Addressing general measurements in quantum Monte Carlo.

Area of Science:

• Quantum physics
• Computational physics
• Statistical mechanics

Background:

• Quantum Monte Carlo (QMC) is vital for large quantum many-body systems and strongly correlated physics.
• However, QMC is limited by the sign problem and general measurement issues.
• Existing methods struggle with calculating overlaps between different distribution functions.

Purpose of the Study:

• To propose a universal scheme for addressing general measurement problems in quantum many-body systems.
• To enable the calculation of target observables as ratios of partition functions.
• To expand the applicability of quantum Monte Carlo methods.

Main Methods:

• Express observables as ratios of two partition functions: $\overline{Z}/Z$.
• Estimate partition functions separately using a reweight-annealing framework.
• Connect the partition functions via a solvable reference point.

Main Results:

• Successfully applied the scheme to XXZ and transverse field Ising models (1D to 2D).
• Demonstrated applicability to various correlations (two-body, multi-body, non-local disorder) and time correlations (equal-time, imaginary-time).
• Showcased reweighting flexibility across physical parameters, space, and time.

Conclusions:

• The proposed scheme effectively solves the problem of calculating overlaps between different distribution functions.
• This universal approach has broad implications for quantum many-body computation, big data, and machine learning.
• The method overcomes limitations in applying quantum Monte Carlo to complex systems.