Project description
Creating materials where interactions change based on movement paths
Designing materials with exotic properties often relies on the geometry of their structure. However, in certain cases, geometry might not be the limit. With the support of the Marie Skłodowska-Curie Actions programme, the CayLat project will use algebraic techniques to engineer new physics in flat spaces. Researchers will use Cayley lattices, which unlike traditional grids, allow for non-commutative translations, where the order of movement matters. This non-commutativity property unlocks new phenomena like path-dependent interactions and unique topological phases. This approach avoids the scaling challenges of hyperbolic lattices, making it practical for real-world applications. By simulating Cayley lattices with electrical circuits, researchers will explore their potential to transform quantum systems, enabling photons or qubits to interact differently based on their path.
Objective
"Most condensed matter physics happens on lattices with commuting translations—move right then up equals up then right. But hyperbolic lattices break this: translations become non-Abelian (NAB) or non-commutative, bringing remarkable physics—novel phases from single particle to many-body, superior quantum error correction, enhanced AI memory. Problem: hyperbolic lattices need exponentially growing connections, impractical to scale.
I propose Cayley lattices (CayLats): NAB translations in flat space without curvature. The trick is algebraic—replace each lattice site with n internal states corresponding to n group elements of Zn. The Hamiltonian splits into Abelian and NAB sectors in the same flat lattice. For Z2 CayLats, I've shown electric fields at different angles produce completely different spectra in NAB vs Abelian sectors—direct proof of non-commutativity without curved space.
Higher Zn gets fascinating. Z3 and Z4 CayLats may break time-reversal in NAB sectors while preserving it in Abelian ones—impossible in regular lattices. Topological phases scale with my ""NABity parameter"" measuring translation non-commutativity. Larger n→more NABity→richer physics.
Theory needs experiments. I construct CayLats using electrical circuits simulation—inductors/capacitors mimicking tight-binding models. Circuit Laplacian becomes Hamiltonian, impedances reveal spectra. LTSpice simulations show path-dependent impedances, NAB-specific boundary modes—ready for ETH's electronics lab.
Impact: In quantum systems, photons between qubits get path-dependent coupling without external control. Same distance, different interaction based on route—fundamentally new. With supervisors Bzdušek (topological band theory) and Neupert (many-body physics) at UZH, we will showcase NAB physics does not need curved space, just algebra. CayLats show translation symmetry is not geometrically fixed—it's engineerable. That revolutionizes how we design materials with exotic properties in flat space."
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics algebra
- engineering and technology electrical engineering, electronic engineering, information engineering electronic engineering computer hardware quantum computers
- natural sciences physical sciences theoretical physics particle physics photons
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Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
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HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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(opens in new window) HORIZON-MSCA-2025-PF
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8006 Zurich
Switzerland
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