- "where $\\sigma_{m}^{+}$ ($\\sigma_{m}^{-}$) are the raising (lowering) operators, and the single term describes the kinetic energy related to hopping from one site to the other. This [quirk circuit](https://algassert.com/quirk#circuit={%22cols%22:[[1,1,%22X%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22]],%22gates%22:[{%22id%22:%22~qcjg%22,%22name%22:%22sqrtISWAP%22,%22matrix%22:%22{{1,0,0,0},{0,%E2%88%9A%C2%BD,%E2%88%9A%C2%BDi,0},{0,%E2%88%9A%C2%BDi,%E2%88%9A%C2%BD,0},{0,0,0,1}}%22}]}) shows the evolution of the charge density.\n",
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