Variational studies of q-deformed Kogut-Susskind lattice gauge theory

We study the SU(2) level k Kogut-Susskind model, which is obtained from the original Kogut-Susskind SU(2) lattice gauge theory via a process that deforms the Lie algebra into a quantum group—in particular, the deformation truncates the local Hilbert space dimension to a finite value, thus making the model amenable to both classical and quantum simulation. This model is interesting from the perspective of quantum simulation of high-energy physics, but is also relevant to condensed matter physics, as it is essentially a perturbation of the Levin-Wen string net model.

Here, we use a mean-field inspired variational ansatz, which can also be interpreted as a tensor network state, that allows efficient analytical calculation of certain quantities. The variational method captures key properties of the ground state and low-lying excitations, including a transition between confined and deconfined (topologically ordered) phases. We also discuss simulation of real-time dynamics using the time-dependent variational principle (TDVP).