(i) We developed a machine learning algorithm, the tensorial-kernel support vector machine (TKSVM) capable of determining the phase diagrams of classical spin models based on Monte Carlo snapshots (Phys Rev B 99, 060404 (2019), Phys Rev B 99, 104410 (2019)). TKSVM is interpretable: the output, the decision function, encodes the order parameter squared in case of phase transitions, or local constraints hinting at an underlying gauge structure of a possible spin liquid. TKSVM is also unsupervised: a graph spectral analysis of the phase diagram can be performed based on the bias of the decision function prior to the interpretability step. In "SVM_pyrochlore.png" (arXiv:1907.12322) one recognizes 6 different parameter regimes of the classical XXZ model defined on the pyrochlore lattice. In a number of follow-up papers (Phys Rev Research 3, 023016(2021), Phys Rev E 105, 015311 (2021), Phys Rev Research 3, 033223 (2021), arXiv:2206.08946) TKSVM was consequently applied to Kitaev magnets: Materials such as RuCl3 are proximate to the exactly solvable Kitaev model known to host spin liquids, but their Hamiltonians have additional competing terms rendering the full phase diagram elusive. TKSVM identified a number of subtly ordered phases/spirals, which significantly contributed to our understanding of these materials. Finally, an extension to quantum data was presented in Phys. Rev. Research 5, 013082 (2023), which opens the way to apply this algorithm to unknown quantum systems realized by a quantum computer.
(ii) The pyrochlore magnets are one of the few examples where fractionalization is generally accepted. In (classical) spin ice the static spin structure factor shows a bow-tie pattern and pinch points as a direct consequence of magnetic monopole excitations with dipolar interactions. Furthermore, the XXZ model defined on the pyrochlore lattice numerically shows a quantum U(1) spin liquid. The experimental realization of a centered pyrochlore lattice opens a new frontier in the field of frustrated magnetism, see Phys Rev Research 5, L022018 (2013). We found a robust classical spin liquid (see phase_diagram_T.png) with very attractive properties such a Heisenberg couplings of the order of a few Kelvin, a strong Ramirez frustration ratio, and a very large degeneracy. The classical spin liquid interestingly features broad pinch points, understood as Debye-Hueckel screening in the Coulomb picture provided by the center spins. The width of those pinch points is a (linear) function of the ratio of the two different Heisenberg couplings involved. At lower temperature, the experimental material orders, presumably because of additional dipolar interactions. we put forward a theoretical ordering model which awaits experimental verification. The possibility of realizing novel quantum spin liquids on this structure is exciting.
(iii) In Phys Rev Lett 125, 256401 (2020) we studied the interplay of spin and charge degrees of freedom in a Hubbard model where the hopping is constrained to one dimension and the spin interactions are of the Ising type. The phase diagram can be understood analytically from a Z2 lattice gauge theory perspective and the quantum Monte Carlo simulations confirm the existence of a chargon and meson gas phase, and of a striped nematic phase. In two follow-up papers, Phys Rev B 107, 075109 (2023) and Phys Rev Research 5, L022027 (2023), other types of anistropic t-J models were studied with Monte Carlo and DMRG, elaborating the physics found in the PRL.
(iv) In Phys Rev Lett 128, 255301 (2022) we revisited the physics of supersolid He-4 and proposed a model that could explain the mysterious pressure and temperature dependence of the UMass sandwich setup, in which flow through a solid sandwiched between liquid reservoirs was experimentally measured. The model goes beyond an explanation in terms of quantum rough dislocations building a Luttinger liquid network, and it was later realized superclimbing edge dislocations are just one example of a new state of matter called transverse quantum superfluids.
(v) arXiv:2301.09636 conjectures that any Hamiltonian exhibiting finite temperature, easy plane ferromagnetism can be used to generate stable spin squeezing, provided that an initial (product) state can be prepared whose energy is below the average energy at the critical temperature. In Arxiv:2305.03673 we provided, for the first time, extensive thermometry to Rydberg systems in optical tweezer arrays. Focusing on the experimental realization of XY order with dipolar interactions, we identified very strong finite size and sizeable heating effects.
(vi) Superfluidity in two dimensions can be destroyed by vortex pair unbinding. However, in analogy to the strong disorder scenario in one dimension at zero temperature, "scratches" provide a viable alternative. This was shown numerically in Phys Rev B 99, 104514 (2019) and confirmed in our controlled renormalization group analysis, where we taylored the finite size effects to a minimum. The figure "scratchedXY.png" (copyright APS, Phys Rev B 99, 104514 (2019)) shows a Weber-Minnhagen fit clearly indicating that the transition belongs to the novel scratched-XY class.
