From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model

Sticlet, Doru; Seabra, Luis; Pollmann, Frank; Cayssol, Jérôme

doi:10.1103/physrevb.89.115430

Cited by 69 publications

(79 citation statements)

References 59 publications

(168 reference statements)

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“…This renders a full non-overlap covering of the lattice in two possible ways (denoted as C1, C2, Fig.1c). These, together with a trivial phase when the cross-linking is weak, form the basic topological features of the Creutz model [32][33][34].…”

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confidence: 92%

Quantum charge pumps with topological phases in a Creutz ladder

Sun

Lim

2017

Phys. Rev. B

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Quantum charge pumping phenomenon connects band topology through the dynamics of a onedimensional quantum system. In terms of a microscopic model, the Su-Schrieffer-Heeger/Rice-Mele quantum pump continues to serve as a fruitful starting point for many considerations of topological physics. Here we present a generalized Creutz scheme as a distinct two-band quantum pump model. By noting that it undergoes two kinds of topological band transitions accompanying with a Zakphase-difference of π and 2π, respectively, various charge pumping schemes are studied by applying an elaborate Peierl's phase substitution. Translating into real space, the transportation of quantized charges is a result of cooperative quantum interference effect. In particular, an all-flux quantum pump emerges which operates with time-varying fluxes only and transports two charge units. This puts cold atoms with artificial gauge fields as an unique system where this kind of phenomena can be realized. PACS numbers:Introduction -Quantum charge pumping was one of the early example of a counterintuitive one-dimensional (1D) transport phenomenon as a result of the subtle interplay between nontrivial band topology and quantum adiabatic transport [1]. It underpins the many facets of understanding topological physics ranging from the integer quantum Hall effect [2, 3] to modern studies of electric polarization [4,5], and most recently, topological Floquet physics [6][7][8][9][10][11][12][13][14][15][16]. Explicit models of a quantum pump, however, are surprisingly rare [17][18][19][20][21]. The prototype of its realization is the one based on the Su-SchriefferHeeger/Rice-Mele (SSH/RM) model [22,23] for polyacetylene. It has generated renewed interests thanks to various recent experimental realizations in ultracold atoms and condensed matter systems, where the Zak phase [24], quantum pumping phenomena [25][26][27], and chiral solitonic edge states [28] are directly measured. In this Letter, we present a generalized Creutz scheme [29] as a distinct microscopic two-band quantum pump model utilizing quantum interference effect. The model points to a new quasi-one-dimensional tight-binding quantum pump displaying rich topological physics, and realizable with artificial gauge fields in a cold atomic setting.In the SSH/RM quantum pump, the physical picture is one based on confining quantum particle in a periodic potential that 'slides' slowly in time [17,30]. Specifically, the sliding potential interpolates the two possible alternations of bond strength, such that two dimerization phases of the SSH are realized in a time periodic manner.In the quasi-1D Creutz model (Fig. 1a with φ = 0) [29,31], there actually exists three distinct phases, a feature not apparent by inspection of the tight-binding model. An intuition is provided as follows. First, notice that cross-link hoppings and external flux in the two-leg ladder lattice enhance quantum interference effect. As a result, a complete basis in the topological regime, as found by Creutz [29], takes the form of pla...

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confidence: 92%

Quantum charge pumps with topological phases in a Creutz ladder

Sun

Lim

2017

Phys. Rev. B

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“…In the most general setting this duality is valid at the level of the projected interaction Hamiltonian presented in Eq. (8) and relates an attractive Hubbard model with time-reversal symmetry and symmetric with respect to rotations of the spin around a chosen axis (the z axis for instance) to a repulsive Hubbard model with SU(2) spin rotational symmetry. Our argument also clarifies why it is natural to relate Hubbard models with precisely the above symmetries.…”

Section: Appendix A: Duality Between Attractive and Repulsive Hubbardmentioning

confidence: 99%

“…It is straightforward to check thatP σniασPσ = P σĉ † iασĉiασPσ =c † iασciασPσ =n iασPσ . Then the projected interaction HamiltonianPĤ intP = H intP is given in terms of the operator (8) with…”

