Decorated two-dimensional lattices are shown to reduce, via isospectral reduction, to energy-dependent Haldane models with latent mass terms, enabling analytic topological phase diagrams.
Isospectral Reductions of Non-negative Matrices
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abstract
Isospectral reduction is an important tool for network/matrix analysis as it reduces the dimension of a matrix/network while preserving its eigenvalues and eigenvectors. The main contribution of this manuscript is a proposed algorithmic scheme to approximate the stationary measure of a stochastic matrix based on isospectral reductions. We run numerical experiments that indicate this scheme is advantageous when there is more than one eigenvalue near 1, precisely the case where iterative methods perform poorly. We give a partial explanation why this scheme should work well, showing that in some situations isospectral reduction improves the spectral gap.
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Latent Haldane Models
Decorated two-dimensional lattices are shown to reduce, via isospectral reduction, to energy-dependent Haldane models with latent mass terms, enabling analytic topological phase diagrams.