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1. Competing itinerant and local spin interactions in kagome metal FeGe

   https://doi.org/10.1038/s41467-023-44190-2  

   Chen, Lebing; Teng, Xiaokun; Tan, Hengxin; Winn, Barry L.; Granroth, Garrett E.; Ye, Feng; Yu, D. H.; Mole, R. A.; Gao, Bin; Yan, Binghai; et al (March 2024, Nature Communications)

   Abstract The combination of a geometrically frustrated lattice, and similar energy scales between degrees of freedom endows two-dimensional Kagome metals with a rich array of quantum phases and renders them ideal for studying strong electron correlations and band topology. The Kagome metal, FeGe is a noted example of this, exhibiting A-type collinear antiferromagnetic (AFM) order atT_N ≈ 400 K, then establishes a charge density wave (CDW) phase coupled with AFM ordered moment belowT_CDW ≈ 110 K, and finally forms ac-axis double cone AFM structure aroundT_Canting ≈ 60 K. Here we use neutron scattering to demonstrate the presence of gapless incommensurate spin excitations associated with the double cone AFM structure of FeGe at temperatures well aboveT_CantingandT_CDWthat merge into gapped commensurate spin waves from the A-type AFM order. Commensurate spin waves follow the Bose factor and fit the Heisenberg Hamiltonian, while the incommensurate spin excitations, emerging belowT_Nwhere AFM order is commensurate, start to deviate from the Bose factor aroundT_CDW, and peaks atT_Canting. This is consistent with a critical scattering of a second order magnetic phase transition with decreasing temperature. By comparing these results with density functional theory calculations, we conclude that the incommensurate magnetic structure arises from the nested Fermi surfaces of itinerant electrons and the formation of a spin density wave order. 

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2. Kitaev spin-orbital bilayers and their moiré superlattices

   https://doi.org/10.1038/s41535-023-00541-2  

   Nica, Emilian Marius; Akram, Muhammad; Vijayvargia, Aayush; Moessner, Roderich; Erten, Onur (February 2023, npj Quantum Materials)

   Abstract We determine the phase diagram of a bilayer, Yao-Lee spin-orbital model with inter-layer interactions (J), for several stackings and moiré superlattices. For AA stacking, a gapped$${{\mathbb{Z}}}_{2}$$ $Z_2$quantum spin liquid phase emerges at a finiteJ_c. We show that this phase survives in the well-controlled large-Jlimit, where an isotropic honeycomb toric code emerges. For moiré superlattices, a finite-qinter-layer hybridization is stabilized. This connects inequivalent Dirac points, effectively ‘untwisting’ the system. Our study thus provides insight into the spin-liquid phases of bilayer spin-orbital Kitaev materials. 

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3. Topological to magnetically ordered quantum phase transition in antiferromagnetic spin ladders with long-range interactions

   https://doi.org/10.21468/SciPostPhys.13.3.060  

   Yang, Luhang; Weinberg, Phillip; Feiguin, Adrian (January 2022, SciPost Physics)

   We study a generalized quantum spin ladder with staggered long rangeinteractions that decay as a power-law with exponent \alpha α .Using large scale quantum Monte Carlo (QMC) and density matrixrenormalization group (DMRG) simulations, we show that this modelundergoes a transition from a rung-dimer phase characterized by anon-local string order parameter, to a symmetry broken N'eel phase. Wefind evidence that the transition is second order. In the magneticallyordered phase, the spectrum exhibits gapless modes, while excitations inthe gapped phase are well described in terms of triplons – bound statesof spinons across the legs. We obtain the momentum resolved spin dynamicstructure factor numerically and find a well defined triplon band thatevolves into a gapless magnon dispersion across the transition. Wefurther discuss the possibility of deconfined criticality in thismodel. 

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4. The Gapped k-Deck Problem

   Rebecca Golm, Mina Nahvi (July 2022, Proceedings of the ISIT)

   The k-deck problem is concerned with finding the smallest positive integer S(k) such that there exist at least two strings of length S(k) that share the same k-deck, i.e., the multiset of subsequences of length k. We introduce the new problem of gapped k-deck reconstruction: For a given gap parameter s, we seek the smallest positive integer Gs(k) such that there exist at least two distinct strings of length Gs(k) that cannot be distinguished based on a "gapped" set of k-subsequences. The gap constraint requires the elements in the subsequences to be at least s positions apart within the original string. Our results are as follows. First, we show how to construct sequences sharing the same 2-gapped k-deck using a nontrivial modification of the recursive Morse-Thue string construction procedure. This establishes the first known constructive upper bound on G2(k). Second, we further improve this bound using the approach by Dudik and Schulman. 

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5. The Gapped k-Deck Problem

   Rebecca Golm, Mina Nahvi (July 2022, International Symposium on Information Theory and its Applications)

   The k-deck problem is concerned with finding the smallest positive integer S(k) such that there exist at least two strings of length S(k) that share the same k-deck, i.e., the multiset of subsequences of length k. We introduce the new problem of gapped k-deck reconstruction: For a given gap parameter s, we seek the smallest positive integer G s (k) such that there exist at least two distinct strings of length G s (k) that cannot be distinguished based on a "gapped" set of k-subsequences. The gap constraint requires the elements in the subsequences to be at least s positions apart within the original string. Our results are as follows. First, we show how to construct sequences sharing the same 2-gapped k-deck using a nontrivial modification of the recursive Morse-Thue string construction procedure. This establishes the first known constructive upper bound on G 2 (k). Second, we further improve this bound using the approach by Dudik and Schulman [6]. 

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