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Quantum state complexity meets many-body scars.

Sourav Nandy1, Bhaskar Mukherjee2, Arpan Bhattacharyya3

  • 1Jožef Stefan Institute, SI-1000 Ljubljana, Slovenia.

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Summary
This summary is machine-generated.

This study investigates scar eigenstates in many-body systems, specifically in a 1D PXP model. Researchers found that using the forward scattering approximation is crucial for accurately measuring spread complexity in these systems.

Keywords:
Krylov complexityLanczos algorithmRydberg atomsquantum complexityquantum dynamicsquantum many-body scars

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Atomic physics

Background:

  • Scar eigenstates are rare non-thermal states within a thermal spectrum.
  • Observed in experiments with Rydberg atom chains simulating a 1D PXP model.
  • These states exhibit novel non-thermal behavior.

Purpose of the Study:

  • To probe scar eigenstates by calculating spread complexity.
  • To understand the role of approximate Lie algebra symmetry in these systems.
  • To determine the optimal method for analyzing scar state dynamics.

Main Methods:

  • Simulating a 1D PXP model using Rydberg atoms.
  • Computing spread complexity via time evolution of specific initial states (|Z2⟩, |Z3⟩, vacuum).
  • Applying the forward scattering approximation (FSA) to extract Lanczos coefficients.

Main Results:

  • The scar subspace in the PXP model forms a weakly broken Lie algebra representation.
  • The forward scattering approximation (FSA) is uniquely suited for extracting relevant Lanczos coefficients due to this symmetry.
  • This method enables a well-defined Krylov subspace and spread complexity calculation.
  • Analysis across three distinct initial states reveals different scar state behaviors.

Conclusions:

  • Accurate analysis of scar eigenstates and their dynamics necessitates the forward scattering approximation (FSA).
  • The approximate symmetry of the scar subspace dictates the choice of analytical method.
  • Systematic improvements to FSA are possible to address imperfections arising from approximate symmetries.