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Memory-Efficient Nonequilibrium Green's Function Framework Built On Quantics Tensor Trains.

Maksymilian Środa1, Ken Inayoshi2, Hiroshi Shinaoka2

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Summary
This summary is machine-generated.

Diagrammatic simulations for nonequilibrium phenomena are memory-intensive. The quantics tensor train (QTT) representation overcomes this, enabling efficient simulations of lattice models and complex dynamics.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Computational Physics

Background:

  • Diagrammatic simulations of nonequilibrium phenomena in lattice models face significant memory challenges due to large momentum-dependent two-time correlation functions.
  • Existing methods struggle with the computational demands for simulating long-time dynamics and high momentum resolution.

Purpose of the Study:

  • To overcome memory limitations in diagrammatic simulations of nonequilibrium phenomena.
  • To demonstrate the efficacy of the quantics tensor train (QTT) representation for these simulations.
  • To enable the study of long-time dynamics, including transient Floquet physics and thermalization.

Main Methods:

  • Utilized the quantics tensor train (QTT) representation to compress multivariable functions, specifically momentum-dependent two-time correlation functions.
  • Implemented nonequilibrium Green's function simulations within the GW and Migdal approximations using QTT-compressed functions.
  • Employed a fully self-contained, self-consistent calculation on the three-leg Kadanoff-Baym contour, incorporating QTT-generated or QTT-interpolated input functions.

Main Results:

  • Successfully demonstrated high-momentum-resolution nonequilibrium Green's function simulations exceeding the capabilities of standard implementations.
  • Achieved simulations of sufficient duration to study transient Floquet physics and thermalization dynamics.
  • Showcased the QTT representation's ability to significantly reduce memory requirements for complex quantum simulations.

Conclusions:

  • The quantics tensor train (QTT) representation provides an effective solution to the memory bottleneck in diagrammatic simulations of nonequilibrium phenomena.
  • This approach enables advanced studies of quantum dynamics in lattice models, previously computationally intractable.
  • The QTT-based method opens new avenues for exploring complex phenomena like Floquet physics and thermalization with high fidelity.