Research group Quantum and Complex Systems

The Bergholtz group explores the world of quantum and complex systems — what it is and what it could be — from the perspective of mathematics and theoretical physics.
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While we have generally broad interests we are particularly interested in quantum many-particle systems for which topology, entanglement and interactions play important roles. These include fractional quantum Hall states, geometrically frustrated magnets, Weyl semimetals and various instances of flat band models. A common feature in these systems is that their low-energy quasiparticles bear little or no resemblance to their electronic constituents. Recently another main interest has been in the topology on non-Hermitian systems as reviewed here.


We are theoretical physicists with diverse backgrounds but with a common interest in describing the world — what it is and what it could be — in terms of mathematics. Our main interest is in the exuberant world of quantum mechanics of collective many-body systems. In this context we  bring together insights from different fields of science ranging from high energy physics and abstract mathematics to materials science, photonics and cold atom systems. Three recent examples include 1) foundational work in the new field of non-Hermitian topology incorporating and extending ideas of condensed matter, photonics and topology, 2) the theoretical prediction of novel strongly correlated states of matter, such as fractional Chern insulators, in engineered moiré heterostructures, and 3) analogies with (and subtle but crucial differences from) black holes and new types of anomalies in symmetry breaking semimetals.   

We also work on complex phenomena in the classical realm, presently including novel dynamical effects in optical waveguides and synchronization effects in epidemics. In fact, most of the early experimental manifestations of our ideas in non-Hermitian topology have been in the classical realm although their conceptual provenance lies in (extensions of) quantum physics.

Our emphasis is on curiosity driven basic research, yet we keep alert to possible practical applications of our findings, such as our recent proposal of hyper-sensitive “Non-Hermitian Topological Sensors”.

NEWS: We have several openings. Prospective PhD students can contact the PI by email (emil.bergholtz@fysik.su.se) while potential postdocs can apply here (deadline Nov 1, 2022).


Alumni (with with Emil Bergholtz as main advisor; present members are listed under a separate tab below):

PhD students:

Marcus Stålhammar, PhD 2022; Next: Nordita Fellow

Flore Kunst, PhD 2019, Winner of the Sigrid Arrhenius Prize from Stockholm University as well as the Oseen Medal of the Swedish Physical Society for her PhD thesis; Next: joint postdoc fellowship at MPQ Munich and Harvard & from 2021 group leader at Max Planck (MPI-MPL)

Maximilian Trescher, PhD 2018; Next: computer scientist in Berlin

Jörg Behrmann; Next: permanent staff position at FU Berlin

Postdocs/researchers:
Fan Yang (PhD Ecole Polytechnique, Paris), 2020-2022; Next: Postdoc at EPFL Lausanne

Daniel Varjas (PhD Berkeley), 2020-2022; Next: Researcher at Max Planck (MPI-PKS)

Ipsita Mandal (PhD Harish-Chandra Institute), 2021-2022; Next: Associate Professor at the Polish Academy of Sciences

Qingdong Jiang (PhD Peking University), 2020-2021; Next: Associate Professor at TD Lee Institute, Shanghai

Kang Yang (PhD Paris), 2019-2022; Next: Postdoc at FU Berlin

Johan Carlström (PhD KTH), 2017–2019; Next: VR Starting grant & group leader at Stockholm University

Yaron Kedem (PhD Tel Aviv), 2016–2019; Next: postdoc with Prof. Frank Wilczek at SU

Zhao Liu (PhD CAS Beijing), 2014–2017; Next: Thousand Talents Awardee & Assistant Professor at Zhejiang University


Master students: Theresa Leistner (2020-2021), Fanny Terrier (2019), Naemi Florin (2017), Yann Salimi (2015-2016), Kevin Madsen (2015-2016), Irina Gancheva (2015-2016), Jann Launer (2015-2016), David Schneider (2015-2016), Yann Salimi (2015-2016), Alexander Nietner (shared 2014-2015), Diana Prychynenko (co-advised 2013-2014), Jörg Behrmann (2012-2013) and Samuel Sanchez (2012-2013).

Bachelor students: Marlon Rueck (2015), Huaiyu Li (internship project 2015), Gunnar Riemenschneider (2014), Kevin Madsen (2013), Gregor Pohl (internship project 2013), Maximilian Trescher (2012), Diana Prychynenko (2012).




