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The concept of the inertia tensor is employed to depict the mass distribution and rotational inertia of a solid or rigid object. This tensor is expressed through a three-by-three matrix. Each component within this matrix corresponds to varying moments of inertia about specific axes.
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Fermionic Isometric Tensor Network States in Two Dimensions.

Zhehao Dai1,2, Yantao Wu1,3, Taige Wang1,4

  • 1University of California, Berkeley, Department of Physics, California 94720, USA.

Physical Review Letters
|February 6, 2025
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Summary
This summary is machine-generated.

We generalized isometric tensor network states for fermionic systems, enabling 1D tensor network algorithms for 2D systems. This new method accurately calculates ground-state energies and simulates fermion dynamics, including edge phenomena.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Information Theory

Background:

  • Tensor network states are powerful tools for simulating quantum many-body systems.
  • Generalizing these methods to fermionic systems is crucial for studying realistic materials.

Purpose of the Study:

  • To generalize isometric tensor network states to fermionic systems.
  • To develop and benchmark a time-evolving block-decimation (TEBD) algorithm for 2D fermionic systems.

Main Methods:

  • Generalization of isometric tensor network states to accommodate fermionic anti-commutation relations.
  • Implementation and benchmarking of a TEBD algorithm for both real-time and imaginary-time evolution.

Main Results:

  • Accurate ground-state energies for gapped, Dirac point, and gapless edge mode systems using imaginary-time evolution.
  • Successful simulation of two-fermion scattering and chiral edge dynamics in Chern insulators via real-time TEBD.

Conclusions:

  • The generalized formalism provides an efficient pathway for applying 1D tensor network techniques to 2D fermionic problems.
  • The developed TEBD algorithm is a valuable tool for investigating dynamics and ground states in fermionic quantum systems.