Section: B Schrieffer-wolff Transformation and Projected Hamiltonianmentioning

confidence: 99%

“…A prime example is the fractional quantum Hall effect [1]. Beyond the physics in a strong magnetic field, flat or nearly flat bands are a relatively common occurrence in lattice Hamiltonians where they can be realized by engineering suitable hopping matrix elements [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Given the vanishing group velocity, one could expect an electronic flat band system to be a particularly bad conductor.…”

Section: Introductionmentioning

confidence: 99%

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Effective theory and emergent SU(2) symmetry in the flat bands of attractive Hubbard models

et al. 2016

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In a partially filled flat Bloch band electrons do not have a well defined Fermi surface and hence the low-energy theory is not a Fermi liquid. Nevertheless, under the influence of an attractive interaction, a superconductor well described by the Bardeen-Cooper-Schrieffer (BCS) wave function can arise. Here we study the low-energy effective Hamiltonian of a generic Hubbard model with a flat band. We obtain an effective Hamiltonian for the flat band physics by eliminating higher-lying bands via the perturbative Schrieffer-Wolff transformation. At first order in the interaction energy we recover the usual procedure of projecting the interaction term onto the flat band Wannier functions. We show that the BCS wave function is the exact ground state of the projected interaction Hamiltonian, if a simple uniform pairing condition on the single-particle states is satisfied, and that the compressibility is diverging as a consequence of an emergent SU(2) symmetry. This symmetry is broken by second-order interband transitions resulting in a finite compressibility, which we illustrate for a one-dimensional ladder with two perfectly flat bands. These results motivate a further approximation leading to an effective ferromagnetic Heisenberg model. The gauge-invariant result for the superfluid weight of a flat band can be obtained from the ferromagnetic Heisenberg model only if the maximally localized Wannier functions in the Marzari-Vanderbilt sense are used. Finally, we prove an important inequality D W 2 between the Drude weight D and the winding number W, which guarantees ballistic transport for topologically nontrivial flat bands in one dimension.

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“…For example, considerable progress has been made towards developing number preserving theories of the Majorana modes, [15][16][17][18][19][20] as well as a growing body of work which examines how free-topological superconducting phases are affected by the addition of interacting electron-electron terms. [21][22][23][24][25][26][27][28][29][30][31][32][33] One aspect of this latter story is concerned with the stability and structure of the Majorana zero-modes themselves and how they are affected by the presence of density-density interaction terms that break the exactly solvable nature of the underlying model. The issue of stable zero-modes has also been addressed in the related context of 1-d parafermionic chains.…”

Section: Introductionmentioning

confidence: 99%

Multiparticle content of Majorana zero modes in the interactingp-wave wire

Kells

2015

Phys. Rev. B

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In the topological phase of p-wave superconductors, zero-energy Majorana quasi-particle excitations can be well-defined in the presence of local density-density interactions. Here we examine this phenomenon from the perspective of matrix representations of the commutator H = [H, •] ,with the aim of characterising the multiparticle content of the many-body Majorana mode. To do this we show that, for quadratic fermionic systems, H can always be decomposed into sub-blocks that act as multi-particle generalisations of the BdG/Majorana forms that encode single-particle excitations. In this picture, density-density like interactions will break this exact excitation-number symmetry, coupling different sub-blocks and lifting degeneracies so that the eigen-operators of the commutator H take the form of individual eigenstate transitions | n m |. However, the Majorana mode is special in that zero-energy transitions are not destroyed by local interactions and it becomes possible to define many-body Majoranas as the odd-parity zero-energy solutions of H that minimise their excitation number. This idea forms the basis for an algorithm which is used to characterise the multi-particle excitation content of the Majorana zero modes of the one-dimensional p-wave lattice model. We find that the multi-particle content of the Majorana zero-mode operators is significant even at modest interaction strengths. This has important consequences for the stability of Majorana based qubits when they are coupled to a heat bath. We will also discuss how these findings differ from previous work regarding the structure of the many-body-Majorana operators and point out that this should affect how certain experimental features are interpreted.

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From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model

Cited by 69 publications

References 59 publications

Quantum charge pumps with topological phases in a Creutz ladder

Quantum charge pumps with topological phases in a Creutz ladder

Effective theory and emergent SU(2) symmetry in the flat bands of attractive Hubbard models

Multiparticle content of Majorana zero modes in the interactingp-wave wire

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