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Updated: Oct 6, 2025

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
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A multisite decomposition of the tensor network path integrals.

Amartya Bose1, Peter L Walters2

  • 1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.

The Journal of Chemical Physics
|January 16, 2022
PubMed
Summary
This summary is machine-generated.

We developed a new tensor network method to efficiently simulate large open quantum systems. This approach overcomes exponential scaling issues, enabling the study of complex quantum dynamics in extended systems coupled to environments.

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Area of Science:

  • Quantum Physics
  • Computational Physics
  • Condensed Matter Physics

Background:

  • Tensor network methods are powerful for simulating quantum systems.
  • Simulating open quantum systems, especially extended ones with environments, faces computational challenges due to exponential scaling.
  • Existing methods struggle with non-equilibrium dynamics of large, coupled quantum systems.

Purpose of the Study:

  • To extend the tensor network path integral (TNPI) framework for efficient simulation of extended open quantum systems.
  • To develop a method that overcomes the exponential scaling limitations of current approaches.
  • To enable the study of non-equilibrium dynamics in complex quantum systems coupled to local dissipative environments.

Main Methods:

  • Developed a multisite tensor network path integral (MS-TNPI) framework.
  • Combined matrix product state (MPS) decomposition with a tensor network representation of the time axis to create a 2D tensor network.
  • Incorporated the Feynman-Vernon influence functional to account for environmental effects.
  • Outlined an iterative scheme to simulate beyond non-Markovian memory effects.

Main Results:

  • The 2D MS-TNPI network efficiently yields the time-dependent reduced density tensor as an MPS.
  • The algorithm is independent of the specific system Hamiltonian.
  • Simulations of spin chains (Ising, XXZ, Heisenberg models) coupled to local harmonic baths demonstrated entanglement dissipation due to local environments.
  • Identified factors driving transitions from coherent to incoherent dynamics.

Conclusions:

  • The MS-TNPI method provides an efficient and versatile tool for simulating extended open quantum systems.
  • This framework is applicable to a wide range of quantum systems interacting with solvents or local baths.
  • The method facilitates the investigation of entanglement dynamics and coherence-incoherence transitions in complex quantum environments.