Minimizing the trace of S^{-1}H over non-orthogonal variational states simultaneously finds several low-lying eigenstates, demonstrated with matrix product states, quantics tensor trains, and quantum circuits.
Wölfle, Quasiparticles in condensed matter systems, Reports on Progress in Physics81, 032501 (2018)
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A Unified Variational Framework for Quantum Excited States
Minimizing the trace of S^{-1}H over non-orthogonal variational states simultaneously finds several low-lying eigenstates, demonstrated with matrix product states, quantics tensor trains, and quantum circuits.