Relativistic matrix product states and an application to the Sinh-Gordon model

April 26, 2023
11:00am to 12:30pm

Grey Room 3

Specialist level
Antoine Tilloy
Mines ParisTech

Grey Room 3


I will present a variational method, relativistic matrix product states (RCMPS), and its application to a not-so-simple low dimensional field theory, the Sinh-Gordon model. Relativistic quantum field theories are difficult to solve with lattice tensor network methods near the continuum limit, because relativistic invariance implies criticality in the UV. This translates into a divergent entanglement entropy as the lattice spacing is sent to zero. One way to bypass this issue is to resort to finite entanglement scaling as for IR critical theories. Another option is to work in a basis in which this UV behavior is tamed, and entanglement entropy is finite. This is precisely what RCMPS achieves in 1+1 dimensions, combining insights from tensor networks and Hamiltonian truncation (HT). I will present the ansatz and explain how it is used, optimised, and how (some) physical observables can be extracted from it. I will then apply it to the Sinh-Gordon model in the strong coupling regime, where the methods comforts recently proposed scenarios and HT simulations. However, dragons still lie beyond the self-dual point, and improvements of the method are still needed.