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1. Subdiffusive hydrodynamics of nearly integrable anisotropic spin chains

   https://doi.org/10.1073/pnas.2202823119  

   De Nardis, Jacopo; Gopalakrishnan, Sarang; Vasseur, Romain; Ware, Brayden (August 2022, Proceedings of the National Academy of Sciences)

   We address spin transport in the easy-axis Heisenberg spin chain subject to different integrability-breaking perturbations. We find subdiffusive spin transport characterized by dynamical exponent z = 4 up to a timescale parametrically long in the anisotropy. In the limit of infinite anisotropy, transport is subdiffusive at all times; for finite anisotropy, one eventually recovers diffusion at late times but with a diffusion constant independent of the strength of the perturbation and solely fixed by the value of the anisotropy. We provide numerical evidence for these findings, and we show how they can be understood in terms of the dynamical screening of the relevant quasiparticle excitations and effective dynamical constraints. Our results show that the diffusion constant of near-integrable diffusive spin chains is generically not perturbative in the integrability-breaking strength. 

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2. From deconfined spinons to coherent magnons in an antiferromagnetic Heisenberg chain with long range interactions

   https://doi.org/10.21468/SciPostPhys.10.5.110  

   Yang, Luhang; Feiguin, Adrian (January 2021, SciPost Physics)

   We study the nature of the excitations of an antiferromagnetic (AFM) Heisenberg chain with staggered long range interactions using the time-dependent density matrix renormalization group method and by means of a multi-spinon approximation. The chain undergoes true symmetry breaking and develops long range order, transitioning from a gapless spin liquid to a gapless ordered AFM phase. The spin dynamic structure factor shows that the emergence of Néel order can be associated to the formation of bound states of spinons that become coherent magnons. The quasiparticle band leaks out from the two-spinon continuum that is pushed up to higher energies. Our physical picture is also supported by an analysis of the behavior of the excitations in real-time. 

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3. Quasispins of vacancy defects in Ising chains with nearest- and next-to-nearest-neighbor interactions

   https://doi.org/10.1103/PhysRevB.108.174436  

   Sun, Shijun; Ramirez, Arthur P; Syzranov, Sergey (November 2023, Physical Review B)

   Motivated by frustrated magnets and quasi-one-dimensional magnetic materials, we study the magnetic properties of one-dimensional (1D) Ising chains with nearest-neighbor (NN) and weaker next-to-nearest-neighbor (NNN) interactions in the presence of vacancy defects. The effect of a vacancy on the magnetic susceptibility of a spin chain is twofold: it reduces the length of the chain by an effective “vacancy size” and may also act as a free spin, a “quasispin,” with a Curie-type 𝜒_{quasi}=⟨𝑆^2⟩/𝑇 contribution to the susceptibility. In chains with antiferromagnetic short-range order, the susceptibility of vacancy-free chains is exponentially suppressed at low temperatures, and quasispins dominate the effect of impurities on the chains' magnetic properties. For chains with antiferromagnetic NN interactions, the quasispin matches the value ⟨𝑆^2⟩=1 of the Ising spins in the chain for ferromagnetic NNN interactions and vanishes for antiferromagnetic NNN interactions. For chains with ferromagnetic short-range order, quasispin effects are insignificant due to exponentially large low-temperature susceptibilities, and the dominant effect of a vacancy is effectively changing the length of the chain. 

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4. Disordered Lieb-Robinson Bounds in One Dimension

   https://doi.org/10.1103/PRXQuantum.4.020349  

   Baldwin, Christopher L.; Ehrenberg, Adam; Guo, Andrew Y.; Gorshkov, Alexey V. (June 2023, PRX Quantum)

   By tightening the conventional Lieb-Robinson bounds to better handle systems that lack translation invariance, we determine the extent to which “weak links” suppress operator growth in disordered one dimensional spin chains. In particular, we prove that ballistic growth is impossible when the distribution of coupling strengths μ(J ) has a sufficiently heavy tail at small J and we identify the correct dynamical exponent to use instead. Furthermore, through a detailed analysis of the special case in which the couplings are genuinely random and independent, we find that the standard formulation of Lieb-Robinson bounds is insufficient to capture the complexity of the dynamics—we must distinguish between bounds that hold for all sites of the chain and bounds that hold for a subsequence of sites and we show by explicit example that these two can have dramatically different behaviors. All the same, our result for the dynamical exponent is tight, in that we prove by counterexample that there cannot exist any Lieb-Robinson bound with a smaller exponent. We close by discussing the implications of our results, both major and minor, for numerous applications ranging from quench dynamics to the structure of ground states. 

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5. On Mixing of Markov Chains: Coupling, Spectral Independence, and Entropy Factorization.

   Antonio Blanca, Pietro Caputo (January 2022, SODA 2022)

   For general spin systems, we prove that a contractive coupling for an arbitrary local Markov chain implies optimal bounds on the mixing time and the modified log-Sobolev constant for a large class of Markov chains including the Glauber dynamics, arbitrary heat-bath block dynamics, and the Swendsen-Wang dynamics. This reveals a novel connection between probabilistic techniques for bounding the convergence to stationarity and analytic tools for analyzing the decay of relative entropy. As a corollary of our general results, we obtain O(n log n) mixing time and Ω(1/n) modified log-Sobolev constant of the Glauber dynamics for sampling random q-colorings of an n-vertex graph with constant maximum degree Δ when q > (11/6–∊0)Δ for some fixed ∊0 > 0. We also obtain O(log n) mixing time and Ω(1) modified log-Sobolev constant of the Swendsen-Wang dynamics for the ferromagnetic Ising model on an n-vertex graph of constant maximum degree when the parameters of the system lie in the tree uniqueness region. At the heart of our results are new techniques for establishing spectral independence of the spin system and block factorization of the relative entropy. On one hand we prove that a contractive coupling of any local Markov chain implies spectral independence of the Gibbs distribution. On the other hand we show that spectral independence implies factorization of entropy for arbitrary blocks, establishing optimal bounds on the modified log-Sobolev constant of the corresponding block dynamics. 

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