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Theory Group Lunchtime Seminars

Scheduled seminars are listed below.

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Thu, Oct 25, '18
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Theory Seminar: John Biggins (Cambridge), Large strain elasticity: geometry, instability and brains
PS1.28

We are all familiar with the prototypical elastic instability: the buckling of a slender column under a compressive load. Soft elastic solids, such as rubbers, gels, and biological tissues, are united by their ability to sustain very large shape changes, and consequently undergo a range of more exotic elastic instabilities underpinned by the non-linear geometry of large strains. I will discuss several such instabilities, including fingering in soft solid layers under tension, beading in solid cylinders subject to surface tension, and a brand new "peristaltic" instability in inflated cylindrical channels. In the second half of the talk, I will discuss the buckling of a growing layer adhered to a soft substrate. I will argue on symmetry grounds that such buckling will inevitably produce patterns of hexagonal dents near threshold, and then make a biological case that this buckling process leads to the folded shape of the human brain.

Thu, Nov 1, '18
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Theory Seminar: Shigeyuki Komura (Tokyo), A three-sphere microswimmer in a structured fluid
PS1.28

We discuss the locomotion of a three-sphere microswimmer in a viscoelastic structured fluid characterized by typical length and time scales [1]. We derive a general expression to link the average swimming velocity to the sphere mobilities. In this relationship, a viscous contribution exists when the time-reversal symmetry is broken, whereas an elastic contribution is present when the structural symmetry of the microswimmer is broken. As an example of a structured fluid, we consider a polymer gel, which is described by a ``two-fluid" model. We demonstrate in detail that the competition between the swimmer size and the polymer mesh size gives rise to the rich dynamics of a three-sphere microswimmer.

[1] K. Yasuda, R. Okamoto, and S. Komura, EPL 123, 34002 (2018).

Thu, Nov 8, '18
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Theory Seminar: Fabian Maucher (Durham), tba
PS1.28
Thu, Nov 15, '18
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Theory Seminar: Robert Jack (Cambridge), tba
PS1.28
Thu, Nov 22, '18
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Theory Seminar: Patricia Bassereau (Institut Curie)
PS1.28
Thu, Nov 29, '18
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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.

Thu, Dec 6, '18
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Theory Seminar: Gabriele Sosso (Warwick, Chemistry)
PS1.28

tba

Thu, Dec 13, '18
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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)