This research group has no members.

There are no research project connections.

Department of Physics

Scientists turn the faint quantum “glow” of empty space into a measurable flash

Researchers from Stockholm University and the Indian Institute of Science Education and Research (IISER) Mohali have reported a practical way to spot one of physics’ strangest predictions: the Unruh effect, which says that an object speeding up (accelerating) would perceive empty space as faintly warm. But, trying to heat something up by accelerating it unimaginably fast is a non-starter in the lab. The team shows how to convert that tiny effect into a clear, timestamped flash of light.

Department of Physics

Oscar Arandes Tejerina - bridging the gap between math and physics

Oscar is the recipient of Magnus Axelsson Prize 2025. "My main goal will be to bring more physics into the problem-solving process so that students can better understand the meaning behind the abstract calculations," says Oscar. He is in charge of the tutorials for the course Advanced Quantum Mechanics. Oscar completed his bachelor's at the University of Barcelona and his master's at Uppsala University. In 2022, he got a PhD position at Fysikum and became part of Professor Emil Bergholtz's research group, Quantum and Complex Systems.

Department of Physics

Stockholm University researchers predict new intertwined quantum states in moiré materials

In the rapidly evolving field of quantum materials, theorists at Stockholm University are pushing the frontier of what kinds of exotic matter can exist. Two new works—one just published in Nature Communications and another selected as an Editors’ Suggestion in Physical Review Letters—reveal strikingly unconventional states of electrons that could pave the way for future quantum technologies.

Department of Physics

Fysikum team unveils promising avenue towards the realization of elusive parafermions

In their latest publication in Nature Communications, researchers Hui Liu, Raul Perea-Causin, and Emil J. Bergholtz demonstrate that Fibonacci parafermions—exotic quasi-particles which have so far evaded experimental realization—can emerge in experimentally accessible moiré structures formed by overlaying two-dimensional materials with a twist.

Department of Physics

Emil became a physicist thanks to the research branch

Emil Johansson Bergholtz is Professor of Theoretical Physics at Fysikum. He has been appointed both a Wallenberg Academy Fellow and a Wallenberg Academy Scholar. "It was a coincidence that I got into the subject of physics. I liked solving problems and things that gave resistance. But without the research branch, it is not certain that I would have continued with physics. It was fun and inspiring with the advanced problem solving in the program, says Emil Bergholtz.

Department of Physics

Non-Hermitian extended midgap states and bound states in the continuum

Maria Zelenayová, PhD student at Fysikum, and her supervisor Professor Emil Bergholtz looked into localization phenomena in non-Hermitian systems that challenge traditional beliefs about states within the energy continuum and those in the gap. The understanding of non-Hermitian extended band gaps and bound states holds significant implications across various domains. In quantum mechanics, this opens up new possibilities for controlling and manipulating the properties of materials. In technology, these insights can be utilized to develop more efficient semiconductors and other advanced materials.

Department of Physics

Particles protected by Braids and Knots

We present a class of systems in which a particle - antiparticle pair cannot annihilate each other after they have moved along a loop, and instead form a new type of composite particle. This occurs in so-called non-Hermitian systems; classical metamaterials or "open" quantum systems that are coupled to the rest of the universe. Lukas Königis a PhD Student at Fysikum and is part of the research group Quantum and Complex Systems.

Department of Physics

Quantum metric unveils defect freezing in non-Hermitian systems

The fundamental postulates of quantum mechanics rest upon the fact that the Hamiltonian, which quantifies the energy of the system, is given by a Hermitian operator. This means that the complex conjugate and transpose of the Hamiltonian should be equal to itself. Almost a century after the formulation of quantum mechanics, researchers are now trying to break free from this constraint — non-Hermitian Hamiltonians, which do not satisfy the aforementioned property, are now a new frontier of exploration in both theoretical and experimental physics. Paolo Molignini is part of the project and is a Postdoctor in Condensed Matter and Quantum Optics at Fysikum.

Department of Physics

New quantum communication infrastructure

Mohamed Bourenanne is part of the National Quantum Communication Infrastructure in Sweden (NQCIS) project, which received SEK 30 million from Vinnova and is coordinated by KTH. His research group works in the field of quantum communication and their laboratory is located at AlbaNova. - All eavesdropping attempts can be revealed thanks to the basic theories of quantum mechanics, thus increasing information security.

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