Open accessJournal Article

Two-Dimensional Quantum Walk with Non-Hermitian Skin Effects

02 Mar 2021-Chinese Physics Letters (Chinese Physical Society)-Vol. 38, Iss: 3, pp 030301
Abstract: We construct a two-dimensional, discrete-time quantum walk exhibiting non-Hermitian skin effects under open-boundary conditions. As a confirmation of the non-Hermitian bulk-boundary correspondence, we show that the emergence of topological edge states are consistent with Floquet winding numbers calculated using a non-Bloch band theory invoking time-dependent generalized Billouin zones. Further, the non-Bloch topological invariants associated with quasienergy bands are captured by a non-Hermitian local Chern marker in real space, defined through local biorthogonal eigen wave functions of the non-unitary Floquet operator. Our work would stimulate further studies of non-Hermitian Floquet topological phases where skin effects play a key role.

Topics: Hermitian matrix (58%), Floquet theory (57%), Operator (physics) (57%) ... show more
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6 results found

Open accessJournal Article
Hao-Qing Zhang1, Ming-Zhong Ai1, Jin-Ming Cui1, Yong-Jian Han1  +2 moreInstitutions (1)
23 Aug 2021-Physical Review A
Abstract: The quantum walk, as the quantum analog of the classical random walk, provides a feasible platform to study the topological phenomenon and nonequilibrium dynamics. Here we propose a scheme to realize the quantum walk with a single trapped ion where the Fock states provides the walk space and the zero-phonon state $|n=0\ensuremath{\rangle}$ serves as its natural boundary. Thus, our scheme offers an opportunity to investigate the dynamics of the bound states of the corresponding topological systems. In particular, the quench dynamics of the bound states can be extensively studied by tuning the bulk parameters and the local boundary operator, which are experimentally accessible. Our proposal not only offers an alternative approach to exploring the character of the bound states of the topological systems, but also offers a way to determine different phases through the dynamical processes.

Topics: Quantum walk (60%), Bound state (55%), Operator (physics) (54%) ... show more

4 Citations

Open accessJournal Article
Wenjie Xi1, Zhi-Hao Zhang2, Zhi-Hao Zhang1, Zheng-Cheng Gu  +1 moreInstitutions (2)
Abstract: Topological phases in non-Hermitian systems have become fascinating subjects recently. In this paper, we attempt to classify topological phases in 1D interacting non-Hermitian systems. We begin with the non-Hermitian generalization of the Su-Schrieffer-Heeger (SSH) model and discuss its many-body topological Berry phase, which is well defined for all interacting quasi-Hermitian systems (non-Hermitian systems that have real energy spectrum). We then demonstrate that the classification of topological phases for quasi-Hermitian systems is exactly the same as their Hermitian counterparts. Finally, we construct the fixed point partition function for generic 1D interacting non-Hermitian local systems and find that the fixed point partition function still has a one-to-one correspondence to their Hermitian counterparts. Thus, we conclude that the classification of topological phases for generic 1D interacting non-Hermitian systems is still exactly the same as Hermitian systems.

Topics: Hermitian matrix (60%), , Fixed point (55%)

4 Citations

Open accessJournal Article
Tianyu Li1, Jia-Zheng Sun1, Yong-Sheng Zhang1, Yong-Sheng Zhang2  +2 moreInstitutions (2)
07 Apr 2021-
Abstract: The authors proposed a dynamic detection scheme of non-Bloch topology in the presence of non-Hermitian skin effects.

Topics: Topology (chemistry) (60%)

3 Citations

Open accessJournal Article
Y. Q. Guo1, Yi-Cong Yu1, Rui-Zhen Huang1, Li-Ping Yang2  +3 moreInstitutions (2)
Abstract: We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry using the correlation matrix technique. Our results show that the entanglement entropy has a logarithmic correction to the area law in both one-dimensional and two-dimensional systems. For any one-dimensional one-band system, we prove that each Fermi point of the system contributes exactly 1/2 to the coefficientcof the logarithmic correction. Moreover, this relation betweencand Fermi point is verified for more general one-dimensional and two-dimensional cases by numerical calculations and finite-size scaling analysis. In addition, we also study the single-particle and density-density correlation functions.

