Publisher’s Pick: Quantum dimensions from local operator excitations in the Ising model

By Rebecca Gillan on April 19, 2017

We talk to Pawel Caputa and Marek Rams to find out what motivated their recent J.Phys.A paper on the time evolution of entanglement measures.

Who are you?

We are Dr. Pawel Caputa of the Yukawa Institute for Theoretical Physics in Kyoto, Japan and Dr. Marek Rams of the Jagiellonian University in Krakow, Poland.

Marek Rams

Pawel Caputa

What prompted you to pursue this field of research?

Both of us have been working on entanglement in many-body quantum systems but from completely different angles. Marek is an expert on numerical simulations of quantum lattice models and Pawel works on entanglement in conformal field theories (CFT) and AdS/CFT. Our areas of research meet in critical points where lattice models are described by conformal field theories. We met at a school on tensor networks in Ghent and discussed how much data about CFT can be extracted using numerical simulations of entanglement entropy or other quantum information tools. Over a great Belgian beer we came up with exciting questions that we both could work on using our own tools and compare the predictions at criticality.

What is this latest paper all about?

In our recent work we study how excitations by local operators change the entanglement between a given region (set of spins) and its complement. In CFT this question has a beautiful answer given by the logarithm of quantum dimension if we choose the operator to be a member of a given conformal family. We performed various simulations to test this predictions in the critical Ising model and found perfect agreement for the spin operator but also some surprising discrepancies for the energy operator.

Our results indicate that entanglement measures are not only useful to extract the central charge of the CFT that governs the critical point but, in locally excited states, other very non-trivial information like quantum dimensions or the elements of the modular S-matrix can be extracted numerically.

What do you plan to do next?

In this work we also managed to derive a very useful formula that allowed us for the first time to perform a real time evolution of the relative entropy between our locally excited states. We are now working on various extensions of this result and exploring the properties of relative entropy in other excited states of many body quantum systems at, and away from criticality.

Read more recent Journal of Physics A papers on the Ising model:

The random-bond Ising model in 2.01 and 3 dimensions

RG boundaries and interfaces in Ising field theory

The appropriateness of ignorance in the inverse kinetic Ising model

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