My research is focused on the development of novel theoretical and numerical tools for modelling quantum many-body systems.

Research Interests:

  • Tensor network states and algorithms

  • Real-space renormalization group

  • Numerical methods for systems of strongly correlated electrons

  • Entanglement and quantum information

  • Quantum criticality and phase transitions

  • AdS/CFT duality and holography

  • Machine learning and tensor networks

My research website on tensor networks (containing tutorials, example codes and links to further resources) can be found at:


Hyper-invariant Tensor Networks and Holography:

Tensor network states such as MERA are currently of significant interest as models for holography and, in particular, for the AdS/CFT correspondence. In this work I propose a new class of tensor network state that retain key features of the MERA, including algebraic correlations and efficient contractibility, yet are also built according to a uniform tiling of hyperbolic space, and thus capture the desired symmetries of AdS space.

Entanglement Renormalization and Wavelets:

A key result of this project was the establishment of a precise connection between MERA quantum circuits and discrete wavelet transforms (DWTs). This connection gave exciting new insights both into MERA (allowing the first analytic construction of a MERA for the ground state of a critical system) and also into DWTs (allowing construction of improved families of wavelets, with application to more efficient data/image compression).

Implicitly Disentangled Renormalization:

Many powerful methods for the efficient simulation of quantum many-body systems are based on the renormalization group (RG). In this work I propose a new implementation of real-space RG transformations for quantum states on the lattice. This new approach reproduces the key features of entanglement renormalization (ER), but without the need for unitary disentanglers, which allows a variety of numeric simulation algorithms to be substantially improved.

Tensor Network Renormalization:

This project involved the development of a new tensor network algorithm for the simulation of quantum many-body systems, dubbed tensor network renormalization (TNR). A significant result was the demonstration that TNR realizes both an accurate and computationally sustainable coarse-graining transformation even at a critical point, whereas previous approaches diverge near criticality. TNR also produces, for the first time, a scale-invariant fixed point for critical systems.