# QUANTUM COMPUTING MANY-BODY EXCITED STATES: FROM ELECTRONIC EXCITED STATES TO ULTRACOLD GASES

## Julia Liebert, Ludwig-Maximilians-Universität Münich

2 pm

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**Reduced Density Matrix Functional Theory for Bosonic Quantum Systems: Ground and Excited States**

One-particle reduced density matrix functional theory (RDMFT) offers significant conceptual advantages over traditional density functional while remaining computationally less costly than wave function methods. Notably, RDMFT allows for the exact determination of the kinetic energy as a functional of the one-particle reduced density matrix (1RDM). Additionally, it effectively addresses the strong correlation problem in many-body quantum systems, as the 1RDM provides direct insights into the correlation strength through its degree of mixedness. In this talk, we will first establish the foundational principles of RDMFT and discuss its applications to both fermionic and bosonic quantum systems. For bosons, we will derive a universal functional applicable to homogeneous Bose-Einstein condensates with arbitrary pair interactions. Remarkably, the general form of this universal functional reveals the existence of a universal Bose-Einstein condensation force which provides an alternative and fundamental explanation for quantum depletion. In the second part of the talk, we will introduce an ensemble RDMFT that allows to target ensembles of low-lying excited states variationally. In particular, we solve the underlying N-representability problem for the corresponding refined sets of ensemble 1RDMs. This further reveals that crucial information about the excitation structure of quantum systems is contained in the functional’s domain. Moreover, a generalization of Pauli’s famous exclusion principle for mixed states follows for both fermions and, remarkably, also bosons. This work highlights the potential of RDMFT in advancing our understanding of complex quantum systems.

## Sara Giarrusso, Université Paris-Saclay, CNRS

2:30 pm

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**Exact Excited-State Functionals of the Asymmetric Hubbard Dimer**

While linear-response time-dependent DFT is, to date, the most widespread method in electronic structure to calculate properties of excited states, such as optical spectra, it remains inadequate in dealing with certain types of excitations, such as double or charge-transfer excitations, owing to the final state being too perturbed compared to the reference. Lately, there has been significant enthusiasm surrounding another procedure that is practically very similar to the standard Kohn-Sham DFT procedure for ground states: a procedure called orbital-optimised DFT or simply DSCF [1].

This procedure seems to be much more robust in the calculation of excitations where the final state is far from the ground. It also has the remarkable advantage of requiring only a pure-state calculation over ensemble theories (such as ensemble-DFT or ensemble-1RDMFT). However, the theory underpinning this procedure is not yet fully established and several questions remain open, such as: 1) should state-specific functional approximations be used? 2) how large is the extent of the error introduced by using ground-state functionals? 3) are there spurious solutions one can erroneously converge to via the SCF cycle? I will adopt the simple two-site asymmetric Hubbard model, which has been used to exemplify central concepts or test new density-functional methods in the past, to address some of these issues in an exact and controlled way [2].

[1] Hait, D.; Head-Gordon, M. J. Chem. Theory Comput. 2020, 16, 1699−1710.

[2] Giarrusso, S.; Loos, P. F. J. Phys. Chem. Lett. 2023, 14, 8780−8786.

### Organizing Committee

Dr. Carlos Leonardo Benavides Riveros

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**This initiative is part of the Royal Society of Chemistry:**