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arXiv:2509.03387 · Nature Communications

Topology meets superconductivity in a one-dimensional t-J model of magnetic atoms

Leonardo Bellinato Giacomelli, Thomas Bland, Louis Lafforgue, Francesca Ferlaino, Manfred J. Mark, Luca Barbiero

Published Apr 17, 2026• 0 citations
arXivHTMLPDF

Abstract

Strongly interacting fermions represent the key constituent of several intriguing phases of matter. However, due to the inherent complexity of these systems, important regimes are still inaccessible. Here, we derive a realistic and flexible setup based on ultracold magnetic lanthanide atoms trapped in a one-dimensional optical lattice. Leveraging their large magnetic moments, we design a fermionic t-J model with independently tunable hopping, spin-spin couplings, and onsite interaction. Through combined analytical and numerical analysis, we uncover a variety of many-body quantum phases-including superconducting and topological states. Crucially, in the regime of attractive onsite interaction, we reveal that topology and superconductivity coexist, thus giving rise to an exotic state of matter: a topological triplet superconductor. We also outline a practical protocol to prepare and detect all discovered phases using current experimental techniques. Our results establish an alternative and powerful route for a deeper understanding of strongly interacting fermionic quantum matter.

DOI
10.1038/s41467-026-71248-8

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Strongly interacting fermions represent the key constituent of several intriguing phases of matter. However, due to the inherent complexity of these systems, important regimes are still inaccessible. Here, we derive a realistic and flexible setup based on ultracold magnetic lanthanide atoms trapped in a one-dimensional optical lattice. Leveraging their large magnetic moments, we design a fermionic t-J model with independently tunable hopping, spin-spin couplings, and onsite interaction. Through combined analytical and numerical analysis, we uncover a variety of many-body quantum phases-including superconducting and topological states. Crucially, in the regime of attractive onsite interaction, we reveal that topology and superconductivity coexist, thus giving rise to an exotic state of matter: a topological triplet superconductor. We also outline a practical protocol to prepare and detect all discovered phases using current experimental techniques. Our results establish an alternative and powerful route for a deeper understanding of strongly interacting fermionic quantum matter.
We present a simple scheme for implementing a one-dimensional (1D) magnetic-flux lattice of ultracold fermionic spin-1/2 atoms. The resulting tight-binding model supports gapped and gapless topological phases and chiral currents for Meissner and vortex phases. Its single-particle spectra exhibit topological flat bands at small flux, and the flatness sensitively depends on hopping strength. An effective ppp-wave interaction arises in a sss-wave paired superfluid. Treating atomic internal states as forming a synthetic dimension and balancing the interplay of magnetic flux and Zeeman field, our model describes a tunable topological Fermi superfluid, which paves the way towards experimental explorations of non-Abelian topological matter in 1D atomic quantum gases.
In recent years, topology has become increasingly prevalent in condensed matter physics. It has allowed us to understand, and even predict, a variety of striking and remarkable physical phenomena. The study of strongly interacting systems has similarly lavished us with a diverse range of exotic phases and unconventional transitions, many of which are still poorly understood. In this thesis we will explore the interplay between topology and interactions in an effort to uncover new and novel phases. First we study how interactions impact the quantum phase transition between a topologically non-trivial phase and a trivial phase. The combination of interactions and the low-energy degrees of freedom associated with the transition leads to the emergence of a dome of lattice-symmetry breaking nematic order. Such behaviour is reminiscent of a number of strongly correlated electronic systems. We move on to study the strongly interacting limit of one of the earliest and best-known non-interacting topological phases, Haldane's model of a Chern insulator. Recently realized with ultracold atoms in a shaken optical lattice, the model has a non-trivial topological invariant associated with its band structure. In the strongly interacting limit the spin degrees of freedom are all that survive and we find a rich phase diagram of magnetically ordered phases, using a combination of both classical and quantum techniques. Supplementing the model with an additional term we can `quantum-melt' one of these ordered states to produce a disordered, liquid state that we positively identify as a chiral spin liquid, a highly entangled state of matter with fractionalised excitations. We generalise this mechanism to other two dimensional lattices, uncovering a possible unifying framework with which to understand the emergence of chiral spin liquids in lattice spin models. Finally, motivated by groundbreaking experiments in the ultracold atoms community, we investigate a model of two-component bosons with an artificial spin-orbit coupling. The interplay between the lattice, interactions and spin-orbit coupling produces a variety of unusual superfluid phases. Using a novel Monte Carlo technique we reveal the finite temperature phase diagram that appears close to the Mott transition.
