In the limit of small (g_{2}) and t values, the dominant presence of the on-site interactions stabilize the system into a MI phase with exactly one polariton per cavity ((bar{n} = 1)), and where the charge energy gap has a finite value.
They said the learning process could have been more dynamic by including various activities such as on-site interactions.
'Looking back on the entire experiment, I felt as though I was only looking at my mobile phone throughout the process, without any on-site interactions.' (Participant 3).
As such, in the future, we will revise our design of the learning tasks to facilitate on-site interactions, such as posting guiding questions on the forum beforehand.
The 'impurity' itself consists of a single lattice site taken from the original problem, and so inherits on-site interactions from the Hubbard model.
In this paper, we propose a 1D array of coupled nanomechanical resonators for simulating the Anderson Hamiltonian, namely, a discrete tight-binding model without on-site interactions.
Try not to display too much information.' (Participant 4) 'Looking back on the entire experiment, I felt as though I was only looking at my mobile phone throughout the process, without any on-site interactions.' (Participant 3).
Moreover, given the ability to control individual resonator excitations by scanning the transmon frequency, it is possible to extend the present investigation to the situation including on-site interactions.
When several realizations are taken into account the effective Hamiltonian averages out to (4) plus on-site interactions on all sites, in a similar way to the Bose-Hubbard model, allowing investigation of the allowed phases and respective quantum phase transitions when the parameters are varied [61, 62].
Typically, these models incorporated only on-site interactions (i.e. the interaction range for competing species is taken to be infinitesimally small).
This has been particularly true in attempts to observe quantum magnetism in optical lattices within strongly interacting regimes, where U is the on-site interaction energy, and indicates the tunneling amplitude for particles moving between neighboring sites.
