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arXiv:1604.07512 · Physical Review Letters

Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice

Wei Kang Zhu, Shou-Shu Gong, Tian-Sheng Zeng, Liang Fu, D. N. Sheng

Published Aug 23, 2016• 81 citations
arXivHTMLPDF

Abstract

Topological states of matter have been widely studied as being driven by an external magnetic field, intrinsic spin-orbital coupling, or magnetic doping. Here, we unveil an interaction-driven spontaneous quantum Hall effect (a Chern insulator) emerging in an extended fermion-Hubbard model on a kagome lattice, based on a state-of-the-art density-matrix renormalization group on cylinder geometry and an exact diagonalization in torus geometry. We first demonstrate that the proposed model exhibits an incompressible liquid phase with doublet degenerate ground states as time-reversal partners. The explicit spontaneous time-reversal symmetry breaking is determined by emergent uniform circulating loop currents between nearest neighbors. Importantly, the fingerprint topological nature of the ground state is characterized by quantized Hall conductance. Thus, we identify the liquid phase as a quantum Hall phase, which provides a "proof-of-principle" demonstration of the interaction-driven topological phase in a topologically trivial noninteracting band.

DOI
10.1103/physrevlett.117.096402

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Topological states of matter have been widely studied as being driven by an external magnetic field, intrinsic spin-orbital coupling, or magnetic doping. Here, we unveil an interaction-driven spontaneous quantum Hall effect (a Chern insulator) emerging in an extended fermion-Hubbard model on a kagome lattice, based on a state-of-the-art density-matrix renormalization group on cylinder geometry and an exact diagonalization in torus geometry. We first demonstrate that the proposed model exhibits an incompressible liquid phase with doublet degenerate ground states as time-reversal partners. The explicit spontaneous time-reversal symmetry breaking is determined by emergent uniform circulating loop currents between nearest neighbors. Importantly, the fingerprint topological nature of the ground state is characterized by quantized Hall conductance. Thus, we identify the liquid phase as a quantum Hall phase, which provides a "proof-of-principle" demonstration of the interaction-driven topological phase in a topologically trivial noninteracting band.
We study the quantum phases of spinless fermions at one-third filling on a kagome lattice featuring a quadratic band touching Fermi point. In the presence of weak first and second nearest-neighbor repulsive interactions (V1{V}_{1}V1​ and V2{V}_{2}V2​), we demonstrate an interaction driven quantum anomalous Hall effect by employing exact diagonalization and density-matrix renormalization group methods. The time-reversal symmetry is broken spontaneously by forming loop currents that exhibit long-range correlation. Quantized Hall conductance corresponding to a Chern number of $\ifmmode\pm\else\textpm\fi{}1$ is obtained by measuring the pumped charge through inserting flux in a cylinder geometry. We find that the energy gap, which topologically protects the emerging ground states, can be enhanced remarkably by a moderate V2<V1{V}_{2}<{V}_{1}V2​<V1​ via calculating the spectrum and charge excitation gaps, which highlights the experimentally feasible scheme of realizing the interaction driven topological phase by spatially decaying interactions on topologically trivial lattice models.
There has been a growing interest in realizing topologically nontrivial states of matter in band insulators, where a quantum Hall effect can appear as an intrinsic property of the band structure. While ongoing progress is under way with a number of directions, the possibility of realizing novel interaction-generated topological phases, without the requirement of a nontrivial invariant encoded in single-particle wave function or band structure, can significantly extend the class of topological materials and is thus of great importance. Here, we show an interaction-driven topological phase emerging in an extended Bose-Hubbard model on a kagome lattice, where the noninteracting band structure is topological trivial with zero Berry curvature in the Brillouin zone. By means of an unbiased state-of-the-art density-matrix renormalization group technique, we identify that the ground state in a broad parameter region is equivalent to a bosonic fractional quantum Hall Laughlin state, based on the characterization of universal properties including ground-state degeneracy, edge excitations, and anyonic quasiparticle statistics. Our work paves a way to finding an interaction-induced topological phase at the phase boundary of conventionally ordered solid phases.
Fermi-liquid-like phase driven by next-nearest-neighbor couplings in a lightly doped kagome-lattice ttt-JJJ model