This thesis reports original research on strongly interacting fermions described by Hubbard-like models which can be realized with ultracold atom experiments. In particular, two main directions have been pursued: (i) the control of magnetic and topological properties in a honeycomb lattice through a suitable tuning of the trapping potential, and (ii) the possibility to observe orbital-selective Mott physics in a multicomponent Fermi system where the SU(N) symmetry is broken in a controlled way. The first line of research is based on the idea that increasing the strength of a trapping potential, one can trap a strongly interacting fermions in a limited portion of space, thereby changing their average density and the related magnetic properties. In particular it was demonstrated that this confinement protocol can be used to designeffective “nanoflakes” which are reminiscent of a solid-state proposal [1]. The second step was to extend the same philosophy to the so-called Kane-Mele model, a spinful version of the paradigmatic model proposed by Haldane which presents quantum Hall states. This model can be realized with cold-atom systems using artificial gauge fields. In this thesis we consider a Kane-Mele-Hubbard model where the electronic structure of the Kane-Mele model is supplemented by the onsite Hubbard interaction, allowing us to study the interplay between the correlations and magnetism induced by the repulsion, with the non-trivial topological properties. Also for this model, we follow the strategy discussed above, namely the possibility to engineer an effective “nanoflake” by tuning the lattice potential. The final outcome in this case is even reacher, because it leads, among other results, to a situation where the effective flake hosts an inhomogeneous state which presents at the same time topologically non-trivial properties and magnetism, realizing a spin-Chern insulator [2]. Besides the remarkable application for topological matter, artificial gauge fields, which rely on the coupling of spin states, offer also great insides into mutli-orbital physics. In the second main research line reported in the thesis we study in collaboration with the experimental group of Leonardo Fallani, the controlled symmetry breaking on a 173Yb many-body system, where coupling between spin states is exploited to simulate the mechanism relevant for the physics of multi-orbital materials, such as iron-based superconductors. In order to reveal this mechanism in cold atoms we focus on interacting SU(3) lattice fermions where the SU(3) spin symmetry is explicitly broken by a Raman coupling between the spin states. Combining experiments and theory, we demonstrate that this setup reveals orbital-selective physics and it shows that the SU(3)-symmetry-breaking Raman coupling favours Mott localization and selective properties [3]. Our results show a clear evidence of orbital-selective correlations, which reflect in contrasting transport properties in different orbitals, the extreme case being an orbital-selective Mott state where only some of the orbitals are Mott localized while others remain metallic. Moreover, the coupling between spin states favors Mott localization with respect to the symmetric case, hence it reduces the critical interaction needed for a full Mott localization.
Interacting cold-atomic gases in optical lattices offer an experimental approach to outstanding problems of many body physics. One important example is the interplay of interaction and topology which promises to generate a variety of exotic phases such as the fractionalized Chern insulator or the topological Mott insulator. Both theoretically understanding these states of matter and finding suitable systems that host them have proven to be challenging problems. Here we propose a cold-atom setup where Hubbard on-site interactions give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of an interacting and topological quantum state with fractionalized spinon excitations that inherit the topology of the non-interacting system. Our proposal shall help to pave the way for a controlled experimental investigation of this exotic state of matter in optical lattices. Furthermore, it allows for the investigation of a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers.
Interacting cold-atomic gases in optical lattices offer an experimental approach to outstanding problems of many body physics. One important example is the interplay of interaction and topology which promises to generate a variety of exotic phases such as the fractionalized Chern insulator or the topological Mott insulator. Both theoretically understanding these states of matter and finding suitable systems that host them have proven to be challenging problems. Here we propose a cold-atom setup where Hubbard on-site interactions give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of an interacting and topological quantum state with fractionalized spinon excitations that inherit the topology of the non-interacting system. Our proposal shall help to pave the way for a controlled experimental investigation of this exotic state of matter in optical lattices. Furthermore, it allows for the investigation of a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers.
We present an ab initio, numerically exact study of attractive fermions in square lattices with Rashba spin-orbit coupling. The ground state of this system is a supersolid, with coexisting charge and superfluid order. The superfluid is composed of both singlet and triplet pairs induced by spin-orbit coupling. We perform large-scale calculations using the auxiliary-field quantum Monte Carlo method to provide the first full, quantitative description of the charge, spin, and pairing properties of the system. In addition to characterizing the exotic physics, our results will serve as essential high-accuracy benchmarks for the intense theoretical and especially experimental efforts in ultracold atoms to realize and understand an expanding variety of quantum Hall and topological superconductor systems.