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.
Rommer,Thermodynamiclimitofden- sity matrix renormalization, Physical Review Letters75, 3537 (1995)
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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.