“Quantum Information meets Quantum Matter”, it sounds like the beginning of a perfect romance story. It is probably not the kind that makes an Oscar movie, but it does get many physicists excited, physicists including Bei, Duanlu, Xiaogang and me. Actually we find the story so compelling that we decided to write a book about it, and it all started one day in 2011 when Bei popped the question ‘Do you want to write a book about it?’ during one of our conversations.
This idea quickly sparked enthusiasm among the rest of us, who have all been working in this interdisciplinary area and are witness to its rising power. In fact Xiao-Gang has had the same idea of book writing for some time. So now here we are, four years later, posting the first version of the book on arXiv last week. (arXiv link)
The book is a condensed matter book on the topic of strongly interacting many-body systems, with a special focus on the emergence of topological order. This is an exciting topic, with new developments everyday. We are not trying to cover the whole picture, but rather to present just one perspective – the quantum information perspective – of the story. Quantum information ideas, like entanglement, quantum circuit, quantum codes are becoming ever more popular nowadays in condensed matter study and have lead to many important developments. On the other hand, they are not usually taught in condensed matter courses or covered by condensed matter books. Therefore, we feel that writing a book may help bridge the gap.
We keep the writing in a self-consistent way, requiring minimum background in quantum information and condensed matter. The first part introduces concepts in quantum information that is going to be useful in the later study of condensed matter systems. (It is by no means a well-rounded introduction to quantum information and should not be read in that way.) The second part moves onto explaining one major topic of condensed matter theory, the local Hamiltonians and their ground states, and contains introduction to the most basic concepts in condensed matter theory like locality, gap, universality, etc. The third part then focuses on the emergence of topological order, first presenting a historical and intuitive picture of topological order and then building a more systematic approach based on entanglement and quantum circuit. With this framework established, the fourth part studies some interesting topological phases in 1D and 2D, with the help of the tensor network formalism. Finally part V concludes with the outlook of where this miraculous encounter of quantum information and condensed matter would take us – the unification between information and matter.
We hope that, with such a structure, the book is accessible to both condensed matter students / researchers interested in this quantum information approach and also quantum information people who are interested in condensed matter topics. And of course, the book is also limited by the perspective we are taking. Compared to a standard condensed matter book, we are missing even the most elementary ingredient – the free fermion. Therefore, this book is not to be read as a standard textbook on condensed matter theory. On the other hand, by presenting a new approach, we hope to bring the readers to the frontiers of current research.
The most important thing I want to say here is: this arXiv version is NOT the final version. We posted it so that we can gather feedbacks from our colleagues. Therefore, it is not yet ready for junior students to read in order to learn the subject. On the other hand, if you are a researcher in a related field, please send us criticism, comments, suggestions, or whatever comes to your mind. We will be very grateful for that! (One thing we already learned (thanks Burak!) is that we forgot to put in all the references on conditional mutual information. That will be corrected in a later version, together with everything else.) The final version will be published by Springer as part of their “Quantum Information Science and Technology” series.
I guess it is quite obvious that me writing on the blog of the Institute for Quantum Information and Matter (IQIM) about this book titled “Quantum Information meets Quantum Matter” (QIQM) is not a simple coincidence. The romance story between the two emerged in the past decade or so and has been growing at a rate much beyond expectations. Our book is merely an attempt to record some aspects of the beginning. Let’s see where it will take us.