*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.

**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.

**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.