Articles
Publication Date: 2024
Quantum Information Processing (15700755)23(5)
A novel method has been devised to compute the local integrals of motion (LIOMs) for a one-dimensional many-body localized system. In this approach, a class of optimal unitary transformations is deduced in a tensor network formalism to diagonalize the Hamiltonian of the specified system. To construct the tensor network, we utilize the eigenstates of the subsystems’ Hamiltonian to attain the desired unitary transformations. Subsequently, we optimize the eigenstates and acquire appropriate unitary localized operators that will represent the LIOMs tensor network. The efficiency of the method was assessed and found to be both fast and almost accurate. In framework of the introduced tensor network representation, we examine how the entanglement spreads along the considered many-body localized system and evaluate the outcomes of the approximations employed in this approach. The important and interesting result is that in the proposed tensor network approximation, if the length of the blocks is greater than the length of localization, then the entropy growth will be linear in terms of the logarithmic time. Also, it has been demonstrated that the entanglement can be calculated by only considering two blocks next to each other, if the Hamiltonian has been diagonalized using the unitary transformation made by the provided tensor network representation. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
Publication Date: 2024
Physical Review B (24699950)110(16)
This study is devoted to the profound implications of tilted Dirac cones on the quantum transport properties of two-dimensional (2D) Dirac materials. These materials, characterized by their linear conic energy dispersions in the vicinity of Dirac points, exhibit unique electronic behaviors, including the emulation of massless Dirac fermions and the manifestation of relativistic phenomena such as Klein tunneling. Expanding beyond the well-studied case of graphene, the manuscript focuses on materials with tilted Dirac cones, where the anisotropic and tilted nature of the cones introduces additional richness to their electronic properties that arises from an emergent underlying spacetime geometry. The investigation begins by considering a heterojunction of 2D Dirac materials, where electrons undergo quantum tunneling between regions with upright and tilted Dirac cones. The role of tilt in characterizing the transmission of electrons across these interfaces is thoroughly examined, shedding light on the influence of the tilt parameter on the transmission probability and the fate of the pseudospin of the Dirac electrons, particularly upon a sudden change in the tilting. We also investigate the probability of reflection and transmission from an intermediate slab with arbitrary subcritical tilt, focusing on the behavior of electron transmission across regions with varying Dirac cone tilts. The study demonstrates that for certain thicknesses of the middle slab, the transmission probability is equal to unity, and both reflection and transmission exhibit periodic behavior with respect to the slab thickness. This is reminiscent of Klein tunneling across scalar potential barriers in PNP junctions, no gate voltage is applied. Such a tilt-induced potential can be considered as the quantum transport manifestation of the "gravitomagnetic"effect of underlying spacetime structure. © 2024 American Physical Society.
