Quantum many-body Hamiltonians with two-body interactions can be represented by graphs, with sites as nodes and two-site couplings as edges. We investigate how the geometry of these graphs affects transport and entanglement growth. To do so, we study dynamics for quantum hopping on a random graph model with an effective range parameter. Tuning it, we interpolate between nearest-neighbor and all-to-all graphs, identifying a new localization regime that is robust in both single-particle and finite-density cases. This provides a model of Anderson localization induced by structural disorder, with implications for amorphous materials and tunable-range analog quantum simulators.
Quantum many-body Hamiltonians with two-body interactions can be represented by graphs, with sites as nodes and two-site couplings as edges. We investigate how the geometry of these graphs affects transport and entanglement growth. To do so, we study dynamics for quantum hopping on a random graph model with an effective range parameter. Tuning it, we interpolate between nearest-neighbor and all-to-all graphs, identifying a new localization regime that is robust in both single-particle and finite-density cases. This provides a model of Anderson localization induced by structural disorder, with implications for amorphous materials and tunable-range analog quantum simulators.
Motivated by recent advances in quantum technologies, we investigate entanglement spreading and excitation transport within quantum complex networks. For this purpose, we adopt a description in which network nodes represent sites of the physical system (e.g. qubits), and links represent pairs of sites coupled by the Hamiltonian [Bentsen et al., Phys Rev Lett (2019)]. We consider a random tunable-range model [Gori et al., Phys Rev E (2017)] which, in terms of only two parameters, encompasses a large variety of graphs and reduces, in limiting cases, to well-studied benchmarks. Then, it is equipped with a paradigmatic Hamiltonian consisting of hopping terms on the network links. Building on known results [Gori et al., Phys Rev E (2017)], we first study the classical case, providing new semi-analytical estimates. We then address quantum dynamics: For the single-particle case, we analyse the asymptotic entanglement entropy between two halves of the system, computed by Exact Diagonalization. Surprisingly, we observe a new localization region for intermediate ranges of the network links. To understand this phenomenon, we introduce an approximate one-dimensional model and try to relate dynamics to network measures. The analysis is extended to half-filling using fermionic Gaussian states, obtaining results close to the single-particle ones that raise new interesting questions for future work. It is concluded that this model exhibits non-trivial behaviour, especially in the region where unexpected localization occurs. We infer that this is determined by the interplay between network features and quantum effects, possibly induced by structural disorder.
We numerically investigate the dynamics of entanglement in a chain of spinless fermions with nonrandom but long-range hopping and interactions, and with random on-site energies. For moderate disorder in the absence of interactions, the chain hosts delocalized states at the top of the band which undergo a delocalization-localization transition with increasing disorder. We find an interesting regime in this noninteracting disordered chain where the long-time entanglement entropy scales as $S(t)\ensuremath{\sim}lnt$ and the saturated entanglement entropy scales with system size L as $S(L,t\ensuremath{\rightarrow}\ensuremath{\infty})\ensuremath{\sim}lnL$. We further study the interplay of long-range hopping and interactions on the growth of entanglement and the many-body localization (MBL) transition in this system. We develop an analogy to higher-dimensional short-range systems to compare and contrast such behavior with the physics of MBL in a higher dimension.
We investigate the stationary and dynamical behavior of an Anderson localized chain coupled to a single central bound state. Although this coupling partially dilutes the Anderson localized peaks towards nearly resonant sites, the most weight of the original peaks remains unchanged. This leads to multifractal wave functions with a frozen spectrum of fractal dimensions, which is characteristic for localized phases in models with power-law hopping. Using a perturbative approach we identify two different dynamical regimes. At weak couplings to the central site, the transport of particles and information is logarithmic in time, a feature usually attributed to many-body localization. We connect such transport to the persistence of the Poisson statistics of level spacings in parts of the spectrum. In contrast, at stronger couplings the level repulsion is established in the entire spectrum, the problem can be mapped to the Fano resonance, and the transport is ballistic.
Many-body localization in interacting quantum systems can be cast as a disordered hopping problem on the underlying Fock-space graph. A crucial feature of the effective Fock-space disorder is that the Fock-space site energies are strongly correlated-maximally so for sites separated by a finite distance on the graph. Motivated by this, and to understand the effect of such correlations more fundamentally, we study Anderson localization on Cayley trees and random regular graphs, with maximally correlated disorder. Since such correlations suppress short distance fluctuations in the disorder potential, one might naively suppose they disfavor localization. We find however that there exists an Anderson transition, and indeed that localization is more robust in the sense that the critical disorder scales with graph connectivity K as sqrt[K], in marked contrast to KlnK in the uncorrelated case. This scaling is argued to be intimately connected to the stability of many-body localization. Our analysis centers on an exact recursive formulation for the local propagators as well as a self-consistent mean-field theory; with results corroborated using exact diagonalization.
Understanding how complex entanglement structures emerge is a central problem in quantum many-body physics. Recent work by Zhang et al. [Phys. Rev. Lett. 137, 020404 (2026)] has considered structured initial states prepared by evolving a product state under a chaotic Hamiltonian for a finite time before quenching to the target Hamiltonian. In this setup, total entanglement entropy growth in many-body localized systems exhibits two distinct regimes, first increasing and then decreasing as the initial entanglement is tuned. In this work, we identify the physical origin of this behavior by analyzing the dynamics of both the Rényi entanglement entropy and the Wehrl-Rényi entropy in the random-field XXZ model, the latter of which characterizes multipartite entanglement. We show that a similar non-monotonic dependence on the initial entanglement also appears in the net growth of the Wehrl-Rényi entropy for product states polarized along the z-direction. The first regime is governed by a finite magnetization associated with local integrals of motion, while the second reflects inter-site correlations. In contrast, for product states in the x/y-direction, the entanglement growth exhibits a monotonic decay. Our results provide a more fine-grained picture of how distinct initial-state properties shape entanglement dynamics in many-body localized systems.
The non-equilibrium dynamics of disordered many-body quantum systems after a global quantum quench unveils important insights about the competition between interactions and disorder, yielding in particular an insightful perspective on many body localization (MBL). Still, the experimentally relevant effect of bond randomness in long-range interacting spin chains on the quantum quench dynamics have so far not been investigated. In this letter, we examine the entanglement entropy growth after a global quench in a quantum spin chain with randomly placed spins and long-range tunable interactions decaying with distance with power α. Using a dynamical version of the strong disorder renormalization group (SDRG) we find for α>αc that the entanglement entropy grows logarithmically with time and becomes smaller with larger α as S(t)=Spln(t)/(2α). Here, Sp=2ln2−1. We use numerical exact diagonalization (ED) simulations to verify our results for system sizes up to $ N\sim 16$ spins, yielding good agreement for sufficiently large α>αc≈1.8. For α<αc, we find that the entanglement entropy grows as a power-law with time, S(t)∼tγ(α) with 0<γ(α)<1 a decaying function of the interaction exponent α.