**Non-Topological Majorana Zero Modes in Inhomogeneous Spin Ladders**

**N. J. Robinson**, A. Altland, R. Egger, N. M. Gergs, W. Li, D. Schuricht, A. M. Tsvelik, A. Weichselbaum, R. M. Konik, Phys. Rev. Lett. 122, 027201 (2019).

We proposed that interfaces of different phases in spin ladders can lead to *additional* interficial Majorana zero modes as compared to the naive expectation. Unlike in topological quantum wires, these new modes are void of topological protection, but can nonetheless be resilient, making them interesting candidates for quantum device applications.

**Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods**

A. J. A. James, R. M. Konik, P. Lecheminant, **N. J. Robinson**, and A. M. Tsvelik, Rep. Prog. Phys. **81** 046002 (2018); arXiv:1703.08421 (2017).

With Andrew James, Robert Konik, Philippe Lecheminant and Alexei Tsvelik, we review three important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. We comprehensively introduce non-Abelian bosonization, the truncated spectrum approach, and chain array matrix product states. Numerous example applications of each method are presented.

*Umklapp scattering as the origin of T-linear resistivity in the normal state of high-Tc cuprate superconductors*

T. M. Rice, **N. J. Robinson** and A. M. Tsvelik*,* Phys. Rev. B **96**, 220502(R) (2017). [Open Access Version]

In a collaboration with Maurice Rice and Alexei Tsvelik, we propose a simple “two-fluid model” of the normal state (pseudogap and strange metal phases) of the high-temperature cuprate superconductors. Placing umklapp scattering at the centre of the physics, this captures the behaviour of the resistivity from the superconducting transition to the high temperature regime.

**Excitations in the Yang-Gaudin Bose gas**

**N. J. Robinson **and R. M. Konik,* *J. Stat. Mech. **2017** 063101 (2017). [Open Access Version]

Along with Robert Konik, we presented a detail study of the excitations of the two-component Bose gas. We particular focussed on finite-size effects and bound state excitations, and used the exact Bethe ansatz solution of the model.

*Thermalization and light-cones in a model with weak integrability breaking*

B. Bertini, F. H. L. Essler, S. Groha, and **N. J. Robinson**, Phys. Rev. B **94**, 245117 (2016). [Open Access Version]

With Bruno Bertini, Fabian Essler and Stefan Groha, this is the final in a sequence of works (see also, Phys. Rev. Lett. **115**, 180601 (2015) and Phys. Rev. B **89**, 165104 (2014)) in which we develop an understanding of thermalization and the behaviour of light cones.

**Motion of a distinguishable impurity in the Bose gas: Arrested expansion and impurity snaking**

**N. J. Robinson**, J.-S. Caux and R. M. Konik, Phys. Rev. Lett. **116**, 145302 (2016). [Open Access Version]

In collaboration with Jean-Sébastien Caux and Robert Konik, we studied the non-equilibrium dynamics of a localized impurity injected into the Bose gas. We used integrability to numerically compute the time-evolution away from analytically-tractable limits. The impurity is seen to undergo a stuttering sequence of motion, showing arrested expansion and snaking dynamics.

**Prethermalization and Thermalization in Models with Weak Integrability Breaking**

B. Bertini, F. H. L. Essler, S. Groha, and **N. J. Robinson**, Phys. Rev. Lett. **115**, 180601 (2015). [Open Access Version]

The second in a sequence of works (see also, Phys. Rev. B **94**, 245117 (2016) and Phys. Rev. B **89**, 165104 (2014)) with Bruno Bertini, Fabian Essler and Stefan Groha aimed at understanding how quantum systems thermalize. We develop a semi-analytical technique to compute the real-time dynamics of weakly interacting systems and compare to time-dependent DMRG calculations, showing our method to be very accurate. As with our previous work, when integrability breaking is weak, we find robust prethermalization.

**Quasi-particle breakdown in the quasi-one-dimensional Ising ferromagnet CoNb2O6**

**N. J. Robinson**, F. H. L. Essler, I. Cabrera and R. Coldea, Phys. Rev. B **90**, 174406 (2014). [Open Access Version]

Working closely with Oxford experimentalists, Ivelisse Cabrera and Radu Coldea, we studied quasi-particle breakdown in the quasi-one-dimensional spin-1/2 ferromagnet CoNb2O6. Quasi-particle breakdown is a fascinating quantum many-body phenomenon where single-particle excitations become unstable to decay to multi-particle excitations and cannot easily be observed in experimental probes.

**Quench dynamics in a model with tuneable integrability breaking**

F. H. L. Essler, S. Kehrein, S. R. Manmana and **N. J. Robinson**, Phys. Rev. B **89**, 165104 (2014). [Open Access Version]

This work with Fabian Essler, Stefan Kehrein and Salvatore Manama was the first in a series (see also Phys. Rev. Lett. **115**, 180601 (2015) and Phys. Rev. B **94**, 245117 (2016)) that addressed a rather fundamental question: when you inject energy into a quantum system, how does it heat up? When integrability breaking is weak, we show that at intermediate times the system is not thermal, instead relaxing to a “pre thermal” regime.

**Umklapp scattering and finite-wavevector pairing in the extended-Hubbard model on the two-leg ladder**

**N. J. Robinson**, F. H. L. Essler, E. Jeckelmann and A. M. Tsvelik, Phys. Rev. B **85**, 195103 (2012). [Open Access Version]

In this work with Fabian Essler, Eric Jeckelmann and Alexei Tsvelik, we studied how an unusual types of superconductivity can emerge in a system of electrons hopping on a two-leg ladder.

**Smooth electron waveguides in Graphene**

R. R. Hartmann, **N. J. Robinson** and M. E. Portnoi, Phys. Rev. B **81**, 245431 (2010). [Open Access Version]

With Richard Hartmann and Misha Portnoi at the University of Exeter, we studied how to trap electrons in graphene using electric or magnetic fields. In particular, we proposed a model of a top-gate nanostructure (pictured above) that traps electrons, much like a fibre optical cable traps and guides light. Our predictions have been confirmed in the recent experimental work Nature Physics **12**, 128 (2016) and has spurred various other theoretical works.