I always wanted to be a string theorist.

However, my career took a different turn and I ended up a quantum information theorist. Nevertheless, my fascination with particle physics and quantum gravity has never lessened. I suppose this has had a direct impact on what I chose to work on, namely, complex quantum systems and entanglement. Luckily this was to prove a good choice: I got to be part of an excitating revolution in quantum many body theory where entanglement-inspired thinking led to the development of a dazzling array of new variational classes, namely, *tensor network states*.

Tensor network states have proved to be a very useful tool in trying to reason about the dynamics of many strongly interacting quantum systems because they provide a wonderfully parsimonious description of the degrees of freedom that are actually *relevant* for observable physics without needing to keep direct track of the exponentially diverging set of complex numbers required to specify a general quantum state in the hilbert space of *N* particles.

But my first love was always quantum field theory and string theory so I was delighted when, in late 2009, I realised that one could take a continuum limit of a matrix product state (a tensor network state that I’d spent a lot of time working with) to produce a nontrivial quantum field state. With great excitement I worked out the details of the construction and started writing it up for publication. However, as is often the case with a good idea, it occurs to many people at the same time — such ideas are somehow “in the air”. This was no exception: to my astonishment I discovered a paper submitted some two weeks prior entitled “Continuous matrix product states for quantum fields” which read, almost *word for word*, like my draft. This was doubly embarrassing because the paper had *already* appeared on the arXiv and I had somehow missed it and, further, it had been written by my good friends and collaborators Frank Verstraete and Ignacio Cirac!

Thus began a very fruitful time where we worked out many of the details of this new approach to quantum field theory: in the past few years myself and my collaborators have been enthusiastically extending cMPS to a variety of settings and along the way developing a continuous limit of the PEPS and MERA tensor network states.

My hope, all this time, has been that these new continuous tensor network states would immediately lead to progress on the major unsolved problems in quantum field theory, just as they had in quantum many body theory. With the arrogance of the ignorant I was convinced we’d solve the problem of “infinities” and usher in a new era of quantum information-inspired quantum field theory.

*It turned out not to be so easy*.

During the past five years I’ve thrown myself into the deep end of quantum field theory: I realised early on I’d have to go back to basics and actually really learn the subject properly. Along the way I realised that my original naive enthusiasm was somewhat misguided and misdirected. But I also discovered some truly fascinating things that I’m very excited about. I’d like to share some of these with you today; although my initial conception of quantum field theory was indeed wrongheaded, I discovered that quantum information theorists are really very well-suited to think about all sorts of interesting problems in quantum field theory. Read the rest of this entry »