Generalized Reduced-Density-Matrix Quantum Monte Carlo Gives Access to More

For a long time, people have been focusing on how to extract more information, such as off-diagonal observables, from the quantum Monte Carlo (QMC) simulation of the partition function, but there have been numerous difficulties, and many of them are insurmountable. In this article, we point out that all the difficulties stem from the starting point of the simulation: calculating a partition function. We introduce a paradigm shift: when we transform the simulated object from a partition function to a generalized reduced density matrix (GRDM), the difficult problem of measurement can be readily solved. By designing the GRDM, both equal-time and nonequal-time off-diagonal observables have been measured easily in QMC with a polynomial computation complexity. As a demonstration, the GRDM enables direct access to nonequal-time correlators for dynamical spectra as well as R\'enyi-1 correlators that reveal strong-to-weak symmetry breaking in the mixed state, capabilities that lie beyond the reach of prior methods. This establishes a unified framework for holographic characterization within QMC.