# 2019

**Signatures of rare states and thermalization in a theory with confinement**

**N. J. Robinson**, A. J. A. James, and R. M. Konik, Phys. Rev. B **99**, 195108 (2019).

Expanding upon Phys. Rev. Lett. **122**, 130603 (2019), we consider the eigenstate thermalization hypothesis and non-equilibrium dynamics of a simple one-dimensional model of quantum magnetism which exhibits confinement. We reveal that “meson-like” states of linearly-confined pairs of domain walls can persist far into the many-body spectrum and have non-thermal properties. Thus this model presents a simple counterexample to the eigenstate thermalization hypothesis, despite being non-integrable.

**Nonthermal states arising from confinement in one and two dimensions**

A. J. A. James, R. M. Konik, and **N. J. Robinson**, Phys. Rev. Lett. **122**, 130603 (2019).

In work with Andrew James (Open University) and Robert Konik (Brookhaven National Laboratory), we showed that confinement and the associated formation of meson-like excitations leads to non-thermal eigenstates in simple models of quantum magnetism. These states persist far into the many-body spectrum, signalling a failure of the eigenstate thermalization hypothesis in a non-integrable model, and leading to anomalous non-equilibrium dynamics and absence of thermalization in these magnetic systems.

**Magnetism in iridate heterostructures leveraged by structural distortions**

D. Meyers, Y. Cao, G. Fabbris, **N. J. Robinson** and coworkers, Sci. Rep. **9**, 4263 (2019).

With colleagues from Brookhaven National Laboratory, Argonne National Laboratory and a team of international collaborators, we showed how magnetic interactions can be tuned in Iridate-based superlattice structures by modification of the superlattice stacking. In turn, the tuning of the magnetic interactions lead to a large reduction in the size of the magnetic excitation gap, as measured via resonant inelastic X-ray scattering. The superlattice structure can thus be brought towards the magnetic phase transition, and the corresponding competition between competing magnetic phases. Our findings demonstrated how large changes in the magnetic interactions can be tailored by engineering subtle structural modulations. Here I was the supporting theorist on this (majority) experimental project.

*Ladderlike optical conductivity in the spin-fermion model*

L. Classen, **N. J. Robinson**, A. M. Tsvelik, Phys. Rev. B **99**, 115110 (2019).

With Laura Classen and Alexei Tsvelik at Brookhaven National Lab, we computed the optical conductivity in a nested limit of the spin-fermion model. This limit is particularly interesting as one can separate the carries on the Fermi surface into patches of 2D “Fermi-liquid” quasiparticles and quasi-1D “non-Fermi-liquid” ones. This leads to transport phenomenology that is very reminiscent of the behaviour of the high-temperature cuprate superconductors. A surprising result of our work is that the optical conductivity in the pseudogap phase is dominated by the antinodal, quasi-1D quasiparticles. An analysis of experimental data seems to also support this unconventional conclusion.

**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.

A popular summary highlighting this article, from Brookhaven National Laboratory.

## 2018

**Viewpoint: Cold Atoms Bear a Quantum Scar **

**N. J. Robinson, **Physics **11**, 105 (2019) [Open Access]

In this invited article, I discuss some of the recent excitement surrounding quantum many-body scars and experiments on Rydberg atom chains.

**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). [Open Access Version]

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.

# 2017

*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.

# 2016

*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 in models with weak integrability breaking.

**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.

# 2015

**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.

# 2014

**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 “prethermal” regime.

# 2012

**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.

# 2010

**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.