability problem, leading to a remarkable generalization of Pauli’s exclusion principle to bosons and fermionic excited states. One of our ongoing research directions is to explore the physical relevance of these generalized exclusion principles and to develop first functional approximations for computing excitation energies.