Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping

• URL: http://arxiv.org/abs/2205.14715v4
• Date: Wed, 8 May 2024 17:02:04 GMT
• Title: Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping
• Authors: Xiaolong Deng, Ivan M. Khaymovich, Alexander L. Burin,
• Abstract summary: localization problem in the crossover regime for the dimension $d=2$ and hopping $V(r) propto r-2$ is not resolved yet. We show that for the hopping determined by two-dimensional anisotropic dipole-dipole interactions there exist two distinguishable phases at weak and strong disorder.
• Score: 45.873301228345696
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Although it is recognized that Anderson localization takes place for all states at a dimension $d$ less or equal $2$, while delocalization is expected for hopping $V(r)$ decreasing with the distance slower or as $r^{-d}$, the localization problem in the crossover regime for the dimension $d=2$ and hopping $V(r) \propto r^{-2}$ is not resolved yet. Following earlier suggestions we show that for the hopping determined by two-dimensional anisotropic dipole-dipole interactions in the presence of time-reversal symmetry there exist two distinguishable phases at weak and strong disorder. The first phase is characterized by ergodic dynamics and superdiffusive transport, while the second phase is characterized by diffusive transport and delocalized eigenstates with fractal dimension less than $2$. The transition between phases is resolved analytically using the extension of scaling theory of localization and verified numerically using an exact numerical diagonalization.

Related papers

• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Tunable quantum criticality and pseudocriticality across the fixed-point annihilation in the anisotropic spin-boson model [0.26107298043931204]
  We study the nontrivial renormalization-group scenario of fixed-point annihilation in spin-boson models. We find a tunable transition between two localized phases that can be continuous or strongly first-order. We also find scaling behavior at the symmetry-enhanced first-order transition, for which the inverse correlation-length exponent is given by the bath exponent.
  arXiv  Detail & Related papers  (2024-03-04T19:00:07Z)
• Measurement-induced phase transition for free fermions above one dimension [46.176861415532095]
  Theory of the measurement-induced entanglement phase transition for free-fermion models in $d>1$ dimensions is developed. Critical point separates a gapless phase with $elld-1 ln ell$ scaling of the second cumulant of the particle number and of the entanglement entropy.
  arXiv  Detail & Related papers  (2023-09-21T18:11:04Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• SYK meets non-Hermiticity II: measurement-induced phase transition [16.533265279392772]
  We analytically derive the effective action in the large-$N$ limit and show that an entanglement transition is caused by the symmetry breaking in the enlarged replica space. We also verify the large-$N$ critical exponents by numerically solving the Schwinger-Dyson equation.
  arXiv  Detail & Related papers  (2021-04-16T17:55:08Z)
• Discrete truncated Wigner approach to dynamical phase transitions in Ising models after a quantum quench [0.0]
  We study dynamical phase transitions arising in the steady state of transverse-field Ising models after a quantum quench. We find identical exponents for $alpha lesssim 0.5$, suggesting that the dynamical transitions in this regime fall into the same universality class as the nonergodic mean-field limit.
  arXiv  Detail & Related papers  (2020-04-21T08:20:15Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)
• Observing localisation in a 2D quasicrystalline optical lattice [52.77024349608834]
  We experimentally and numerically study the ground state of non- and weakly-interacting bosons in an eightfold symmetric optical lattice. We find extended states for weak lattices but observe a localisation transition at a lattice depth of $V_0.78(2),E_mathrmrec$ for the non-interacting system.
  arXiv  Detail & Related papers  (2020-01-29T15:54:42Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.