Quantum Transports in Two-Dimensions with Long Range Hopping: Shielding, Localization and the Extended Isolated State

We investigate the effects of disorder and shielding on quantum transports in a two dimensional system with all-to-all long range hopping. In the weak disorder, cooperative shielding manifests itself as perfect conducting channels identical to those of the short range model, as if the long range hopping does not exist. With increasing disorder, the average and fluctuation of conductance are larger than those in the short range model, since the shielding is effectively broken and therefore long range hopping starts to take effect. Over several orders of disorder strength (until $\sim 10^4$ times of nearest hopping), although the wavefunctions are not fully extended, they are also robustly prevented from being completely localized into a single site. Each wavefunction has several localization centers around the whole sample, thus leading to a fractal dimension remarkably smaller than 2 and also remarkably larger than 0, exhibiting a hybrid feature of localization and delocalization. The size scaling shows that for sufficiently large size and disorder strength, the conductance tends to saturate to a fixed value with the scaling function $\beta\sim 0$, which is also a marginal phase between the typical metal ($\beta>0$) and insulating phase ($\beta<0$). The all-to-all coupling expels one isolated but extended state far out of the band, whose transport is extremely robust against disorder due to absence of backscattering. The bond current picture of this isolated state shows a quantum version of short circuit through long hopping.Comment: 15 pages, 8 figure

Ground-state properties via machine learning quantum constraints

Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert space has made such studies costly, if not prohibitive, on sufficiently large system sizes. Here, we propose an alternative strategy based upon the expectation values of an ensemble of operators and the elusive yet vital quantum constraints between them, where the search for ground-state properties simply equates to simple, classical constrained minimization. These quantum constraints are generally obtainable via machine learning on a large number of sample quantum many-body states systematically consistent with physical presumptions. We showcase our perspective on 1D fermion chains and spin chains for applicability, effectiveness, and several unique advantages, especially for strongly correlated systems, thermodynamic-limit systems, property designs, etc.Comment: 6 pages, 4 figure

Correlation function of flavored fermion in holographic QCD

By using the gauge-gravity duality, we investigate the correlation function of flavored fermion in the $\mathrm{D}_{p}/\mathrm{D}_{p+4}$ model as top-down approaches of holographic QCD for $p=4,3$. The bulk spinor, as the source of the flavored fermion in QCD, is identified to the worldvolume fermion on the flavor $\mathrm{D}_{p+4}$-branes and the standard form of its action can be therefore obtained by the T-duality rules in string theory. Keeping this in hand, we afterwards generalize the prescription for two-point correlation function in AdS/CFT dictionary into general D-brane backgrounds and apply it to the case of $p=4,3$, i.e. the D4/D8 and D3/D7 approach respectively. Resultantly, our numerical calculation with the bubble background always displays discrete peaks in the correlation functions which imply the bound states created by the flavored fermions as the confinement in QCD. With the black brane background, the onshell condition illustrated by the correlation function covers basically the dispersion curves of fermion obtained by the hard thermal loop approximation in the hot medium. In this sense, we conclude remarkably that our top-down approach in this work could reveal the fundamental properties of QCD both in the confined and deconfined phase.Comment: 41 pages; 11 figures; 1 table; fix Figure 7 and Figure 1

Orbital Magnetization under an Electric Field and Orbital Magnetoelectric Polarizabilty for a Bilayer Chern System

In the the real space formalism of orbital magnetization (OM) for a Chern insulator without an external electric field, it is correct to average the local OM either over the bulk region or over the whole sample. However for a layered Chern insulator in an external electric field, which is directly related to the nontrivial nature of orbital magnetoelectric coupling, the role of boundaries remains ambiguous in this formalism. Based on a bilayer model with an adjustable Chern number at half filling, we numerically investigate the OM with the above two different average types under a nonzero perpendicular electric field. The result shows that in this case, the nonzero Chern number gives rise to a gauge shift of the OM with the bulk region average, while this gauge shift is absent for the OM with the whole sample average. This indicates that only the whole sample average is reliable to calculate the OM under a nonzero electric field for Chern insulators. On this basis, the orbital magnetoelectric polarizablity (OMP) and the Chern-Simons orbital magnetoelectric polarizablity (CSOMP) with the whole sample average are studied. We also present the relationship between the OMP (CSOMP) and the response of Berry curvature to the electric field. The stronger the response of Berry curvature to electric field, the stronger is the OMP (CSOMP). Besides clarify the calculation methods, our result also provides an effective method to enhance OMP and CSOMP of materials.Comment: 11 pages, 11 figure