Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model

Abstract

We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d-density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionic symmetry-protected topological phase. This state -protected by time-reversal and reflection symmetries -cannot be connected adiabatically to a free-fermion topological phase. Introduction. The discovery of topological band insulators (TBI) of noninteracting electrons in certain strongly spin-orbit coupled semiconductors is one of the most important advances of the last decade in condensed matter physics [1]. TBI are an example of symmetry-protected topological phases (SPT) [2], which are devoid of intrinsic topological order such as that found in fractional quantum Hall systems, but possess protected edge/surface states with exotic characteristics. A major focus of current research is to discover interacting SPT phases that cannot be adiabatically deformed into noninteracting TBI. While progress has been made in the classification [3][4][5][6][7] and theoretical realization in model of SPT phases of bosons, much less is known about SPT phases of fermions, which are relevant for electrons in solids. Although recent theories suggest that fermionic SPT phases distinct from free-fermion TBI should exist in principle [14,15], apart from the special case of one spatial dimension (1D) there has been no explicit realization of a fermionic SPT as the ground state of a microscopic model Hamiltonian. In this paper, we provide evidence that a 2D fermionic SPT protected by time-reversal and reflection symmetries and distinct from a free-fermion TBI can be realized as the ground state of a simple Hubbard model for spin-1/2 electrons on a decorated honeycomb lattice.Fermionic Hubbard model. We consider the Hubbard model for spin-1/2 fermions hopping on the decorated triangular and honeycomb lattices (Fig. 1), where each site R of the original triangular and honeycomb lattices is decorated by a single hexagon. Fermions hop within each hexagon with a nearest-neighbor amplitude t and a next-nearest-neighbor amplitude t 2 , and interact via an

Exchange interactions, Jahn-Teller coupling, and multipole orders in pseudospin one-half $5\boldsymbol{d}^\mathbf{2}$ Mott insulators

“…3(a), which are realized when the parameter λ = 2J/J τ varies from pure J τ limit to a dominant J regime. Stripy-quadrupole phase I at small λ is essentially the same state as found earlier in compass model [25,26]; note, however, that the spin pattern in our "anti-compass" τ model is rotated by 90 • , for the reasons discussed in Sec. III A.…”

“…( 10) by τ ]. This point has to be kept in mind while comparing the present τ -model results with those in canonical compass model studies [23][24][25][26][27].…”

Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models

“…However, the exact ground state is not known in this case and its nature is in fact not clear, as several past works came to inconsistent conclusions. One study found a Néel state [96], others suggested a stabilization of a dimer pattern [97], a superposition of dimer coverings [98], or a quantum spin liquid state [99]. With the link to the compass model, the apparent special role of the −J = K = Γ point marked by a competition of four long-range ordered phases in its vicinity is confirmed.…”

Classical many-particle systems with unique disordered ground states

“…The fact that ground states of many-body systems can be disordered have intrigued condensed-matter physicists. Although quantum effects are the cause of groundstate disorder in many systems (for example, helium under normal pressure [1] and certain spin systems [2][3][4][5]), classical systems can also have disordered ground states [6][7][8][9][10][11][12][13]. A ground state of a classical many-particle or spin system is simply a global minimum of the potential energy.…”