Quasi-one-dimensional spin-Peierls and spin-ladder systems are characterized by a gap in the spin-excitation spectrum, which can be modeled at low energies by that of Dirac fermions with a mass. In the presence of disorder, these systems can still be described by a Dirac fermion model, but with a random mass. Some peculiar properties, like the Dyson singularity in the density of states, are well known and attributed to creation of low-energy states due to the disorder. We take one step further and study single-particle correlations by means of Berezinskii's diagram technique. We find that, at low energy $\ensuremath{\epsilon}$, the single-particle Green function decays in real space like $G(x,\ensuremath{\epsilon})\ensuremath{\propto}{(1/x)}^{3/2}$. It follows that at these energies the correlations in the disordered system are strong --- even stronger than in the pure system without the gap. At distances $x\ensuremath{\sim}{L}_{\ensuremath{\epsilon}}\ensuremath{\propto}{\mathrm{ln}}^{2}(1/\ensuremath{\epsilon})$, the Green function crosses over to a standard exponential decay. The scale ${L}_{\ensuremath{\epsilon}}$ is different from the Thouless localization length ${\ensuremath{\lambda}}_{\ensuremath{\epsilon}}\ensuremath{\propto}\mathrm{ln}(1/\ensuremath{\epsilon})$. Additionally, we study the effects of boundaries on the local density of states. We find that the latter is logarithmically (in the energy) enhanced close to the boundary. This enhancement decays into the bulk as $1/\sqrt{x}$ saturating at $x\ensuremath{\sim}{L}_{\ensuremath{\epsilon}}.$ We also discuss some implications of these results for the spin systems and their relation to the investigations based on the real-space renormalization group approach.Quasi-one-dimensional spin-Peierls and spin-ladder systems are characterized by a gap in the spin-excitation spectrum, which can be modeled at low energies by that of Dirac fermions with a mass. In the presence of disorder, these systems can still be described by a Dirac fermion model, but with a random mass. Some peculiar properties, like the Dyson singularity in the density of states, are well known and attributed to creation of low-energy states due to the disorder. We take one step further and study single-particle correlations by means of Berezinskii's diagram technique. We find that, at low energy $\ensuremath{\epsilon}$, the single-particle Green function decays in real space like $G(x,\ensuremath{\epsilon})\ensuremath{\propto}{(1/x)}^{3/2}$. It follows that at these energies the correlations in the disordered system are strong --- even stronger than in the pure system without the gap. At distances $x\ensuremath{\sim}{L}_{\ensuremath{\epsilon}}\ensuremath{\propto}{\mathrm{ln}}^{2}(1/\ensuremath{\epsilon})$, the Green function crosses over to a standard exponential decay. The scale ${L}_{\ensuremath{\epsilon}}$ is different from the Thouless localization length ${\ensuremath{\lambda}}_{\ensuremath{\epsilon}}\ensuremath{\propto}\mathrm{ln}(1/\ensuremath{\epsilon})$. Additionally, we study the effects of boundaries on the local density of states. We find that the latter is logarithmically (in the energy) enhanced close to the boundary. This enhancement decays into the bulk as $1/\sqrt{x}$ saturating at $x\ensuremath{\sim}{L}_{\ensuremath{\epsilon}}.$ We also discuss some implications of these results for the spin systems and their relation to the investigations based on the real-space renormalization group approach.

arXiv:cond-mat/9706096Physical review. B, Condensed matterApr 1, 199845 citations

Memory-assisted advantage for state transfer in disordered quantum many-body scar system

Paranjoy Chaki, Ujjwal Sen

We analyze how memory in disorder facilitates quantum communication in many-body scar systems. We consider three distinct types of disorder, viz., memoryful, and memoryless uniform and Gaussian, and compare their respective performances in facilitating quantum state transfer. Using the maximum transfer fidelity and fidelity area as figures of merit, we find that memoryful disorder yields a better performance than the memoryless disordered channels. Furthermore, the maximum transfer fidelity exhibits an initial parabolic decay with disorder strength, followed by a linear decrease, for all the disorder models considered. We introduce a degree of scarness, and show that it is higher for memoryful disorder in comparison to memoryless disorders, implying a role of scarness in the quantum state transfer protocol. We further perform a scaling analysis, revealing that memory effect in disorder is not only beneficial for short-distance but also long-distance quantum state transfer. Finally, we show that the state yielding the maximum transfer fidelity has larger inverse participation ratio for memoryful disorder in comparison to the other two disorders, highlighting the role of nonergodicity in enhancing state transfer.We analyze how memory in disorder facilitates quantum communication in many-body scar systems. We consider three distinct types of disorder, viz., memoryful, and memoryless uniform and Gaussian, and compare their respective performances in facilitating quantum state transfer. Using the maximum transfer fidelity and fidelity area as figures of merit, we find that memoryful disorder yields a better performance than the memoryless disordered channels. Furthermore, the maximum transfer fidelity exhibits an initial parabolic decay with disorder strength, followed by a linear decrease, for all the disorder models considered. We introduce a degree of scarness, and show that it is higher for memoryful disorder in comparison to memoryless disorders, implying a role of scarness in the quantum state transfer protocol. We further perform a scaling analysis, revealing that memory effect in disorder is not only beneficial for short-distance but also long-distance quantum state transfer. Finally, we show that the state yielding the maximum transfer fidelity has larger inverse participation ratio for memoryful disorder in comparison to the other two disorders, highlighting the role of nonergodicity in enhancing state transfer.

quant-pharXiv:2606.18720Jun 18, 20260 citations

1/\sqrt{x}

saturating at $x\ensuremath{\sim}{L}_{\ensuremath{\epsilon}}.$ We also discuss some implications of these results for the spin systems and their relation to the investigations based on the real-space renormalization group approach.