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arXiv:1911.01263 · Physical review. B./Physical review. B

Scattering of spinon excitations by potentials in the one-dimensional Heisenberg model

Alexander Pavlis, X. Zotos

Published Oct 1, 2019• 0 citations
arXivHTMLPDF

Abstract

By a semianalytical Bethe ansatz method and a $T$-matrix approach we study the scattering of a spinon, the elementary quantum many-body topological excitation in the one-dimensional (1D) Heisenberg model, by local and phonon potentials. In particular, we contrast the scattering of a spinon to that of a free spinless fermion in the XY model to highlight the effect of strong correlations. For the one-spinon scattering in an odd-site chain, we find regular behavior of the scattering coefficients. In contrast, in an even-site chain there is a transfer of transmission probability between the two spinon branches that grows exponentially with system size. We link the exponent of the exponential behavior to the dressed charge that characterizes the critical properties of the 1D Heisenberg model, an interplay of topological and critical properties. The aim of this study is a microscopic understanding of spinon scattering by impurities, barriers, or phonons, modeled as prototype potentials, an input in the analysis of quantum spin transport experiments.

DOI
10.1103/physrevb.100.134401

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By a semianalytical Bethe ansatz method and a TTT-matrix approach we study the scattering of a spinon, the elementary quantum many-body topological excitation in the one-dimensional (1D) Heisenberg model, by local and phonon potentials. In particular, we contrast the scattering of a spinon to that of a free spinless fermion in the XY model to highlight the effect of strong correlations. For the one-spinon scattering in an odd-site chain, we find regular behavior of the scattering coefficients. In contrast, in an even-site chain there is a transfer of transmission probability between the two spinon branches that grows exponentially with system size. We link the exponent of the exponential behavior to the dressed charge that characterizes the critical properties of the 1D Heisenberg model, an interplay of topological and critical properties. The aim of this study is a microscopic understanding of spinon scattering by impurities, barriers, or phonons, modeled as prototype potentials, an input in the analysis of quantum spin transport experiments.
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Using a variational ansatz based on matrix product states, the authors present a methodology for determine the elementary excitations and their low energy scattering matrices of general quasi-one-dimensional spin systems. From these scattering matrices, the authors map the system unto an effective integrable model and then employ the thermodynamic Bethe ansatz so as to determine thermodynamic properties of the spin system. As a demonstration of the method, the authors apply it to a Heisenberg spin ladder.
The excitations of the Heisenberg antiferromagnetic spin chain in zero field are known as spinons. As pairwise-created fractionalized excitations, spinons are important in the understanding of inelastic neutron scattering experiments in (quasi-)one-dimensional materials. In the present paper, we consider the real space-time dynamics of spinons originating from a local spin flip on the antiferromagnetic ground state of the (an)isotropic Heisenberg spin-1/2 model and the Babujan-Takhtajan spin-1 model. By utilizing algebraic Bethe ansatz methods at finite system size to compute the expectation value of the local magnetization and spin-spin correlations, spinons are visualized as propagating domain walls in the antiferromagnetic spin ordering with anisotropy dependent behavior. The spin-spin correlation after the spin flip displays a light cone, satisfying the Lieb-Robinson bound for the propagation of correlations at the spinon velocity.
Magnon bound states emerging in one-dimensional (1D) spin chains still lack a rigorous understanding. In this Rapid Communication we show that the length-1 spin strings significantly dominate the critical properties of spinons, magnons, and free fermions in the 1D antiferromagnetic spin-1/2 chain. Using the Bethe ansatz solution, we analytically calculate the scaling functions of the thermal and magnetic properties of the model, providing a rigorous understanding of the quantum criticality of spinons. It turns out that the double maxima in specific heat elegantly mark two crossover temperatures fanning out from the critical point, indicating three quantum phases: the Tomonaga-Luttinger liquid (TLL), the quantum critical, and fully polarized ferromagnetic phases. For the TLL phase, the Wilson ratio RW=4Ks{R}_{W}=4{K}_{s}RW​=4Ks​ remains almost temperature independent, where Ks{K}_{s}Ks​ is the Luttinger parameter. Furthermore, by applying our results, we precisely determine the quantum scalings and critical exponents of all magnetic properties in the ideal 1D spin-1/2 antiferromagnet Cu(C4H4N2)(NO3)2\mathrm{Cu}(\mathrm{C}{}_{4}\mathrm{H}{}_{4}\mathrm{N}{}_{2})(\mathrm{NO}{}_{3}){}_{2}Cu(C4​H4​N2​)(NO3​)2​, recently studied by Kono et al. [Phys. Rev. Lett. 114, 037202 (2015)]. We further find that the magnetization maximum used in experiments is not a good quantity to map out the finite-temperature TLL phase boundary.
Heisenberg spin-1/2 chains are the archetype of quantum integrable one-dimensional models describing magnetic properties of a wide range of compounds (like the KCuF 3 crystal), which can be probed experimentally through neutron scattering experiments, while being at the same time at the root of the invention of Bethe ansatz and Yang-Baxter structures that led in turn to quantum groups discovery. The aim of this contribution is to describe these algebraic ingredients and to show how to obtain from them (using combined analytical and numerical analysis) dynamical correlation functions of integrable Heisenberg spin-1/2 chains, the Fourier transform of which, the so-called dynamical structure factors, being directly measured in inelastic neutron scattering experiments. Our method is based on the algebraic Bethe ansatz and the resolution of the quantum inverse scattering problem. It leads to recent progress in the computation of integrable Heisenberg spin-1/2 chains correlation functions that we review here. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.