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Register a new userPhase diagram of the Kane-Mele-Coulomb model
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We determine the phase diagram of the Kane-Mele model with a long-range Coulomb interaction using an exact quantum Monte Carlo method. Long-range interactions are expected to play a role in honeycomb materials because the vanishing density of states in the semimetallic weak-coupling phase suppresses screening. According to our results, the Kane-Mele-Coulomb model supports the same phases as the Kane-Mele-Hubbard model. The nonlocal part of the interaction promotes short-range sublattice charge fluctuations, which compete with antiferromagnetic order driven by the onsite repulsion. Consequently, the critical interaction for the magnetic transition is significantly larger than for the purely local Hubbard repulsion. Our numerical data are consistent with $SU(2)$ Gross-Neveu universality for the semimetal to antiferromagnet transition, and with 3D XY universality for the quantum spin Hall to antiferromagnet transition.
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We study the two-dimensional Kane-Mele-Hubbard model at half filling by means of quantum Monte Carlo simulations. We present a refined phase boundary for the quantum spin liquid. The topological insulator at finite Hubbard interaction strength is adiabatically connected to the groundstate of the Kane-Mele model. In the presence of spin-orbit coupling, magnetic order at large Hubbard U is restricted to the transverse direction. The transition from the topological band insulator to the antiferromagnetic Mott insulator is in the universality class of the three-dimensional XY model. The numerical data suggest that the spin liquid to topological insulator and spin liquid to Mott insulator transitions are both continuous.
The description of interactions in strongly-correlated topological phases of matter remains a challenge. Here, we develop a stochastic functional approach for interacting topological insulators including both charge and spin channels. We find that the Mott transition of the Kane-Mele-Hubbard model may be described by the variational principle with one equation. We present different views of this equation from the electron Greens function, the free-energy and the Hellmann-Feynman theorem. The band gap remains finite at the transition and the Mott phase is characterized by antiferromagnetism in the $x-y$ plane. The interacting topological phase is described through a $mathbb{Z}_2$ number related to helical edge modes. Our results then show that improving stochastic approaches can give further insight on the understanding of interacting phases of matter.
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.
The entanglement Chern number, the Chern number for the entanglement Hamiltonian, is used to charac- terize the Kane-Mele model, which is a typical model of the quantum spin Hall phase with the time reversal symmetry. We first obtain the global phase diagram of the Kane-Mele model in terms of the entanglement spin Chern number, which is defined by using a spin subspace as a subspace to be traced out in preparing the entanglement Hamiltonian. We further demonstrate the effectiveness of the entanglement Chern number without the time reversal symmetry and spin conservation by extending the Kane-Mele model to include the Zeeman term. The numerical results confirm that the sum of the entanglement spin Chern number equals to the Chern number.
We investigate the magnetic response in the quantum spin Hall phase of the layered Kane-Mele model with Hubbard interaction, and argue a condition to obtain the Meissner effect. The effect of Rashba spin orbit coupling is also discussed.
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