Research

My current research is focused around non-equilibrium phenomena in complex interacting many-body systems, ranging from ultra-cold atoms to strongly-correlated electron materials. Below is an overview of the main topics:

Tensor Network Theory


A major research theme of mine is understanding the nature of entanglement, correlations and quantum mutual information in ground states and thermal states of commonly encountered many-body systems with striking and deep connections to their classical simulability.

This has mainly involved exploiting and further developing sophisticated tensor network theory (TNT) techniques for efficiently simulating many-body quantum systems. Currently this most prominently includes the density matrix renormalization group (DMRG) method and its generalization to time-dependent phenomena via the time-evolving block decimation (TEBD) algorithm applicable to 1D systems. A major long term effort to extend the success of these methods to 2D quantum lattice systems is underway.

In collaboration with Dieter Jaksch's group in Oxford I am helping to develop a comprehensive and highly optimized freely available open-source software library for tensor network theory algorithms which can be found at www.tensornetworktheory.org.

Other goals are to eventually connecting tensor network theory to other extremely successful techniques in condensed matter physics such as density functional theory (DFT) and dynamical mean-field theory (DMFT).

Some of my contributions to this area are:

Quantum Materials Control

Strong periodic driving of a system has been long known to dramatically alter the behaviour of a system. The classic example is the Kaptiza pendulum where vertically shaking the pivot point of a pendulum very fast can make the inverted position a dynamically stable configuration. Can we do the same for strongly-correlated electron systems? If we drive molecular or lattice distortions strongly can we stabilise desired forms of order in a material or even cause new phases of matter to emerge which are not possible in equilibrium? If we can then this may permit the controlled manipulation of material properties giving quantum enhanced functionality.  

Working towards this goal is the aim of the ERC-funded Quantum Materials' control (Q-MAC) project which I am involved in. It is a challenging research topic combining the need to tackle interacting many-body systems and to understand the largely unexplored complexities of far-from-equilibrium physics. Use of tensor network theory and other techniques will be essential.  

So far my work in this area includes:

Ultra-cold atoms and optical lattices

My original interest in many-body quantum lattice systems came from studying the "perfect" synthetic crystals formed from neutral ultra-cold atoms trapped in laser light. Optical lattice systems have the unique properties of being coherent quantum many-body systems that can be engineered and controlled. As such many situations can be considered mimicking real systems as a form of quantum simulator, or even implementing systems that do not occur naturally.  

Over the last decade my main focus has been on:

 

Foundational problems

I have done some work on exploring foundational issues in quantum theory including non-locality, quantifying quantumness, as well as connections to thermodynamics of small systems and fluctuation relations.

In particular I have focused on: