# Theory Group Lunchtime Seminars

Scheduled seminars are listed below.

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PS1.28
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###### Theory Seminar: Thorsten Wahl (Oxford), Tensor network approaches to many-body localisation
PS1.28

We propose a tensor network encoding the set of all eigenstates of a fully many-body localized system in one dimension. Our construction, conceptually based on the ansatz introduced in Phys. Rev. B 94, 041116(R) (2016), is built from two layers of unitary matrices which act on blocks of contiguous sites. We argue that this yields an exponential reduction in computational time and memory requirement as compared to all previous approaches for finding a representation of the complete eigenspectrum of large many-body localized systems with a given accuracy. Concretely, we optimize the unitaries by minimizing the magnitude of the commutator of the approximate integrals of motion and the Hamiltonian, which can be done in a local fashion. This further reduces the computational complexity of the tensor networks arising in the minimization process compared to previous work. We test the accuracy of our method by comparing the approximate energy spectrum to exact diagonalization results for the random-field Heisenberg model on 16 sites. We find that the technique is highly accurate deep in the localized regime and maintains a surprising degree of accuracy in predicting certain local quantities even in the vicinity of the predicted dynamical phase transition. To demonstrate the power of our technique, we study a system of 72 sites, and we are able to see clear signatures of the phase transition. Our work opens a new avenue to study properties of the many-body localization transition in large systems.

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PS1.28

tba

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###### Theory Seminar: Manuel dos Santos Dias (Forschungszentrum Jülich), Spin interactions, excitations and fluctuations in magnetic adatoms and small clusters from first principles
PS1.28

Single atoms are the smallest possible magnets, of interest for fundamental physics and of great promise for technological applications. When assembled on a surface, their properties can be probed and manipulated via scanning tunneling microscopy (STM) and inelastic scanning tunneling spectroscopy (ISTS). However, the theoretical description is challenging, due to the interplay between the reduced dimensionality, the interactions driving the magnetism, and the coupling to the surface. Furthermore, an accurate description of the low-energy physics due to the spin-orbit interaction and external magnetic fields is essential.

In Jülich, we have recently developed a hierarchical theoretical approach to the static and dynamics properties of surface-supported magnetic nanostructures. The materials-specific information is supplied by density functional theory (DFT), which gives access to ground-state magnetic properties and magnetic interactions. The dynamics of the magnetic moments follows from time-dependent DFT (TDDFT), accounting for the impact of the surface electrons on the spin dynamics. The final level of theory addresses many-body effects, either through many-body perturbation theory (MBPT) or by solving a multi-orbital Anderson impurity model with quantum Monte Carlo, yielding realistic inelastic transport spectra.

In this talk I will present an overview of these theoretical methods while focusing on concrete physical systems: magnetic adatoms and small clusters on metallic surfaces, such as Cu(111) or Pt(111), in close connection with the available experimental information. Different magnetic adatoms on the same surface have very different static and dynamic properties [1-3], which influence their magnetic stability via zero-point spin fluctuations [4-6], while their tunneling spectra are only adequately described in MBPT [7-9]. The interactions between magnetic adatoms depend not only on their separation but also on their arrangement with respect to the surface, leading to widely different properties of apparently similar clusters [10-12]. I conclude by discussing the possible shortcomings and future research directions.

References:
[1] Phys Rev Lett 111, 157204 (2013); [2] Phys Rev B 91, 075405 (2015); [3] Nat Commun 7, 10454 (2016); [4] Nano Lett 16, 4305 (2016); [5] Phys Rev Lett 119, 017203 (2017); [6] Phys Rev B 96, 144410 (2017); [7] Phys Rev B 89, 235439 (2014); [8] Phys Rev B 93, 115123 (2016); [9] Phys Rev B 93, 035451 (2016); [10] Nat Commun 7, 10620 (2016); [11] Phys Rev B 96, 144401 (2017); [12] Nat Commun 8, 642 (2017)