Order in quantum chaos

When Annabelle Bohrdt talks about her research, the world of electrons suddenly sounds less like abstract quantum physics than like a social experiment. “We want to know what many quantum particles do when they interact with each other,” she says. This is a simple formulation of a daunting problem, as the space of possible quantum states is so large that no computer in the world can calculate it.

Yet this is precisely what the quantum physicist and her group do: predict how materials behave when you cool them, compress them, irradiate them, or place them in magnetic fields. It is the attempt, with the aid of models, to bring some order to the chaos of interactions between different particles.

Basic rules in a quantum system

When you talk to the physicist, who recently joined LMU from the University of Regensburg, you quickly appreciate how much she enjoys explaining her world to ordinary people. This is no easy task, however, as her main research interest is many-body quantum theory. Bohrdt is a theoretical physicist, and at the heart of her work are mathematical constructs like the so-called Hamiltonian, a key operator in theoretical solid-state physics. “It gives us the basic rules, as it were, in a system that we want to investigate,” explains Bohrdt. It specifies, for example, what electrons can do in a lattice and what they can’t – which neighbors they feel, how they move, how strongly they repel or attract each other – and what symmetries determine the overall system. The Hamiltonian is kind of like the rules of the game for the material. From the Hamiltonian, you obtain the ground state of a system, a state that every quantum mechanical system prefers to occupy.

But calculating this ground state would entail simulating the material down to the very last detail – and then squashing the solution into a single equation – a pretty much unsolvable task. And so Bohrdt and her team work with approximations: “We have to reduce a complicated system down to what really counts, while making sure we don’t omit crucial details.”

A research career that began with an act of deception

Bohrdt owes her career as a physicist to the toss of a coin – and the deception of a schoolfriend in Mannheim. Shortly before beginning the final stage of high school, she asked this friend over the phone whether she should choose biology or physics to study as an advanced subject. He tossed a coin and told her: physics. Later, he confessed that the coin had actually fallen on biology. Bohrdt would go on to study physics in Kaiserslautern, before completing her doctorate in the group of Michael Knap at TUM in 2021. She carried out much of her research during this period at Harvard. This was followed by a postdoc in the United States, her first professorship in Regensburg – and now her move to LMU. “I didn’t come here only on account of my partner, who also works at LMU, but because Munich is one of the world’s leading centers of quantum physics,” says Bohrdt.

Born in 1992, Bohrdt plans to use novel analysis tools as a member of the MCQST Cluster of Excellence to describe strongly interacting many-body quantum systems. For these descriptions, she combines state-of-the-art numerical methods from solid-state physics with machine learning techniques – especially neural networks, which are better able to capture complex patterns in quantum states. The hope is that these networks will automatically recognize what counts in a quantum system – and what can safely be ignored.

Where theory meets real atoms

Bohrdt does not only test her results on a computer, but collaborates closely with the experimental groups at the MCQST Cluster of Excellence in Munich – such as the groups of Immanuel Bloch, Monika Aidelsburger, and Johannes Zeiher. What Bohrdt investigates theoretically, the various research groups recreate in experiments with ultracold atoms – model materials that exactly follow the rules of their Hamiltonians. It is as if a theoretical diagram were suddenly transformed into a real, controllable solid body.

Bohrdt describes this connection with the research groups as “invaluable.” If the theory agrees with the experiment, it bolsters her models. And if not, the difference often precisely reveals which part of the simplification was false – in a process of reciprocal correction between theory in the model and reality in the laboratory.

A prediction that becomes reality

A particularly memorable moment in her career to date was the prediction of an unexpectedly stable phenomenon. She proposed that pairs of charge carriers, a possible precursor of superconductivity, would become visible in a certain model at higher temperatures. An experiment confirmed the calculation – and years later scientists discovered a real material, a bilayer nickelate, that could be described astonishingly well by this model. “The theory was there first,” says Bohrdt. For a theoretician, that is the ultimate affirmation.

But quantum physics would not be quantum physics if it did not also hold disappointments in store. In the largest numerical calculations ever conducted, the famous Fermi-Hubbard model, which for decades had been the frontrunner to explain high-temperature superconductivity, exhibited no superconducting signatures in precisely those areas where they had been expected. For a whole field this was a shock – and for Bohrdt it was a wake-up call.

In her new ERC project “QuaQuaMA,” she plans to revisit these basic assumptions: Which model really describes unconventional superconductors? Instead of ‘repairing’ the old model by adding further terms to it, she is searching for a systematic path from the real material to the matching Hamiltonian. “I’m trying to reconnect model building with experimental reality,” she says.

At LMU, Bohrdt leads a constantly growing research group, supervises students and doctoral candidates, works on her new theoretical models – and at the same time, together with her partner Fabian Grusdt, who is also a quantum physicist at LMU, manages everyday life with their two small children. Her erstwhile passion for soccer has had to take a back seat. “Although maybe I can pass on my enthusiasm to my daughters,” remarks Bohrdt. And who would doubt it? Inspiring enthusiasm is certainly one of her fortes.