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Register a new userQuantum anomalous Hall state from spatially decaying interactions on the decorated honeycomb lattice
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Topological phases typically encode topology at the level of the single particle band structure. But a remarkable class of models shows that quantum anomalous Hall effects can be driven exclusively by interactions, while the parent non-interacting band structure is topologically trivial. Unfortunately, these models have so far relied on interactions that do not spatially decay and are therefore unphysical. We study a model of spinless fermions on a decorated honeycomb lattice. Using complementary methods, mean-field theory and exact diagonalization, we find a robust quantum anomalous Hall phase arising from spatially decaying interactions. Our finding paves the way for observing the quantum anomalous Hall effect driven entirely by interactions.
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We study the one-band Hubbard model on the honeycomb lattice using a combination of quantum Monte Carlo (QMC) simulations and static as well as dynamical mean-field theory (DMFT). This model is known to show a quantum phase transition between a Dirac semi-metal and the antiferromagnetic insulator. The aim of this article is to provide a detailed comparison between these approaches by computing static properties, notably ground-state energy, single-particle gap, double occupancy, and staggered magnetization, as well as dynamical quantities such as the single-particle spectral function. At the static mean-field level local moments cannot be generated without breaking the SU(2) spin symmetry. The DMFT approximation accounts for temporal fluctuations, thus captures both the evolution of the double occupancy and the resulting local moment formation in the paramagnetic phase. As a consequence, the DMFT approximation is found to be very accurate in the Dirac semi-metallic phase where local moment formation is present and the spin correlation length small. However, in the vicinity of the fermion quantum critical point the spin correlation length diverges and the spontaneous SU(2) symmetry breaking leads to low-lying Goldstone modes in the magnetically ordered phase. The impact of these spin fluctuations on the single-particle spectral function -- textit{waterfall} features and narrow spin-polaron bands -- is only visible in the lattice QMC approach.
Tight binding models like the Hubbard Hamiltonian are most often explored in the context of uniform intersite hopping $t$. The electron-electron interactions, if sufficiently large compared to this translationally invariant $t$, can give rise to ordered magnetic phases and Mott insulator transitions, especially at commensurate filling. The more complex situation of non-uniform $t$ has been studied within a number of situations, perhaps most prominently in multi-band geometries where there is a natural distinction of hopping between orbitals of different degree of overlap. In this paper we explore related questions arising from the interplay of multiple kinetic energy scales and electron-phonon interactions. Specifically, we use Determinant Quantum Monte Carlo (DQMC) to solve the half-filled Holstein Hamiltonian on a `decorated honeycomb lattice, consisting of hexagons with internal hopping $t$ coupled together by $t^{,prime}$. This modulation of the hopping introduces a gap in the Dirac spectrum and affects the nature of the topological phases. We determine the range of $t/t^{,prime}$ values which support a charge density wave (CDW) phase about the Dirac point of uniform hopping $t=t^{,prime}$, as well as the critical transition temperature $T_c$. The QMC simulations are compared with the results of Mean Field Theory (MFT).
The anomalous Hall effect (AHE), a Hall signal occurring without an external magnetic field, is one of the most significant phenomena. However, understanding the AHE mechanism has been challenging and largely restricted to ferromagnetic metals. Here, we investigate the recently discovered AHE in the chiral antiferromagnet Mn3Sn by measuring a thermal analog of the AHE, known as an anomalous thermal Hall effect (ATHE). The amplitude of the ATHE scales with the anomalous Hall conductivity of Mn3Sn over a wide temperature range, demonstrating that the AHE of Mn3Sn arises from a dissipationless intrinsic mechanism associated with the Berry curvature. Moreover, we find that the dissipationless AHE is significantly stabilized by shifting the Fermi level toward the magnetic Weyl points. Thus, in Mn3Sn, the Berry curvature emerging from the proposed magnetic Weyl fermion state is a key factor for the observed AHE and ATHE.
In numerical simulations, spontaneously broken symmetry is often detected by computing two-point correlation functions of the appropriate local order parameter. This approach, however, computes the square of the local order parameter, and so when it is {it small}, very large system sizes at high precisions are required to obtain reliable results. Alternatively, one can pin the order by introducing a local symmetry breaking field, and then measure the induced local order parameter infinitely far from the pinning center. The method is tested here at length for the Hubbard model on honeycomb lattice, within the realm of the projective auxiliary field quantum Monte Carlo algorithm. With our enhanced resolution we find a direct and continuous quantum phase transition between the semi-metallic and the insulating antiferromagnetic states with increase of the interaction. The single particle gap in units of the Hubbard $U$ tracks the staggered magnetization. An excellent data collapse is obtained by finite size scaling, with the values of the critical exponents in accord with the Gross-Neveu universality class of the transition.
Working in a subspace with dimensionality much smaller than the dimension of the full Hilbert space, we deduce exact 4-particle ground states in 2D samples containing hexagonal repeat units and described by Hubbard type of models. The procedure identifies first a small subspace ${cal{S}}$ in which the ground state $|Psi_grangle$ is placed, than deduces $|Psi_grangle$ by exact diagonalization in ${cal{S}}$. The small subspace is obtained by the repeated application of the Hamiltonian $hat H$ on a carefully chosen starting wave vector describing the most interacting particle configuration, and the wave vectors resulting from the application of $hat H$, till the obtained system of equations closes in itself. The procedure which can be applied in principle at fixed but arbitrary system size and number of particles, is interesting by its own since provides exact information for the numerical approximation techniques which use a similar strategy, but apply non-complete basis for ${cal{S}}$. The diagonalization inside ${cal{S}}$ provides an incomplete image about the low lying part of the excitation spectrum, but provides the exact $|Psi_grangle$. Once the exact ground state is obtained, its properties can be easily analyzed. The $|Psi_grangle$ is found always as a singlet state whose energy, interestingly, saturates in the $U to infty$ limit. The unapproximated results show that the emergence probabilities of different particle configurations in the ground state present Zittern (trembling) characteristics which are absent in 2D square Hubbard systems. Consequently, the manifestation of the local Coulomb repulsion in 2D square and honeycomb types of systems presents differences, which can be a real source in the differences in the many-body behavior.
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