Supersymmetry shows up in condensed matter, not colliders
New findings based on neutron scattering experiments performed at the ILL and ISIS reveal supersymmetric behaviour in a quantum material, demonstrating that it can emerge naturally in condensed matter. This has promising practical implications for making stable qubits for quantum computing. The study, led by researchers at PSI, is published in Nature Communications.
The theory of supersymmetry tells us that every matter particle (fermion) should have a supersymmetric force-carrying partner (boson). If proven relevant to the physics of our universe, this would provide crucial evidence of physics beyond the Standard Model of particle physics, with implications for unresolved mysteries in physics such as dark matter. Yet, despite decades of searches at large colliders no direct evidence of its existence has been found.
In condensed matter, the concept that strong, many-body correlations (see box) can produce fractional bosonic and fermionic collective states is well established in low dimensions but possible supersymmetries between these states are rarely invoked.
Although supersymmetry has yet to – and may never – be discovered at the high energies where new particles are created, its mathematical structure can still emerge in materials at lower energies, governing the behaviour of quantum states, as a new study led by PSI researchers shows.
Supersymmetry in a quantum spin ladder
The researchers studied a class of materials known as quantum spin ladders, a type of insulating magnetic material where atoms are arranged in pairs of coupled chains. In the ladder, charge appears as a hole in the magnetic pattern, with its properties intrinsically tied to the spins of the electrons. These spins and these charge-like excitations, or quasi-particles, influence their neighbours along the chains and across the rungs of the ladder, following quantum rules – much like how filling in one number in a Sudoku puzzle constrains the possibilities for surrounding numbers. This interconnectedness leads to unusual, highly correlated behaviour.
Quantum spin ladders are a real playground for theorists to test models describing many body effects in strongly coupled condensed matter systems. In such materials, a 3D crystal implements a 1D magnetic interactions system in which quantum fluctuations are enhanced (due to high anisotropy). In this study, the researchers studied two spin ladder compounds, (C₅D₁₂N)₂CuBr₄ and (C₅D₁₂N)₂CuCl₄, where magnetic copper ions form the chains of the ladder.
To model these ladder excitations with high accuracy, theorists from PSI together with the University of Geneva and University of Bonn used state-of-the-art numerical methods known as matrix-product-state (MPS) simulations.
Neutrons, great explorers of (quantum) matter
The team experimentally studied the two spin ladder compounds. Using inelastic neutron scattering experiments at the Institut Laue Langevin in France and the ISIS Pulsed Neutron Source in the UK, By bombarding the materials with neutrons and measuring how they scattered, they could infer how the neutrons had interacted with the material and hence gain insight into the spin and charge excitations in the spin ladder. Neutron scattering experiments were performed on the triple-axis spectrometer THALES at the ILL and on the time-of-flight spectrometer LET37 at ISIS.
“Neutrons’ sensitivity to spin makes them ideal for such studies, and inelastic scattering is the key argument, as we really needed to look at the energy and momentum transfer to see the fundamental excitation,” says Martin Böhm, ILL scientist and one of the authors of the paper, adding that "The success of this study relies on the extensive expertise and unique infrastructure built over the years at the ILL, with complex sample environments and continuously improved spectrometers".
A first-time observation
The researchers observed a distinct spectral signature: a peak that remained sharp whatever the temperature. Normally, quantum states are disrupted by thermal fluctuations, causing spectral features to broaden and sometimes shift. Guided by their theoretical models, the researchers could explain the persistence of this peak with the mathematics of supersymmetry. In the same way that in particle physics supersymmetry pairs fermions with bosons, in the quantum spin ladder, supersymmetry emerges not as new particles but as a deep mathematical relationship between spin and charge excitations. This stable link between excitations protects them from thermal fluctuations.
“Within this work we have discovered that supersymmetry can emerge in condensed matter and provided the first experimental observation of supersymmetric spinon-holon excitations in a quantum magnet,” says Björn Wehinger, first author of the study.
Wehinger highlights the fundamental role of neutron scattering and the associated technical achievements: “Neutron spectroscopy allowed us to measure the full excitation spectrum with great precision, which opened the possibility to investigate how supersymmetry affects it. We used quantum magnets realised in single crystals, which offer the great advantage of very homogeneous systems with immense number magnetic sites.”
The neutron scattering measurements were performed under different magnetic fields and across different temperatures. “In the experiments we can control the quasi-particle density precisely using magnetic field and are able to access the relevant temperatures using readily available cryostats,” details Björn Wehinger, “Interestingly, we find that supersymmetry protects specific features against thermal decay which manifests itself in temperature-independent scattering intensities,” he concludes.
Quantum phenomena, collective effects and quantum spin ladders
All matter is governed by the laws of quantum physics. Yet, at the macroscopic scale quantum effects are usually not perceivable – they are smeared out by the random movement of atoms. It is close to the absolute zero (-273 C) that such effects may become macroscopically visible, in the form of unexpected behaviours or uncommon phases. Indeed, atoms may display a rather different behaviour when extremely tightly confined at temperatures close to absolute zero.
The collective behaviour of groups of particles in condensed matter can sometimes be treated as if they were a single ‘particle’ (a so-called quasiparticle) with specific properties. Taking a semiconductor as example, an electron traveling through it and interacting with a multitude of electrons and nuclei around can be described as a single ‘electron’ with a different mass travelling in the vacuum; and the aggregate motion of electrons in its valence band can be described as if the material contained positive quasipartices (holes).
Spin–charge separation is an unusual behaviour of electrons in some materials in which they seem to 'split' into three independent ‘particles’: the spinon (carrying the spin of the electron), the holon (carrying its charge) and the orbiton (carrying the orbital angular momentum). While theoretically the electron can always be seen as a bound state of the three, in certain conditions they can actually behave as independent quasiparticles. This is an example of the phenomenon called fractionalisation.
Finding the right materials to study in detail such complex effects and their modelling is a real challenge. In quantum spin ladder materials, a 3D crystal implements a 1D magnetic interactions system in which quantum fluctuations are enhanced (due to high anisotropy).
Implications for quantum computing
Scientists have theorised for some time that condensed matter systems could show supersymmetric behaviour, but this is the first time that it has been directly observed in a real material.
“What we’ve observed is not fundamental supersymmetry as would be discovered at CERN with the observation of a supersymmetric partner particle,” explains Bruce Normand, senior scientist at PSI, who worked on the numerical modelling. “Nonetheless being able to see a new symmetry for the first time is intrinsically very exciting; and, importantly, seeing it enables us to do experiments with it.”
Beyond the implications for our fundamental understanding of materials, there is a practical consequence of their discovery. “The manifestation of supersymmetry that we see is this peak - this quantum state - that is protected. This is a quality that is extremely sought after in quantum information processing,” says Normand. In quantum computing, decoherence – whereby qubits rapidly lose quantum information – is a major obstacle to scaling-up toward fully functional quantum processors. Supersymmetry may not yet give us the answers to the meaning of life, the universe and dark matter. But it may, in the future, be a means to stable qubits.
Text: Miriam Arrell, PSI (adapted)
Reference:
Wehinger, B., Lisandrini, F.T., Kestin, N. et al. Fingerprints of supersymmetric spin and charge dynamics observed by inelastic neutron scattering. Nat Commun16, 3228 (2025). https://doi.org/10.1038/s41467-025-58380-7
ILL instruments: ThALES
ILL Contacts: Martin Boehm