Critical Dynamics in Short-Range Quadratic Hamiltonians

• URL: http://arxiv.org/abs/2503.02828v1
• Date: Tue, 04 Mar 2025 17:51:40 GMT
• Title: Critical Dynamics in Short-Range Quadratic Hamiltonians
• Authors: Miroslav Hopjan, Lev Vidmar,
• Abstract summary: We consider critical dynamics that emerges when the Thouless time, i.e., the saturation time of the mean-squared displacement, approaches the typical Heisenberg time.<n>We establish a relation, $z=d_l/d_s$, linking the critical dynamical exponent $z$ to $d_l$ and to the spectral fractal dimension $d_s$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate critical transport and the dynamical exponent through the spreading of an initially localized particle in quadratic Hamiltonians with short-range hopping in lattice dimension $d_l$. We consider critical dynamics that emerges when the Thouless time, i.e., the saturation time of the mean-squared displacement, approaches the typical Heisenberg time. We establish a relation, $z=d_l/d_s$, linking the critical dynamical exponent $z$ to $d_l$ and to the spectral fractal dimension $d_s$. This result has notable implications: it says that superdiffusive transport in $d_l\geq 2$ and diffusive transport in $d_l\geq 3$ cannot be critical in the sense defined above. Our findings clarify previous results on disordered and quasiperiodic models and, through Fibonacci potential models in two and three dimensions, provide non-trivial examples of critical dynamics in systems with $d_l\neq1$ and $d_s\neq1$.

Related papers

• Measurement-induced Lévy flights of quantum information [38.68022950138448]
  We explore a model of free fermions in one dimension subject to frustrated local measurements across adjacent sites.<n>For maximal misalignment, superdiffusive behavior emerges from the vanishing of the measurement-induced quasiparticle decay rate.<n>Our findings show how intricate fractal-scaling entanglement can be produced for local Hamiltonians.
  arXiv  Detail & Related papers  (2025-01-22T14:29:13Z)
• Superdiffusive transport in chaotic quantum systems with nodal interactions [1.7934794154114089]
  We introduce a class of interacting fermionic quantum models in $d$ dimensions with nodal interactions that exhibit superdiffusive transport. We establish non-perturbatively that the nodal structure of the interactions gives rise to long-lived quasiparticle excitations that result in a diverging diffusion constant.
  arXiv  Detail & Related papers  (2025-01-14T19:00:04Z)
• 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)
• Convergence of Kinetic Langevin Monte Carlo on Lie groups [21.76159063788814]
  We propose a Lie-group MCMC sampler, by delicately discretizing the resulting kinetic-Langevin-type sampling dynamics. This is the first convergence result for kinetic Langevin on curved spaces, and also the first quantitative result that requires no convexity or, at least not explicitly, any common relaxation such as isoperimetry.
  arXiv  Detail & Related papers  (2024-03-18T17:50:20Z)
• Family-Vicsek dynamical scaling and Kardar-Parisi-Zhang-like superdiffusive growth of surface roughness in a driven one-dimensional quasiperiodic model [0.0]
  We investigate the out-of-equilibrium dynamics of spinless fermions in a one-dimensional quasiperiodic model with and without a periodic driving. In absence of periodic driving, the model is interestingly shown to host a subdiffusive critical phase. We construct an effective Floquet Hamiltonian, which qualitatively captures this feature occurring in the driven model.
  arXiv  Detail & Related papers  (2023-07-07T19:30:05Z)
• Spatiotemporal Quenches in Long-Range Hamiltonians [0.0]
  We study the fate of Stemporal quenches in models with a fixed velocity $v$ for the propagation of the quench front. We show that optimal cooling is achieved when the front velocity $v$ approaches $c$, the effective speed of excitations in the critical model.
  arXiv  Detail & Related papers  (2022-12-14T20:40:24Z)
• Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping [45.873301228345696]
  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.
  arXiv  Detail & Related papers  (2022-05-29T16:53:20Z)
• Observation of Emergent $\mathbb{Z}_2$ Gauge Invariance in a Superconducting Circuit [14.413924121049094]
  We investigate the emergent $mathbbZ$ gauge invariance in a superconducting circuit with 10 transmon qubits. Despite the absence of gauge structure in the effective Hamiltonian, $mathbbZ$ gauge can still emerge in low-energy regimes.
  arXiv  Detail & Related papers  (2021-11-09T11:02:40Z)
• Universality class of Ising critical states with long-range losses [0.0]
  We show that spatial resolved dissipation can act on $d$-dimensional spin systems in the Ising universality class. We consider power-law decaying spin losses with a Lindbladian spectrum closing at small momenta as $propto qalpha$.
  arXiv  Detail & Related papers  (2021-08-27T17:59:51Z)
• Critical properties of the prethermal Floquet Time Crystal [0.0]
  We investigate the critical properties characterizing the formation of the Floquet time crystal in the prethermal phase. In particular, we focus on the critical line separating the trivial phase with period synchronized dynamics and absence of long-range spatial order. The functional form of the aging is found to depend on whether the system is probed at times that are small or large compared to the drive period.
  arXiv  Detail & Related papers  (2021-03-19T14:06:36Z)
• Continuous-time quantum walks in the presence of a quadratic perturbation [55.41644538483948]
  We address the properties of continuous-time quantum walks with Hamiltonians of the form $mathcalH= L + lambda L2$. We consider cycle, complete, and star graphs because paradigmatic models with low/high connectivity and/or symmetry.
  arXiv  Detail & Related papers  (2020-05-13T14:53:36Z)

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.