Topological Rice-Mele model in an emergent lattice: Exact diagonalization approach

Biedroń, Krzysztof; Dutta, Omjyoti; Zakrzewski, Jakub

doi:10.1103/physreva.93.033631

Cited by 6 publications

(5 citation statements)

References 43 publications

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“…In the present paper we show that the low energy sector of Hamiltonian (1), is described by an exotic gauge theory for b-bosons filling n 1. Note that similar models have been considered recently in [27][28][29][30][31][32][33][34][35][36][37]. We discuss the details of the physical implementations of the Hamiltonian (1) to the later sections.…”

Section: The Modelmentioning

confidence: 91%

Toolbox for Abelian lattice gauge theories with synthetic matter

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Fundamental forces of Nature are described by field theories, also known as gauge theories, based on a local gauge invariance. The simplest of them is quantum electrodynamics (QED), which is an example of an Abelian gauge theory. Such theories describe the dynamics of massless photons and their coupling to matter. However, in two spatial dimension (2D) they are known to exhibit gapped phases at low temperature. In the realm of quantum spin systems, it remains a subject of considerable debate if their low energy physics can be described by emergent gauge degrees of freedom. Here we present a class of simple two-dimensional models that admit a low energy description in terms of an Abelian gauge theory. We find rich phase diagrams for these models comprising exotic deconfined phases and gapless phases - a rare example for 2D Abelian gauge theories. The counter-intuitive presence of gapless phases in 2D results from the emergence of additional symmetry in the models. Moreover, we propose schemes to realize our model with current experiments using ultracold bosonic atoms in optical lattices.Comment: Accepted versio

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Section: The Modelmentioning

confidence: 91%

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“…The topological time crystals we consider should not be confused with the so-called Floquet topological systems. In the latter, a crystalline structure (usually an optical lattice) is present in space and it is periodically driven so that its effective parameters can be changed and the system can reveal topological properties in space but no crystalline structure can be observed in time [46][47][48][49]. Our systems are also different from Floquet-Bloch systems where time periodicity is considered as an additional synthetic dimensional combined with a crystalline structure in space [50][51][52][53][54][55].…”

Section: Introductionmentioning

confidence: 99%

Topological time crystals

et al. 2019

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By analogy with the formation of space crystals, crystalline structures can also appear in the time domain. While in the case of space crystals we often ask about periodic arrangements of atoms in space at a moment of a detection, in time crystals the role of space and time is exchanged. That is, we fix a space point and ask if the probability density for detection of a system at this point behaves periodically in time. Here, we show that in periodically driven systems it is possible to realize topological insulators, which can be observed in time. The bulk-edge correspondence is related to the edge in time, where edge states localize. We focus on two examples: Su-Schrieffer-Heeger model in time and Bose Haldane insulator which emerges in the dynamics of a periodically driven many-body system. 5 Note that due to the negative effective mass m eff , the first energy band is the highest in energy. 2 New J. Phys. 21 (2019) 052003 where = ¢ J J i 2and J 2i−1 =J, which is identical to the SSH model [86]. The latter describes spinless fermions hopping on a 1D-lattice with staggered hopping amplitudes. Changing the ratio λ 1 /λ in (1), allows one to control the ratio ¢ J J . This effective Hamiltonian belongs to the BDI class of the periodic table of the topological insulators and superconductors [87] and is characterized by a  topological invariant, the winding number ν. For an infinite system with ¢ > J J ( ¢ < J J ), the system is in a topological (trivial) phase with winding number ν=1 (ν=0). For a finite system, the topological phase exhibits zero energy edge states protected by the topology of the bulk. The SSH model has been experimentally realized in quantum simulators and both the presence of edge states and the winding number have been measured [63][64][65]. Let us emphasize that the Wannier states w i (x, t) of equation (2) are localized wavepackets of the effective SSH Hamiltonian of equation (3). We then discuss how such states allow one to detect the topology of the SSH Hamiltonian. corresponding to quasi-energies closest to zero, see top panel. In the topological phase, these eigenstates have zero quasi-energy and are linear combinations of the edge states localized at the edge of time. That is, in the laboratory frame, a detector is placed close to the oscillating mirror (x≈0) and the probability density of clicking of the detector is shown versus time for different values of the ratio ¢ J J of the tunneling amplitudes in (3). This behavior is repeated with the period 2π/ω. At sωt/(2π)=1 and sωt/(2π)=40 there are edges where the eigenstate localizes if ¢ > J J 1. The results correspond to ω=0.067, λ=0.06 in (1) and are obtained within the quantum secular approach [84], see the appendix.

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“…Resonant transitions into orbital states of opposite parity can in principle also occur in the presence of interactions, namely when two particles jointly scatter into the excited state(Sowiński, 2012) or in the form of density-induced orbital-changing tunneling processes, as they have recently been shown to give rise to exotic model systems(Dutta et al, 2015b;Biedroń et al, 2016;Przysiezna et al, 2015).…”

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Colloquium: Atomic quantum gases in periodically driven optical lattices

2017

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Time periodic forcing in the form of coherent radiation is a standard tool for the coherent manipulation of small quantum systems like single atoms. In the last years, periodic driving has more and more also been considered as a means for the coherent control of many-body systems. In particular, experiments with ultracold quantum gases in optical lattices subjected to periodic driving in the lower kilohertz regime have attracted a lot of attention. Milestones include the observation of dynamic localization, the dynamic control of the quantum phase transition between a bosonic superfluid and a Mott insulator, as well as the dynamic creation of strong artificial magnetic fields and topological band structures. This article reviews these recent experiments and their theoretical description. Moreover, fundamental properties of periodically driven many-body systems are discussed within the framework of Floquet theory, including heating, relaxation dynamics, anomalous topological edge states, and the response to slow parameter variations.

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Topological Rice-Mele model in an emergent lattice: Exact diagonalization approach

Cited by 6 publications

References 43 publications

Toolbox for Abelian lattice gauge theories with synthetic matter

Toolbox for Abelian lattice gauge theories with synthetic matter

Topological time crystals

Colloquium: Atomic quantum gases in periodically driven optical lattices

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