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1. Quantum spin liquids

   https://doi.org/10.1126/science.aay0668  

   Broholm, C.; Cava, R. J.; Kivelson, S. A.; Nocera, D. G.; Norman, M. R.; Senthil, T. (January 2020, Science)

   null (Ed.)

   Spin liquids are quantum phases of matter with a variety of unusual features arising from their topological character, including “fractionalization”—elementary excitations that behave as fractions of an electron. Although there is not yet universally accepted experimental evidence that establishes that any single material has a spin liquid ground state, in the past few years a number of materials have been shown to exhibit distinctive properties that are expected of a quantum spin liquid. Here, we review theoretical and experimental progress in this area. 

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2. Criticality and Magnetic Phases of Ising Shastry–Sutherland Candidate Holmium Tetraboride

   https://doi.org/10.3390/ma18112504  

   Khundzakishvili, Guga; Belbase, Bishnu Prasad; Mahendran, Pravin; Zhang, Kevin; Xu, Hanjing; Stoyanoff, Eliana; Checkelsky, Joseph George; Liu, Yaohua; Ye, Linda; Banerjee, Arnab (June 2025, Materials)

   Frustrated magnetic systems arising in geometrically constrained lattices represent rich platforms for exploring unconventional phases of matter, including fractional magnetization plateaus, incommensurate orders and complex domain dynamics. However, determining the microscopic spin configurations that stabilize such phases is a key challenge, especially when in-plane and out-of-plane spin components coexist and compete. Here, we combine neutron scattering and magnetic susceptibility experiments with simulations to investigate the emergence of field-induced fractional plateaus and the related criticality in a frustrated magnet holmium tetraboride (HoB4) that represents the family of rare earth tetraborides that crystalize in a Shastry–Sutherland lattice in the ab plane. We focus on the interplay between classical and quantum criticality near phase boundaries, as well as the role of material defects in the stabilization of the ordered phases. We find that simulations using classical annealing can explain certain observed features in the experimental Laue diffraction and the origin of multiple magnetization plateaus. Our results show that defects and out-of-plane interactions play an important role and can guide the route towards resolving microscopic spin textures in highly frustrated magnets. 

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3. Continuous Symmetry Breaking in a Trapped-Ion Spin Chain

   Lei Feng, Or Katz (January 2022, arXivorg)

   One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to 23 spins and is characteristic of the continuous symmetry-breaking phase of matter. Our preparation relies on simultaneous control over an array of tightly focused individual-addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems. 

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4. Deconstructing magnetization noise: Degeneracies, phases, and mobile fractionalized excitations in tetris artificial spin ice

   https://doi.org/10.1073/pnas.2310777120  

   Goryca, Mateusz; Zhang, Xiaoyu; Ramberger, Justin; Watts, Justin D; Nisoli, Cristiano; Leighton, Chris; Schiffer, Peter; Crooker, Scott A (October 2023, Proceedings of the National Academy of Sciences)

   Direct detection of spontaneous spin fluctuations, or “magnetization noise,” is emerging as a powerful means of revealing and studying magnetic excitations in both natural and artificial frustrated magnets. Depending on the lattice and nature of the frustration, these excitations can often be described as fractionalized quasiparticles possessing an effective magnetic charge. Here, by combining ultrasensitive optical detection of thermodynamic magnetization noise with Monte Carlo simulations, we reveal emergent regimes of magnetic excitations in artificial “tetris ice.” A marked increase of the intrinsic noise at certain applied magnetic fields heralds the spontaneous proliferation of fractionalized excitations, which can diffuse independently, without cost in energy, along specific quasi-1D spin chains in the tetris ice lattice. 

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5. Continuous symmetry breaking in a trapped-ion spin chain

   https://doi.org/10.1038/s41586-023-06656-7  

   Feng, Lei; Katz, Or; Haack, Casey; Maghrebi, Mohammad; Gorshkov, Alexey V.; Gong, Zhexuan; Cetina, Marko; Monroe, Christopher (November 2023, Nature)

   One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions1. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to 23 spins and is characteristic of the continuous symmetry-breaking phase of matter2,3. Our preparation relies on simultaneous control over an array of tightly focused individual addressing laser beams, generating long-range spin–spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems. 

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