Neil J. Robinson

Smooth electron waveguides in graphene

We present exact analytical solutions for the zero-energy modes of two-dimensional massless Dirac fermions fully confined within a smooth one-dimensional potential V(x)=-{alpha}/cosh({beta}x), which provides a good fit for potential profiles of existing top-gated graphene structures. We show that there is a threshold value of the characteristic potential strength {alpha}/{beta} for which the first mode appears, in striking contrast to the nonrelativistic case. A simple relationship between the characteristic strength and the number of modes within the potential is found. An experimental setup is proposed for the observation of these modes. The proposed geometry could be utilized in future graphene-based devices with high on/off current ratios.

Quench Dynamics in a Model with Tuneable Integrability Breaking

We consider quantum quenches in an integrable quantum chain with tuneable-integrability-breaking interactions. In the case where these interactions are weak, we demonstrate that at intermediate times after the quench local observables relax to a prethermalized regime, which can be described by a density matrix that can be viewed as a deformation of a generalized Gibbs ensemble. We present explicit expressions for the approximately conserved charges characterizing this ensemble. We do not find evidence for a crossover from the prethermalized to a thermalized regime on the time scales accessible to us. Increasing the integrability-breaking interactions leads to a behaviour that is compatible with eventual thermalization.

Thermalization and light cones in a model with weak integrability breaking

We employ equation of motion techniques to study the non-equilibrium dynamics in a lattice model of weakly interacting spinless fermions. Our model provides a simple setting for analyzing the effects of weak integrability breaking perturbations on the time evolution after a quantum quench. We establish the accuracy of the method by comparing results at short and intermediate times to time-dependent density matrix renormalization group computations. For sufficiently weak integrability-breaking interactions we always observe prethermalization plateaux, where local observables relax to non-thermal values at intermediate time scales. At later times a crossover towards thermal behaviour sets in. We determine the associated time scale, which depends on the initial state, the band structure of the non-interacting theory, and the strength of the integrability breaking perturbation. Our method allows us to analyze in some detail the spreading of correlations and in particular the structure of the associated light cones in our model. We find that the interior and exterior of the light cone are separated by an intermediate region, the temporal width of which appears to scale with a universal power-law

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

t^{1/3}

Motion of a Distinguishable Impurity in the Bose Gas : Arrested Expansion Without a Lattice and Impurity Snaking

.

Finite wave vector pairing in doped two-leg ladders

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1  +  1D quantum chromodynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.We review two important non-perturbative approaches for extracting the physics of low- dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of confor- mal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme- tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro- modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.

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

We consider the real-time dynamics of an initially localized distinguishable impurity injected into the ground state of the Lieb-Liniger model. Focusing on the case where integrability is preserved, we numerically compute the time evolution of the impurity density operator in regimes far from analytically tractable limits. We find that the injected impurity undergoes a stuttering motion as it moves and expands. For an initially stationary impurity, the interaction-driven formation of a quasibound state with a hole in the background gas leads to arrested expansion-a period of quasistationary behavior. When the impurity is injected with a finite center-of-mass momentum, the impurity moves through the background gas in a snaking manner, arising from a quantum Newtons cradlelike scenario where momentum is exchanged back and forth between the impurity and the background gas.

Excitations in the Yang–Gaudin Bose gas

We consider the effects of umklapp processes in doped two-leg fermionic ladders. These may emerge either at special band fillings or as a result of the presence of external periodic potentials. We show that such umklapp processes can lead to profound changes of physical properties and in particular stabilize pair-density wave phases.

Prethermalization and Thermalization in Models with Weak Integrability Breaking

The high-temperature normal state of the unconventional cuprate superconductors has resistivity linear in temperature T, which persists to values well beyond the Mott-Ioffe-Regel upper bound. At low temperatures, within the pseudogap phase, the resistivity is instead quadratic in T, as would be expected from Fermi liquid theory. Developing an understanding of these normal phases of the cuprates is crucial to explain the unconventional superconductivity. We present a simple explanation for this behavior, in terms of the umklapp scattering of electrons. This fits within the general picture emerging from functional renormalization group calculations that spurred the Yang-Rice-Zhang ansatz: Umklapp scattering is at the heart of the behavior in the normal phase.

Quasiparticle breakdown in the quasi-one-dimensional Ising ferromagnet CoNb2O6

We study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang-Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at