Erratum: Luttinger liquid physics and spin-flip scattering on helical edges [Phys. Rev. B<b>85</b>, 081106(R) (2012)]

Hohenadler, Martin; Assaad, F. F.

doi:10.1103/physrevb.86.199901

Cited by 14 publications

(61 citation statements)

References 1 publication

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“…Such a transition requires halffilled edge states and a Rashba spin-orbit term to allow umklapp scattering [15]. Whereas the first condition is rather special, the second is generic for experimental realizations.…”

Section: Introductionmentioning

confidence: 99%

Rashba coupling and magnetic order in correlated helical liquids

Hohenadler

Assaad

2014

Phys. Rev. B

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We study strongly correlated helical liquids with and without Rashba coupling using quantum Monte Carlo simulations of the Kane-Mele model with a Hubbard interaction at the edge. Independent of the Rashba coupling, we find that interactions enhance spin correlations and suppress the spectral weight at the Fermi level. For sufficiently strong interactions, a gap can be observed in the single-particle spectral function. However, based on a finite-size scaling analysis and theoretical arguments, we argue that this gap is closed by order parameter fluctuations in the Luttinger liquid phase even at zero temperature, and filled in by thermally induced kinks in the order parameter in the Mott phase at finite temperatures. While the bosonization suggests an umklapp-driven Mott transition only in the presence of Rashba coupling and hence a significant impact of the latter, our numerical results are almost unaffected by Rashba coupling even at low temperatures.

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Section: Introductionmentioning

confidence: 99%

Rashba coupling and magnetic order in correlated helical liquids

Hohenadler

Assaad

2014

Phys. Rev. B

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“…This makes the transport characteristics of the ideal HTLL quite unique and various subtle dissipative effects that can cause inelastic back-scattering even in the presence of TRS have been investigated [12,[25][26][27][28][29]. In a QSH system with a fixed spin quantization axis, the stability of the holographic HTLL at finite interaction strength has been investigated from first principles [30].…”

Section: A Hallmarks Of the Htllmentioning

confidence: 99%

“…More specifically, we measure various spin-spin correlation functions at positions r 1 and r 2 and fit their decay of to the power-law r −2ξ with r = |r 1 − r 2 |. To minimize finite size effects we keep r 1 and r 2 at fixed fractions of the system length L, namely r 1 = 3L/4, r 2 = L/4 and vary the distance r = L/2 by variation of the system size L [30]. Besides confirming our analytical analysis from first principles, our numerical study also allows us to access a broader parameter range where the model is not amenable to analytical treatment.…”

Section: Numerical Analysismentioning

confidence: 99%

Synthetic helical liquids with ultracold atoms in optical lattices

et al. 2015

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We discuss a platform for the synthetic realization of key physical properties of helical Tomonaga Luttinger liquids (HTLLs) with ultracold fermionic atoms in one-dimensional optical lattices. The HTLL is a strongly correlated metallic state where spin polarization and propagation direction of the itinerant particles are locked to each other. We propose an unconventional one-dimensional Fermi-Hubbard model which, at quarter filling, resembles the HTLL in the long wavelength limit, as we demonstrate with a combination of analytical (bosonization) and numerical (density matrix renormalization group) methods. An experimentally feasible scheme is provided for the realization of this model with ultracold fermionic atoms in optical lattices. Finally, we discuss how the robustness of the HTLL against back-scattering and imperfections, well known from its realization at the edge of two-dimensional topological insulators, is reflected in the synthetic one-dimensional scenario proposed here.

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“…14 via Quantum Monte Carlo and dynamical mean-field approaches, the helical edge states are stable up to a finite Hubbard interaction, and a gaped spin-liquid phase was predicted in the phase diagram of the KM Hubbard model at half filling for small to intermediate range of U . Moreover, the 1D Luttinger liquid physics with power-law correlations for the helical edge states has been studied numerically 16 as well as analytically 19 in the framework of the KM Hubbard model. Meanwhile, the doping effect on the KM Hubbard model was addressed in Ref.…”

mentioning

confidence: 99%

“…Recently, more attention has been put on the stability, exotic quantum phases and phase transitions of the helical edge states and possible exotic quantum phases in the correlated Kane-Mele Hubbard [14][15][16][17][18] model upon including the on-site Coulomb repulsions (the Hubbard U term) in the KM model. In a pioneering work by Meng et al in Ref.…”

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confidence: 99%

Kane-Mele Hubbard model on a zigzag ribbon: Stability of the topological edge states and quantum phase transitions

2014

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We study the quantum phases and phase transitions of the Kane-Mele Hubbard (KMH) model on a zigzag ribbon of honeycomb lattice at a finite size via the weak-coupling renormalization group (RG) approach. In the non-interacting limit, the KM model is known to support topological edge states where electrons show helical property with orientations of the spin and momentum being locked. The effective inter-edge hopping terms are generated due to finite-size effect. In the presence of an on-site Coulomb repulsive interaction and the inter-edge hoppings, special focus is put on the stability of the topological edge states (TI phase) in the KMH model against (i) the charge and spin gaped (II) phase, (ii) the charge gaped but spin gapless (IC) phase and (iii) the spin gaped but charge gapless (CI) phase depending on the number (even/odd) of the zigzag ribbons, doping level (electron filling factor) and the ratio of the Coulomb interaction to the inter-edge tunneling. We discuss different phase diagrams for even and odd numbers of zigzag ribbons. We find the TI-CI, II-IC, and II-CI quantum phase transitions are of the Kosterlitz-Thouless (KT) type. By computing various correlation functions, we further analyze the nature and leading instabilities of these phases.

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Erratum: Luttinger liquid physics and spin-flip scattering on helical edges [Phys. Rev. B85, 081106(R) (2012)]

Cited by 14 publications

References 1 publication

Rashba coupling and magnetic order in correlated helical liquids

Rashba coupling and magnetic order in correlated helical liquids

Synthetic helical liquids with ultracold atoms in optical lattices

Kane-Mele Hubbard model on a zigzag ribbon: Stability of the topological edge states and quantum phase transitions

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