Exact mobility edges and topological phase transition in two-dimensional non-Hermitian quasicrystals

Xu, Zhihao; Xia, X. C.; Chen, Shu

doi:10.1007/s11433-021-1802-4

Cited by 24 publications

(7 citation statements)

References 84 publications

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“…Novel transport phases and topological phases are found when hoppings are long ranged [38][39][40] or quasiperiodic as well [41]. Besides these, twodimensional (2D) quasiperiodic systems provide richer phenomena of localization [42,43], topology [44], flat band [45], and many-body effects [23,46].…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of localization in two-dimensional quasiperiodic mosaic lattice

Wang¹,

Yu²,

Zhang³

et al. 2023

J. Phys.: Condens. Matter

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A one-dimensional lattice model with mosaic quasiperiodic potential is found to exhibit interesting localization properties, e.g., clear mobility edges [Y. Wang et al., Phys. Rev. Lett. \textbf{125}, 196604 (2020)]. We generalize this mosaic quasiperiodic model to a two-dimensional version, and numerically investigate its localization properties: the phase diagram from the fractal dimension of the wavefunction, the statistical and scaling properties of the conductance. Compared with disordered systems, our model shares many common features but also exhibits some different characteristics in the same dimensionality and the same universality class. For example, the sharp peak at $g\sim 0$ of the critical distribution and the large $g$ limit of the universal scaling function $\beta$ resemble those behaviors of three-dimensional disordered systems.

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Section: Introductionmentioning

confidence: 99%

Numerical investigation of localization in two-dimensional quasiperiodic mosaic lattice

Wang¹,

Yu²,

Zhang³

et al. 2023

J. Phys.: Condens. Matter

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show abstract

“…Novel transport phases and topological phases are found when hoppings are long ranged [38][39][40] or quasiperiodic as well [41]. Besides these, two-dimensional (2D) quasiperiodic systems provide richer phenomena of localization [42,43], topology [44], flat band [45], and many-body effects [23,46].…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of Localization in Two-Dimensional Quasiperiodic Mosaic Lattice

Wang¹,

Wang²,

Zhang³

et al. 2023

Preprint

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A one-dimensional lattice model with mosaic quasiperiodic potential is found to exhibit interesting localization properties, e.g., clear mobility edges [Y. Wang et al., Phys. Rev. Lett. 125, 196604 (2020)]. We generalize this mosaic quasiperiodic model to a two-dimensional version, and numerically investigate its localization properties: the phase diagram from the fractal dimension of the wavefunction, the statistical and scaling properties of the conductance. Compared with disordered systems, our model shares many common features but also exhibits some different characteristics in the same dimensionality and the same universality class. For example, the sharp peak at g ∼ 0 of the critical distribution and the large g limit of the universal scaling function β resemble those behaviors of three-dimensional disordered systems.

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“…In realistic experiments, the loss cannot be completely avoided due to the coupling of systems to the environment or measurement [11]; for cold atoms, few-body losses play inevitable roles in the preparation of degenerate quantum gases [2] and in the simulation of quantum many-body physics [3]. On the other hand, the non-Hermitian physics attracts increasing attention of almost all branches of physics in recent years [12], where abundant exotic phenomena, such as the spontaneous breaking of the parity-time (PT ) symmetry [13][14][15][16][17][18], the breakdown of the conventional bulk-boundary correspondence [19][20][21][22][23][24][25][26][27][28][29], the exceptional topology [30], and the interplay with Anderson localization [31][32][33][34][35][36][37], have been widely exploited both in theory and experiment. As for cold atoms, the experimental techniques are mature to engineer state-dependent atom losses [17,18] and the effective nonreciprocal hoppings [38] of non-Hermitian systems, which are fundamental operations for the construction of a non-Hermitian model.…”

Section: Introductionmentioning

confidence: 99%

Gain/loss effects on spin-orbit coupled ultracold atoms in two-dimensional optical lattices

Xu,

Zhou,

Cheng

et al. 2022

Preprint

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Due to the fundamental position of spin-orbit coupled ultracold atoms in the simulation of topological insulators, the gain/loss effects on these systems should be evaluated when considering the measurement or the coupling to the environment. Here, incorporating the mature gain/loss techniques into the experimentally realized spin-orbit coupled ultracold atoms in two-dimensional optical lattices, we investigate the corresponding non-Hermitian tight-binding model, evaluating the gain/loss effects on various properties of the system in the context of non-Hermitian physics. Under periodic boundary conditions, we analytically give, via block diagonalization, the topological phase diagram, which undergoes a non-Hermitian gapless interval instead of a point of the Hermitian counterpart, causing that the complex band inversion is just a necessary but not sufficient condition for the topological phase transition. A gauge-independent non-Hermitian Wilson-line method is developed for numerically calculating the non-Hermitian Chern number of a subspace consisting of multiple complex bands, because the nodal loops of the lower/upper two bands of the Hermitian counterpart can be split into exceptional loops in this non-Hermitian model. Under open boundary conditions, we find that the conventional bulk-boundary correspondence does not break down, but the dynamics of the chiral edge states depend on the boundary selection, which may be used for the control of edge dynamics.

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Exact mobility edges and topological phase transition in two-dimensional non-Hermitian quasicrystals

Cited by 24 publications

References 84 publications

Numerical investigation of localization in two-dimensional quasiperiodic mosaic lattice

Numerical investigation of localization in two-dimensional quasiperiodic mosaic lattice

Numerical Investigation of Localization in Two-Dimensional Quasiperiodic Mosaic Lattice

Gain/loss effects on spin-orbit coupled ultracold atoms in two-dimensional optical lattices

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