Due to the interplay between charge fluctuation and geometry frustration, the doped kagome-lattice Mott insulator is a fascinating platform to realize exotic quantum states. Through the state-of-the-art density matrix renormalization group calculation, we explore the quantum phases of the lightly doped kagome-lattice ttt-JJJ model in the presence of the next-nearest-neighbor electron hopping t2t_2t2​ and spin interaction J2J_2J2​. On the Ly=3L_y = 3Ly​=3 cylinder (LyL_yLy​ is the number of unit cells along the circumference direction), we establish a quantum phase diagram with tuning t2>0t_2 > 0t2​>0 and J2>0J_2 > 0J2​>0, showing an emergent Fermi-liquid-like phase driven by increased t2t_2t2​ and J2J_2J2​, which sits at the neighbor of the previously identified charge density wave (CDW) phase. Compared with the CDW phase, the charge order is significantly suppressed in the Fermi-liquid-like phase, and most correlation functions are greatly enhanced with power-law decay. In particular, we find the absence of hole pairing and a strong three-sublattice magnetic correlation. On the wider Ly=4L_y = 4Ly​=4 cylinder, this Fermi-liquid-like phase persists at low doping levels, strongly suggesting that this state might be stable in the two-dimensional kagome system.
Due to the interplay between charge fluctuation and geometry frustration, the doped kagome-lattice Mott insulator is a fascinating platform to realize exotic quantum states. Through the state-of-the-art density matrix renormalization group calculation, we explore the quantum phases of the lightly doped kagome-lattice $t\text{\ensuremath{-}}J$ model in the presence of the next-nearest-neighbor electron hopping t2{t}_{2}t2​ and spin interaction J2{J}_{2}J2​. On the Ly=3{L}_{y}=3Ly​=3 cylinder (Ly{L}_{y}Ly​ is the number of unit cells along the circumference direction), we establish a quantum phase diagram with tuning t2>0{t}_{2}>0t2​>0 and J2>0{J}_{2}>0J2​>0, showing an emergent Fermi-liquid-like phase driven by increased t2{t}_{2}t2​ and J2{J}_{2}J2​, at the neighbor of the previously identified charge density wave (CDW) phase. Compared with the CDW phase, the charge order is significantly suppressed in the Fermi-liquid-like phase, and most correlation functions are greatly enhanced with a power-law decay. In particular, we find the absence of hole pairing and a strong three-sublattice magnetic correlation. On the wider Ly=4{L}_{y}=4Ly​=4 cylinder, this Fermi-liquid-like phase persists at low doping levels, strongly suggesting that this state might be stable in the two-dimensional kagome system.
The fractional quantum Hall effect (FQHE) realized in two-dimensional electron systems under a magnetic field is one of the most remarkable discoveries in condensed matter physics. Interestingly, it has been proposed that FQHE can also emerge in time-reversal invariant spin systems, known as the chiral spin liquid (CSL) characterized by the topological order and the emerging of the fractionalized quasiparticles. A CSL can naturally lead to the exotic superconductivity originating from the condense of anyonic quasiparticles. Although CSL was highly sought after for more than twenty years, it had never been found in a spin isotropic Heisenberg model or related materials. By developing a density-matrix renormalization group based method for adiabatically inserting flux, we discover a FQHE in a spin-½ isotropic kagome Heisenberg model. We identify this FQHE state as the long-sought CSL with a uniform chiral order spontaneously breaking time reversal symmetry, which is uniquely characterized by the half-integer quantized topological Chern number protected by a robust excitation gap. The CSL is found to be at the neighbor of the previously identified Z2 spin liquid, which may lead to an exotic quantum phase transition between two gapped topological spin liquids.
We investigate the spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg model with a Dzyaloshinskii-Moriya interaction on kagome lattice, making use of the variational Monte Carlo technique. An exotic quantum spin state is found to arise from a melting of the $\mathbit{Q}=0$ long-range magnetic order by a topological transition, when a small anisotropic third-nearest-neighbor antiferromagnetic Heisenberg interaction is turned on. This state is a gapped quantum spin liquid, characterized by a topological order with ground-state degeneracy ng=4{n}_{g}=4ng​=4 and topological entanglement entropy $\ensuremath{\gamma}=ln2$, suggesting it is an Abelian topological phase. Furthermore, the Chern numbers of the spin-up (-down) spinon occupied bands of this state are ${C}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}=\ifmmode\pm\else\textpm\fi{}1$, respectively. From this perspective, this state is also a time-reversal symmetric (total Chern number Ctotal=0{C}_{\text{total}}=0Ctotal​=0) topological insulator with spinons as the chiral edge states, which carry opposite spin and move in the opposite direction. It is analogous to the quantum spin Hall state but the spin current is carried by deconfined spinons in a quantum spin liquid, and so is dubbed as the spinon quantum spin Hall state.