Extensibility of Hohenberg–Kohn Theorem to General Quantum Systems

The Hohenberg–Kohn (HK) theorem for interacting electrons is a cornerstone of modern electronic structure calculations. For general quantum system, HK-type Hamiltonian in the form H ̂ hk { g i } = int + ∑ O $\hat {H}_{\rm hk}\lbrace g_i\rbrace =\hat int}+\sum_i g_i \hat O_i$ can always be defined, by grouping those terms with fixed or preknown coefficients into an internal part int}$ , and factorizing remaining as superposition set Hermitian operators $\lbrace\hat {O}_i\rbrace$ . It asked whether HK extended to such setting, so that ground-state expectation values generalized density principle used fundamental variables determining all properties system. shown question addressed invertibility correlation matrix (GDCM) defined respect operators. This criterion applied several representative examples, including Ising dimer, frustration-free systems, N-level systems fermionic Hubbard chain. suggested finite-size finding invertible GDCM under one single $\lbrace g_i\rbrace$ configuration typically sufficient establish generic extensibility entire parameter space.