Conjectured favorable temperature scaling of QTT representations

Establish the validity and quantitative form of the conjectured very favorable scaling with temperature of the quantics tensor train (QTT) representation for quantum many-body correlation functions by determining how the required maximum bond dimension and computational cost depend on inverse temperature β across representative cases (e.g., local imaginary-time propagators and two-particle vertices).

Background

The computational efficiency of QTT-based methods depends critically on how the required bond dimension scales with system parameters, notably temperature. Demonstrating that the QTT representation remains compact as β increases would justify broad applicability of QTT in low-temperature many-body calculations.

The paper provides empirical evidence of saturation or slow growth of bond dimension with β for the Hubbard atom and notes prior work suggesting compactness at low temperatures, but a general, rigorous characterization remains outstanding.