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Register a new userLocalization properties in Lieb lattices and their extensions
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We study the localization properties of generalized, two- and three-dimensional Lieb lattices, $mathcal{L}_2(n)$ and $mathcal{L}_3(n)$, $n= 1, 2, 3$ and $4$, at energies corresponding to flat and dispersive bands using the transfer matrix method (TMM) and finite size scaling (FSS). We find that the scaling properties of the flat bands are different from scaling in dispersive bands for all $mathcal{L}_d(n)$. For the $d=3$ dimensional case, states are extended for disorders $W$ down to $W=0.01 t$ at the flat bands, indicating that the disorder can lift the degeneracy of the flat bands quickly. The phase diagram with periodic boundary condition for $mathcal{L}_3(1)$ looks similar to the one for hard boundaries. We present the critical disorder $W_c$ at energy $E=0$ and find a decreasing $W_c$ for increasing $n$ for $mathcal{L}_3(n)$, up to $n=3$. Last, we show a table of FSS parameters including so-called irrelevant variables; but the results indicate that the accuracy is too low to determine these reliably. end{abstract}
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We study the localization properties and the Anderson transition in the 3D Lieb lattice $mathcal{L}_3(1)$ and its extensions $mathcal{L}_3(n)$ in the presence of disorder. We compute the positions of the flat bands, the disorder-broadened density of states and the energy-disorder phase diagrams for up to 4 different such Lieb lattices. Via finite-size scaling, we obtain the critical properties such as critical disorders and energies as well as the universal localization lengths exponent $ u$. We find that the critical disorder $W_c$ decreases from $sim 16.5$ for the cubic lattice, to $sim 8.6$ for $mathcal{L}_3(1)$, $sim 5.9$ for $mathcal{L}_3(2)$ and $sim 4.8$ for $mathcal{L}_3(3)$. Nevertheless, the value of the critical exponent $ u$ for all Lieb lattices studied here and across disorder and energy transitions agrees within error bars with the generally accepted universal value $ u=1.590 (1.579,1.602)$.
We study the localization properties of the two-dimensional Lieb lattice and its extensions in the presence of disorder using transfer matrix method and finite-size scaling. We find that all states in the Lieb lattice and its extensions are localized for $W geq 1$. Clear differences in the localization properties between disordered flat band and disordered dispersive bands are identified. Our results complement previous experimental studies of clean photonic Lieb lattices and provide information about their stability with respect to disorder.
The kicked rotor system is a textbook example of how classical and quantum dynamics can drastically differ. The energy of a classical particle confined to a ring and kicked periodically will increase linearly in time whereas in the quantum version the energy saturates after a finite number of kicks. The quantum system undergoes Anderson localization in the angular-momentum space. Conventional wisdom says that in a many-particle system with short-range interactions the localization will be destroyed due to the coupling of widely separated momentum states. Here we provide evidence that for an interacting one-dimensional Bose gas, the Lieb-Linger model, the dynamical localization can persist.
Bipartite graphs are often found to represent the connectivity between the components of many systems such as ecosystems. A bipartite graph is a set of $n$ nodes that is decomposed into two disjoint subsets, having $m$ and $n-m$ vertices each, such that there are no adjacent vertices within the same set. The connectivity between both sets, which is the relevant quantity in terms of connections, can be quantified by a parameter $alphain[0,1]$ that equals the ratio of existent adjacent pairs over the total number of possible adjacent pairs. Here, we study the spectral and localization properties of such random bipartite graphs. Specifically, within a Random Matrix Theory (RMT) approach, we identify a scaling parameter $xiequivxi(n,m,alpha)$ that fixes the localization properties of the eigenvectors of the adjacency matrices of random bipartite graphs. We also show that, when $xi<1/10$ ($xi>10$) the eigenvectors are localized (extended), whereas the localization--to--delocalization transition occurs in the interval $1/10<xi<10$. Finally, given the potential applications of our findings, we round off the study by demonstrating that for fixed $xi$, the spectral properties of our graph model are also universal.
We theoretically study transport properties in one-dimensional interacting quasiperiodic systems at infinite temperature. We compare and contrast the dynamical transport properties across the many-body localization (MBL) transition in quasiperiodic and random models. Using exact diagonalization we compute the optical conductivity $sigma(omega)$ and the return probability $R(tau)$ and study their average low-frequency and long-time power-law behavior, respectively. We show that the low-energy transport dynamics is markedly distinct in both the thermal and MBL phases in quasiperiodic and random models and find that the diffusive and MBL regimes of the quasiperiodic model are more robust than those in the random system. Using the distribution of the DC conductivity, we quantify the contribution of sample-to-sample and state-to-state fluctuations of $sigma(omega)$ across the MBL transition. We find that the activated dynamical scaling ansatz works poorly in the quasiperiodic model but holds in the random model with an estimated activation exponent $psiapprox 0.9$. We argue that near the MBL transition in quasiperiodic systems, critical eigenstates give rise to a subdiffusive crossover regime on finite-size systems.
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