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arXiv:2605.29871 · Physical review. B./Physical review. B

Enhanced Density Fluctuations Near a Disordered Chiral Topological Transition

Hai-Tao Ding, Sen Mu, Leong-Chuan Kwek, Gabriel Lemarié, Jiangbin Gong

cond-mat.dis-nnquant-phSubmitted May 28, 2026• Announced May 29, 2026• 0 citations
v1 · May 28, 2026v2 · Sep 20, 2026
arXivHTMLPDF

Abstract

The universal statistics of density fluctuations of localized quantum states may offer unprecedented opportunities to probe and understand quantum transport in connection with dimensionality, coherence, symmetry and disorder. To date, the possible role of topological phase transitions in the fluctuation statistics is not studied yet. Using a Su-Schrieffer-Heeger chain subject to off-diagonal disorder (so that chiral symmetry is preserved), this work investigates how a disorder driven topological phase transition impacts on the spatial fluctuations of the logarithmic wave-packet density $\ln P(r)$ at distance $r$ from the initial excitation. Away from the transition, in both topological and trivial localized phases, the standard deviation follows the conventional one-dimensional scaling $σ[\ln P(r)]\sim r^θ$ with $θ\simeq 1/2$. Near the transition, however, the fluctuation growth is enhanced: the fitted exponent $θ$ increases above $1/2$ in a nonmonotonic manner before returning close to $1/2$ at criticality. We interpret this behavior from the energy-resolved density of states and localization length. Near the transition, several energy sectors carry appreciable spectral weight and exhibit competitive decay rates, preventing a single localization scale from dominating the accessible wave-packet tail and thereby enhancing the fluctuations of $\ln P(r)$. Our results establish wave-packet fluctuation statistics as a dynamical diagnostic of disordered chiral topological transitions and motivate broader studies of fluctuation phenomena in disordered topological quantum systems.

Journal reference
Phys. Rev. B 114, 134204 (2026)
DOI
10.1103/4tk8-ngrg

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The universal statistics of density fluctuations of localized quantum states may offer unprecedented opportunities to probe and understand quantum transport in connection with dimensionality, coherence, symmetry and disorder. To date, the possible role of topological phase transitions in the fluctuation statistics is not studied yet. Using a Su-Schrieffer-Heeger chain subject to off-diagonal disorder (so that chiral symmetry is preserved), this work investigates how a disorder driven topological phase transition impacts on the spatial fluctuations of the logarithmic wave-packet density ln⁡P(r)\ln P(r)lnP(r) at distance rrr from the initial excitation. Away from the transition, in both topological and trivial localized phases, the standard deviation follows the conventional one-dimensional scaling σ[ln⁡P(r)]∼rθσ[\ln P(r)]\sim r^θσ[lnP(r)]∼rθ with θ≃1/2θ\simeq 1/2θ≃1/2. Near the transition, however, the fluctuation growth is enhanced: the fitted exponent θθθ increases above 1/21/21/2 in a nonmonotonic manner before returning close to 1/21/21/2 at criticality. We interpret this behavior from the energy-resolved density of states and localization length. Near the transition, several energy sectors carry appreciable spectral weight and exhibit competitive decay rates, preventing a single localization scale from dominating the accessible wave-packet tail and thereby enhancing the fluctuations of ln⁡P(r)\ln P(r)lnP(r). Our results establish wave-packet fluctuation statistics as a dynamical diagnostic of disordered chiral topological transitions and motivate broader studies of fluctuation phenomena in disordered topological quantum systems.
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Abstract The dynamics of quantum phase transitions of topological systems has attracted interest. Here we consider the effect of long-range hopping terms on the dynamic behavior. The long-range hoppings preserve chiral symmetry and decay as a function of distance, with an exponent β. We also consider a situation where the hoppings are modulated by oscillations. We compare the results with those obtained for short-range models such as the Su–Schrieffer–Heeger model or its extension to second neighboring cells. While often the lowest critical times coincide with the first peak of the Loschmidt rate, several anomalous cases are identified. Also, the number of critical times often exceeds the absolute value of the change of the winding number in a quench. Various correlation functions are considered, and their time-dependence may often be used to identify the early-time dynamical phase transitions.
In clean and weakly disordered systems, topological and trivial phases having a finite bulk energy gap can transit to each other via a quantum critical point. In presence of strong disorder, both the nature of the phases and the associated criticality can fundamentally change. Here we investigate topological properties of a strongly disordered fermionic chain where the bond couplings are drawn from normal probability distributions which are defined by characteristic standard deviations. Using numerical strong disorder renormalization group methods along with analytical techniques, we show that the competition between fluctuation scales renders both the trivial and topological phases gapless with Griffiths like rare regions. Moreover, the transition between these phases is solely governed by the fluctuation scales, rather than the means, rendering the critical behavior to be determined by an infinite randomness fixed point with an irrational central charge. Our work points to a host of novel topological phases and atypical topological phase transitions which can be realized in systems under strong disorder.
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The question of whether the topological insulators can host a stable nontrivial phase in the presence of spatially correlated disorder is a fundamental question of interest. Based on theoretical investigations, we analyze the effect of random-dimer disorder on the quantum phase transitions of the Su-Schrieffer-Heeger model. We explicitly demonstrate that, due to the absence of symmetry, there are no in-gap edge states in certain disordered topological nontrivial gapped phases and the bulk-boundary correspondence breaks down. However, the fractionalized end charges still appear at the ends of the chain. The energy distribution possibility of the in-gap edge states and the possible values of fractionalized end charges are dependent on the concentration of random-dimer disorder. On the other hand, random-dimer disorder and dimer hopping intertwine in an interesting manner. Reentrant localization transition behavior appears, which is evidenced by the fingerprint of the inverse participation ratio, normalized participation ratio, and tunneling conductivity.