Interacting Hofstadter Interface

Irsigler, Bernhard; Zheng, Jun-Hui; Hofstetter, Walter

doi:10.1103/physrevlett.122.010406

Cited by 34 publications

(24 citation statements)

References 53 publications

(53 reference statements)

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“…Using the Dyson equation, these are used to construct a new lattice Green's function and this procedure is repeated until self-consistency. In 2d, DMFT has provided a successful description of topological systems for many aspects [30,[42][43][44][45][46][47][48]. Reference [49] showed that nonlocal contributions are small already in 2d.…”

Section: Interacting Phasesmentioning

confidence: 99%

“…For detection, Bloch-Zener-Stückelberg interferometry [61], anomalous velocity measurement, or state tomography [24] for bulk states as well as Bragg spectroscopy for surface states [15] have been proposed. Also a 3d version of a topological interface [46] could be used for the detection of the surface states. The local Z 2 marker introduced here could be used to distinguish the topological phase at the inter-face.…”

Section: Surface Statesmentioning

confidence: 99%

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Z2 characterization for three-dimensional multiband Hubbard models

Irsigler

Zheng

Grusdt

et al. 2020

Phys. Rev. Research

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We introduce three numerical methods for characterizing the topological phases of three-dimensional multiband Hubbard models based on twisted boundary conditions, Wilson loops, as well as the local topological marker. We focus on the half-filled, three-dimensional time-reversal-invariant Hofstadter model with finite spinorbit coupling. Besides the weak and strong topological insulator phases we find a nodal line semimetal in the parameter regime between the two three-dimensional topological insulator phases. Using dynamical mean-field theory combined with the topological Hamiltonian approach we find stabilization of these three-dimensional topological states due to the Hubbard interaction. We study surface states which exhibit an asymmetry between left and right surfaces originating from the broken parity symmetry of the system. Our results set the stage for further research on inhomogeneous three-dimensional topological systems, proximity effects, topological Mott insulators, nontrivially linked nodal line semimetals, and circuit-based quantum simulators.

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Section: Interacting Phasesmentioning

confidence: 99%

Section: Surface Statesmentioning

confidence: 99%

Z2 characterization for three-dimensional multiband Hubbard models

Irsigler

Zheng

Grusdt

et al. 2020

Phys. Rev. Research

Self Cite

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“…A second example is the topological interface [12,21,22] which is used to create an in-situ topological phase separation. In Fig.…”

Section: Interfacementioning

confidence: 99%

“…Since its introduction it enjoys great popularity in condensed matter theory as well as in the field of cold atomic gases. Applications range from heterojunctions [9] and quasicrystals [10] to interacting fermions [11] and interacting, spin-orbit coupled fermions at the smooth topological interface [12].…”

Section: Introductionmentioning

confidence: 99%

Microscopic characteristics and tomography scheme of the local Chern marker

2019

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The concept of the local Chern marker has gained a lot of attention especially in the field of ultracold quantum gases in optical lattices and artificial gauge fields. We investigate in further detail the microscopic real-space characteristics of the local Chern marker for the two-band Harper-Hofstadter-Hatsugai model and propose a tomographic scheme for the experimental detection of an approximate local Chern marker neglecting higher orders.

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“…The local Chern marker provides an alternative tool for the calculation of an invariant in inhomogeneous systems. The local Chern marker has originally been introduced to capture aspects of topology in spatially inhomogeneous and/or finite systems [49] such as they arise in the presence of a trapping potential or interfaces (see, e.g., [50]). Here, we use the local Chern marker to obtain the global Chern number of our disordered systems by integration over the spatial coordinate.…”

Section: Introductionmentioning

confidence: 99%

Effect of disorder on topological charge pumping in the Rice-Mele model

et al. 2021

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Recent experiments with ultracold quantum gases have successfully realized integer-quantized topological charge pumping in optical lattices. Motivated by this progress, we study the effects of static disorder on topological Thouless charge pumping. We focus on the half-filled Rice-Mele model of free spinless fermions and consider random diagonal disorder. In the instantaneous basis, we compute the polarization, the entanglement spectrum, and the local Chern marker. As a first main result, we conclude that the space-integrated local Chern marker is best suited for a quantitative determination of topological transitions in a disordered system. In the time-dependent simulations, we use the time-integrated current to obtain the pumped charge in slowly periodically driven systems. As a second main result, we observe and characterize a disorder-driven breakdown of the quantized charge pump. There is an excellent agreement between the static and the time-dependent ways of computing the pumped charge. The topological transition occurs well in the regime where all states are localized on the given system sizes and is therefore not tied to a delocalization-localization transition of Hamiltonian eigenstates. For individual disorder realizations, the breakdown of the quantized pumping occurs for parameters where the spectral bulk gap inherited from the band gap of the clean system closes, leading to a globally gapless spectrum. As a third main result and with respect to the analysis of finite-size systems, we show that the disorder average of the bulk gap severely overestimates the stability of quantized pumping. A much better estimate is the typical value of the distribution of energy gaps, also called mode of the distribution.

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Interacting Hofstadter Interface

Cited by 34 publications

References 53 publications

Z2 characterization for three-dimensional multiband Hubbard models

Z2 characterization for three-dimensional multiband Hubbard models

Microscopic characteristics and tomography scheme of the local Chern marker

Effect of disorder on topological charge pumping in the Rice-Mele model

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