Topics: , Quantum entanglement (55%), Hermitian matrix (51%)

2 Citations

Open accessJournal Article
Tianyu Li1, Jia-Zheng Sun1, Yong-Sheng Zhang1, Yong-Sheng Zhang2  +2 moreInstitutions (2)
Abstract: We study the quench dynamics of non-Hermitian topological models with non-Hermitian skin effects. Adopting the non-Bloch band theory and projecting quench dynamics onto the generalized Brillouin zone, we find that emergent topological structures, in the form of dynamic skyrmions, exist in the generalized momentum-time domain, and are correlated with the non-Bloch topological invariants of the static Hamiltonians. The skyrmion structures anchor on the fixed points of dynamics whose existence are conditional on the coincidence of generalized Brillouin zones of the pre- and post-quench Hamiltonians. Global signatures of dynamic skyrmions, however, persist well beyond such a condition, thus offering a general dynamic detection scheme for non-Bloch topology in the presence of non-Hermitian skin effects. Applying our theory to an experimentally relevant, non-unitary quantum walk, we explicitly demonstrate how the non-Bloch topological invariants can be revealed through the non-Bloch quench dynamics.

Topics: Skyrmion (52%), Brillouin zone (51%), Fixed point (50%)

References
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52 results found

Open accessJournal Article
10 Dec 2010-Physical Review B
Abstract: Topological properties of physical systems can lead to robust behaviors that are insensitive to microscopic details. Such topologically robust phenomena are not limited to static systems but can also appear in driven quantum systems. In this paper, we show that the Floquet operators of periodically driven systems can be divided into topologically distinct (homotopy) classes and give a simple physical interpretation of this classification in terms of the spectra of Floquet operators. Using this picture, we provide an intuitive understanding of the well-known phenomenon of quantized adiabatic pumping. Systems whose Floquet operators belong to the trivial class simulate the dynamics generated by time-independent Hamiltonians, which can be topologically classified according to the schemes developed for static systems. We demonstrate these principles through an example of a periodically driven two-dimensional hexagonal lattice tight-binding model which exhibits several topological phases. Remarkably, one of these phases supports chiral edge modes even though the bulk is topologically trivial.

Topics: Floquet theory (56%), Quantum (50%), Physical system (50%)

788 Citations

Open accessJournal Article
Shunyu Yao1, Zhong Wang1Institutions (1)
Abstract: The bulk-boundary correspondence is among the central issues of non-Hermitian topological states. We show that a previously overlooked "non-Hermitian skin effect" necessitates redefinition of topological invariants in a generalized Brillouin zone. The resultant phase diagrams dramatically differ from the usual Bloch theory. Specifically, we obtain the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by the non-Bloch winding number instead of the Bloch-Hamiltonian-based topological number. Our work settles the issue of the breakdown of conventional bulk-boundary correspondence and introduces the non-Bloch bulk-boundary correspondence.

Topics: Winding number (56%), Hermitian matrix (54%)

708 Citations

Open accessJournal Article
23 Jul 2013-Physical Review X
Abstract: Recently, several authors have investigated topological phenomena in periodically driven systems of noninteracting particles. These phenomena are identified through analogies between the Floquet spectra of driven systems and the band structures of static Hamiltonians. Intriguingly, these works have revealed phenomena that cannot be characterized by analogy to the topological classification framework for static systems. In particular, in driven systems in two dimensions (2D), robust chiral edge states can appear even though the Chern numbers of all the bulk Floquet bands are zero. Here, we elucidate the crucial distinctions between static and driven 2D systems, and construct a new topological invariant that yields the correct edge-state structure in the driven case. We provide formulations in both the time and frequency domains, which afford additional insight into the origins of the “anomalous” spectra that arise in driven systems. Possibilities for realizing these phenomena in solid-state and cold-atomic systems are discussed.

Topics: Floquet theory (52%)

575 Citations

Open accessJournal Article
Abstract: Non-Hermitian systems exhibit striking exceptions from the paradigmatic bulk-boundary correspondence, including the failure of bulk Bloch band invariants in predicting boundary states and the (dis)appearance of boundary states at parameter values far from those corresponding to gap closings in periodic systems without boundaries. Here, we provide a comprehensive framework to unravel this disparity based on the notion of biorthogonal quantum mechanics: While the properties of the left and right eigenstates corresponding to boundary modes are individually decoupled from the bulk physics in non-Hermitian systems, their combined biorthogonal density penetrates the bulk precisely when phase transitions occur. This leads to generalized bulk-boundary correspondence and a quantized biorthogonal polarization that is formulated directly in systems with open boundaries. We illustrate our general insights by deriving the phase diagram for several microscopic open boundary models, including exactly solvable non-Hermitian extensions of the Su-Schrieffer-Heeger model and Chern insulators.

Topics: Biorthogonal system (59%), Hermitian matrix (53%)

530 Citations

Open accessJournal Article
Abstract: We present the first experimental observation of a topological transition in a non-Hermitian system. In contrast to standard methods for examining topological properties, which involve probing edge (or surface) states, we monitor the topological transition by employing bulk dynamics only. The system is composed of a lattice of evanescently coupled optical waveguides, and non-Hermitian behavior is engineered by inducing bending loss by spatially "wiggling" every second waveguide.