PROF. GLEN EVENBLY
My research is focused on the development of novel theoretical and numerical tools for modelling quantum many-body systems.
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:
SOME RECENT RESEARCH PROJECTS
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.
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).
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.
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.