arXiv subjects

Hai-Tao Hu

Publications and source records attributed to Hai-Tao Hu.

3 recordsLinked to original sources

arXiv2025

Divergent density of states and non-analytic Lyapunov exponent in one-dimensional slowly varying systems

Localization of wave functions in disordered systems can be characterized by the Lyapunov exponent, which is zero in the extended phase and nonzero in the localized phase. Previous studies have shown that this exponent is an analytic function of eigenenergy in a given phase, thus its non-analytic behavior has been commonly used to determine the boundaries between the extended and localized phases. In this work, we show that if the localization centers are inhomogeneous across the whole chain and the system possesses (at least) two different localization modes, the Lyapunov exponent can become non-analytic in the localized phase at the boundaries between the different localization modes. We establish this central result by using several one-dimensional slowly varying models, and reveal that the non-analytic feature in the Lyapunov exponent is inherently tied to the singularities in the density of states through the Thouless formula. The possible existence of delicate structures in the localized phase effectively broadens our understanding of Anderson localization.

cond-mat.dis-nn↗

arXiv2025

Exact mobility edges in quasiperiodic network models with slowly varying potentials

Quasiperiodic models are important physical platforms to explore Anderson transitions in low dimensional systems, yet the exact mobility edges (MEs) are generally hard to be determined analytically. To date, the MEs in only a few models can be determined exactly. In this manuscript, we propose a new class of network models characterized by quasiperiodic slowly varying potentials and the absence of hidden self-duality, and exactly determine their MEs. We take the mosaic models with slowly varying potentials as examples to illustrate this result and derive its MEs from the effective Hamiltonian. In this method, we can integrate out the periodic sites to obtain an effective Hamiltonian with energy-dependent potentials $g(E)V$ and effective eigenenergy $f(E)$, which directly yields the MEs at $f(E) = \pm(2t^κ\pm g(E)V)$, where $κ\in \mathbb{Z}^+$. With this idea in hand, we then generalize our method to more quasiperiodic network models, including those with much more complicated geometries and non-Hermitian features. Finally, we propose the realization of these models using optical waveguides and show that the Anderson transition can be observed even in small physical systems (with lattice sites about $L = 50 - 100$). Our results provide some key insights into the understanding and realization of exact MEs in experiments.

cond-mat.dis-nn↗

arXiv2025

Hidden self-duality and exact mobility edges in quasiperiodic network models

In one-dimensional quasiperiodic systems, only a few models with exact mobility edges (MEs) have been constructed using generalized self-duality theory, Avila's global theory, or the renormalization group method. This raises an intriguing question that whether we can realize more physical models with exact solvable MEs. In this work, we uncover the hidden self-duality within a class of quasiperiodic network models constituted by periodic and quasiperiodic sites. Although the original Hamiltonians appear to lack self-duality, their effective Hamiltonians obtained by integrating out the periodic sites exhibit self-duality, which yield MEs. The well-studied mosaic model, which is the simplest case of quasiperiodic network models, was previously thought to exhibit MEs due to the absence of self-duality, but we show that they actually arise from the hidden self-duality. Using the effective Hamiltonian, we further introduce the concept of resonant states to understand the shape of MEs. Finally, we present in detail how to determine the MEs in various network models, including some non-Hermitian models, based on the hidden self-duality. These predictions can be experimentally realized using optical and acoustic waveguide arrays. Our work can greatly advance our understanding of MEs in Anderson transition.

cond-mat.dis-nn↗