@article{15002,
  abstract     = {The lattice Schwinger model, the discrete version of QED in 
1
+
1
 dimensions, is a well-studied test bench for lattice gauge theories. Here, we study the fractal properties of this model. We reveal the self-similarity of the ground state, which allows us to develop a recurrent procedure for finding the ground-state wave functions and predicting ground-state energies. We present the results of recurrently calculating ground-state wave functions using the fractal Ansatz and automized software package for fractal image processing. In certain parameter regimes, just a few terms are enough for our recurrent procedure to predict ground-state energies close to the exact ones for several hundreds of sites. Our findings pave the way to understanding the complexity of calculating many-body wave functions in terms of their fractal properties as well as finding new links between condensed matter and high-energy lattice models.},
  author       = {Petrova, Elena and Tiunov, Egor S. and Bañuls, Mari Carmen and Fedorov, Aleksey K.},
  issn         = {1079-7114},
  journal      = {Physical Review Letters},
  number       = {5},
  publisher    = {American Physical Society},
  title        = {{Fractal states of the Schwinger model}},
  doi          = {10.1103/PhysRevLett.132.050401},
  volume       = {132},
  year         = {2024},
}

@article{13138,
  abstract     = {We consider the spin-
1
2
 Heisenberg chain (XXX model) weakly perturbed away from integrability by an isotropic next-to-nearest neighbor exchange interaction. Recently, it was conjectured that this model possesses an infinite tower of quasiconserved integrals of motion (charges) [D. Kurlov et al., Phys. Rev. B 105, 104302 (2022)]. In this work we first test this conjecture by investigating how the norm of the adiabatic gauge potential (AGP) scales with the system size, which is known to be a remarkably accurate measure of chaos. We find that for the perturbed XXX chain the behavior of the AGP norm corresponds to neither an integrable nor a chaotic regime, which supports the conjectured quasi-integrability of the model. We then prove the conjecture and explicitly construct the infinite set of quasiconserved charges. Our proof relies on the fact that the XXX chain perturbed by next-to-nearest exchange interaction can be viewed as a truncation of an integrable long-range deformation of the Heisenberg spin chain.},
  author       = {Orlov, Pavel and Tiutiakina, Anastasiia and Sharipov, Rustem and Petrova, Elena and Gritsev, Vladimir and Kurlov, Denis V.},
  issn         = {2469-9969},
  journal      = {Physical Review B},
  number       = {18},
  publisher    = {American Physical Society},
  title        = {{Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg chain}},
  doi          = {10.1103/PhysRevB.107.184312},
  volume       = {107},
  year         = {2023},
}