2006/05/08 by Tobias J. Osborne, Osborne, Tobias J. · 1 citation
Physics and Astronomy · #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum Physics (quant-ph) #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.cond-mat/0605194
openalex publication_date 2006/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a certifiable algorithm to calculate the eigenvalue density\nfunction -- the number of eigenvalues within an infinitesimal interval -- for\nan arbitrary 1D interacting quantum spin system. Our method provides an\narbitrarily accurate numerical representation for the smeared eigenvalue\ndensity function, which is the convolution of the eigenvalue density function\nwith a gaussian of prespecified width. In addition, with our algorithm it is\npossible to investigate the density of states near the ground state. This can\nbe used to numerically determine the size of the ground-state energy gap for\nthe system to within a prespecified confidence interval. Our method exploits a\nfinitely correlated state/matrix product state representation of the propagator\nand applies equally to disordered and critical interacting 1D quantum spin\nsystems. We illustrate our method by calculating an approximation to the\neigenvalue density function for a random antiferromagnetic Heisenberg model.\n