Topological phases of generalized Su-Schrieffer-Heeger models

Li, Linhu; Xu, Zhihao; Chen, Shu

doi:10.1103/physrevb.89.085111

Cited by 264 publications

(212 citation statements)

References 32 publications

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“…25 shows rich topological properties of generalized SSH models. We will consider the last inter-cell hopping coefficient to be time dependent with…”

Section: B Ssh Modelmentioning

confidence: 99%

Boundary-induced dynamics in one-dimensional topological systems and memory effects of edge modes

Chien

2016

Phys. Rev. B

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Dynamics induced by a change of boundary conditions reveals rate-dependent signatures associated with topological properties in one-dimensional Kitaev chain and SSH model. While the perturbation from a change of the boundary propagates into the bulk, the density of topological edge modes in the case of transforming to open boundary condition reaches steady states. The steady-state density depends on the transformation rate of the boundary and serves as an illustration of quantum memory effects in topological systems. Moreover, while a link is physically broken as the boundary condition changes, some correlation functions can remain finite across the broken link and keep a record of the initial condition. By testing those phenomena in the non-topological regimes of the two models, none of the interesting signatures of memory effects can be observed. Our results thus contrast the importance of topological properties in boundary-induced dynamics.

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“…25 shows rich topological properties of generalized SSH models. We will consider the last inter-cell hopping coefficient to be time dependent with…”

Section: B Ssh Modelmentioning

confidence: 99%

Boundary-induced dynamics in one-dimensional topological systems and memory effects of edge modes

Chien

2016

Phys. Rev. B

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“…of interesting physical phenomena it displays: topological soliton excitation, fractional charge, and nontrivial edge states [32][33][34][35][36][37]. It was also realized as a system of cold atoms trapped in an optical lattice in one dimension recently [13].…”

Section: Su-schrieffer-heeger and Rice-mele Modelsmentioning

confidence: 99%

Reconstruction of the polarization distribution of the Rice-Mele model

Yahyavi

Hetényi

2017

Phys. Rev. A

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We calculate the gauge-invariant cumulants (and moments) associated with the Zak phase in the Rice-Mele model. We reconstruct the underlying probability distribution by maximizing the information entropy and applying the moments as constraints. When the Wannier functions are localized within one unit cell, the probability distribution so obtained corresponds to that of the Wannier function. We show that in the fully dimerized limit the magnitudes of the moments are all equal. In this limit, if the on-site interaction is decreased towards zero, the distribution shifts towards the midpoint of the unit cell, but the overall shape of the distribution remains the same. Away from this limit, if alternate hoppings are finite and the on-site interaction is decreased, the distribution also shifts towards the midpoint of the unit cell, but it does this by changing shape, by becoming asymmetric around the maximum, and by shifting. We also follow the probability distribution of the polarization in cycles around the topologically nontrivial point of the model. The distribution moves across to the next unit cell, its shape distorting considerably in the process. If the radius of the cycle is large, the shift of the distribution is accompanied by large variations in the maximum.

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“…Controlled access to such terms would allow tunable symmetry breaking (inversion or particle-hole) of topological insulator systems. Additionally, it has been shown [64] that the combination of nearest-neighbor (NN) and next-nearest-neighbor (NNN) tunneling in one dimension can be used to realize systems analogous to the two-dimensional Haldane model [65], allowing study of the anomalous quantum Hall effect in an experimentally simple setting. Such a combination of terms may also allow for the study of Lifshitz-type behavior [66], e.g.…”

Section: B B Unique Featuresmentioning

confidence: 99%

Atom-optics approach to studying transport phenomena

Gadway

2015

Phys. Rev. A

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We present a simple experimental scheme, based on standard atom optics techniques, to design highly versatile model systems for the study of single particle quantum transport phenomena. The scheme is based on a discrete set of free-particle momentum states that are coupled via momentumchanging two-photon Bragg transitions, driven by pairs of interfering laser beams. In the effective lattice models that are accessible, this scheme allows for single-site detection, as well as site-resolved and dynamical control over all system parameters. We discuss two possible implementations, based on state-preserving Bragg transitions and on state-changing Raman transitions, which respectively allow for the study of nearly arbitrary single particle Abelian U(1) and non-Abelian U(2) lattice models. -for the quantum simulation of myriad physical phenomena, especially those related to condensed matter [4,5].For the study of single electron transport phenomena, photonic [6][7][8][9][10][11] and cold atom [12][13][14][15][16][17][18][19][20] simulators have made great progress in the experimental exploration of disordered and topological systems, while offering largely complementary capabilities and challenges. Photonic simulators generally permit control of system parameters and the detection of probability distributions at the microscopic, site-resolved level. However, the use of real materials as the medium for light transport makes these systems susceptible to inherent disorder in sample preparation [21] and to absorption in the material [22], and makes simulations in higher spatial dimensions and timedependent control of system parameters non-trivial. For cold atoms, pristine and dynamically variable potential landscapes can be constructed based on their interaction with laser light. However, a microscopic control over system parameters is difficult to realize in atomic systems. Moreover, finite temperatures and the absence of hardwall system boundaries have limited the observation of topological phenomena.Here, we propose an atom optics-based [23][24][25][26] approach to the study of coherent transport phenomena, which incorporates many of the desired features of atomic and photonic experimental platforms. The scheme we describe is motivated in spirit by magnetic resonance-based * bgadway@illinois.edu techniques for local manipulation via global field addressing [27,28]. In the context of studying transport phenomena, however, we consider an inhomogeneous landscape of site energies, with unique energy differences between neighboring sites, which defines unique tunneling resonances for each site-to-site link. Combined with global field addressing that can drive transitions between neighboring sites, and in particular by simultaneous driving of many such transitions in an amplitude, frequency, and phase-controlled manner, this would allow for local control over the parameters of a discrete lattice model relevant to myriad coherent transport phenomena.Atom optics offers a natural candidate system featuring a quadratic energy lan...

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Topological phases of generalized Su-Schrieffer-Heeger models

Cited by 264 publications

References 32 publications

Boundary-induced dynamics in one-dimensional topological systems and memory effects of edge modes

Boundary-induced dynamics in one-dimensional topological systems and memory effects of edge modes

Reconstruction of the polarization distribution of the Rice-Mele model

Atom-optics approach to studying transport phenomena

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