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Regression relation for pure quantum states and its implications for efficient computing.

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Researchers developed a new method to compute quantum correlations in many-body systems. This approach significantly reduces computational memory, offering a more efficient way to study quantum dynamics and test physical hypotheses.

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Area of Science:

  • Quantum Mechanics
  • Statistical Physics
  • Computational Physics

Background:

  • Studying isolated many-body quantum systems is computationally intensive.
  • Calculating high-temperature time correlation functions often requires complete diagonalization of Hamiltonians.

Purpose of the Study:

  • To develop a more efficient method for computing time correlation functions in many-body quantum systems.
  • To reduce the computational memory requirements compared to traditional diagonalization methods.

Main Methods:

  • Derived a modified Onsager regression relation for quantum states.
  • Utilized direct integration of the Schrödinger equation for randomly sampled pure states.
  • Applied the method to translationally invariant Heisenberg chains.

Main Results:

  • Demonstrated a controllable computation of high-temperature time correlation functions without full diagonalization.
  • Achieved an exponential reduction in computer memory requirements.
  • Numerically computed infinite-temperature correlation functions for Heisenberg chains up to 29 spins 1/2.
  • Found results in satisfactory agreement with the spin diffusion hypothesis.

Conclusions:

  • The developed method provides an efficient alternative for studying quantum dynamics in many-body systems.
  • The approach is applicable to quantum quenches and time-dependent Hamiltonians.
  • The findings are grounded in the principle of quantum typicality.