An Introduction to Gauge Gravity Duality and Its Application in Condensed Matter

The past few years have witnessed a remarkable crossover of string theoretical ideas from the abstract world of geometrical forms to the concrete experimental realm of condensed matter physics. The basis for this --- variously known as holography, the AdS/CFT correspondence or gauge-gravity duality --comes from notions right at the cutting edge of string theory. Nevertheless, the insights afforded can often be expressed in ways very familiar to condensed matter physicists, such as relationships between response functions and new sum rules. The aim of this short, introductory review is to survey the ideas underpinning this crossover, in a way that -- as far as possible -- strips them of sophisticated mathematical formalism, whilst at the same time retaining their fundamental essence. I will sketch the areas in which progress has been made to date and highlight where the challenges and open questions lie. Finally, I will attempt to give a perspective upon these ideas. What contribution can we realistically expect from this approach and how might it be accommodated into the canon of condensed matter theory? Inevitably, any attempt to do this in such a rapidly evolving field will be superseded by events. Nevertheless, I hope that this will provide a useful way to think about gauge-gravity duality and the uncharted directions in which it might take us.Comment: Unedited version of article published in Contemporary Physics. Intended for advanced final-year undergraduate

Hawking Radiation and Non-equilibrium Quantum Critical Current Noise

The dynamical scaling of quantum critical systems in thermal equilibrium may be inherited in the driven steady-state, leading to universal out-of-equilibrium behaviour. This attractive notion has been demonstrated in just a few cases. We demonstrate how holography - a mapping between the quantum critical system and a gravity dual - provides an illuminating perspective and new results. Non-trivial out-of-equilibrium universality is particularly apparent in current noise, which is dual to Hawking radiation in the gravitational system. We calculate this in a 2-dimensional system driven by a strong in-plane electric field and deduce a universal scaling function interpolating between previously established equilibrium and far-from-equilibrium current noise. Since this applies at all fields, out-of-equilibrium experiments no longer require very high fields for comparison with theory.Comment: revised version to appear in PRL, 5 page

Compact Neural Networks based on the Multiscale Entanglement Renormalization Ansatz

This paper demonstrates a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for the fully connected layers in a convolutional neural network and test this implementation on the CIFAR-10 and CIFAR-100 datasets. The proposed method outperforms factorization using tensor trains, providing greater compression for the same level of accuracy and greater accuracy for the same level of compression. We demonstrate MERA layers with 14000 times fewer parameters and a reduction in accuracy of less than 1% compared to the equivalent fully connected layers, scaling like O(N).Comment: 8 pages, 2 figure

Hierarchical quantum classifiers

Quantum circuits with hierarchical structure have been used to perform binary classification of classical data encoded in a quantum state. We demonstrate that more expressive circuits in the same family achieve better accuracy and can be used to classify highly entangled quantum states, for which there is no known efficient classical method. We compare performance for several different parameterizations on two classical machine learning datasets, Iris and MNIST, and on a synthetic dataset of quantum states. Finally, we demonstrate that performance is robust to noise and deploy an Iris dataset classifier on the ibmqx4 quantum computer

Dynamics after a sweep through a quantum critical point

The coherent quantum evolution of a one-dimensional many-particle system after sweeping the Hamiltonian through a critical point is studied using a generalized quantum Ising model containing both integrable and non-integrable regimes. It is known from previous work that universal power laws appear in such quantities as the mean number of excitations created by the sweep. Several other phenomena are found that are not reflected by such averages: there are two scaling regimes of the entanglement entropy and a relaxation that is power-law rather than exponential. The final state of evolution after the quench is not well characterized by any effective temperature, and the Loschmidt echo converges algebraically to a constant for long times, with cusplike singularities in the integrable case that are dynamically broadened by nonintegrable perturbations.Comment: 4 pages, 4 figure

Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices

We study ground states and elementary excitations of a system of bosonic atoms and diatomic Feshbach molecules trapped in a one-dimensional optical lattice using exact diagonalization and variational Monte Carlo methods. We primarily study the case of an average filling of one boson per site. In agreement with bosonization theory, we show that the ground state of the system in the thermodynamic limit corresponds to the Pfaffian-like state when the system is tuned towards the superfluid-to-Mott insulator quantum phase transition. Our study clarifies the possibility of the creation of exotic Pfaffian-like states in realistic one-dimensional systems. We also present preliminary evidence that such states support non-Abelian anyonic excitations that have potential application for fault-tolerant topological quantum computation.Comment: 10 pages, 10 figures. Matching the version published Phys.Rev.

Introducing fluctuation-driven order into density functional theory using the quantum order-by-disorder framework

Density functional theory in the local or semi-local density approximation is a powerful tool for materials simulation, yet it struggles in many cases to describe collective electronic order that is driven by electronic interactions. In this work it is shown how arbitrary, fluctuation-driven electronic order may be introduced into density functional theory using the quantum order-by-disorder framework. This is a method of calculating the free energy correction due to collective spin and charge fluctuations about a state that hosts static order, in a self-consistent manner. In practical terms, the quantum order-by-disorder method is applied to the Kohn-Sham auxiliary system of density functional theory to give an order-dependent correction to the exchange-correlation functional. Calculation of fluctuation propagators within density functional theory renders the result fully first-principles. Two types of order are considered as examples -- fluctuation-driven superconductivity and spin nematic order -- and implementation schemes are presented in each case.Comment: 20 pages, 2 figure