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This study introduces a new quantum Monte Carlo scheme to overcome general measurement challenges in many-body systems. The method successfully calculates observables as partition function ratios, expanding its applicability.

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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: 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.