Abstract The authors review recent density‐matrix renormalization group studies of lightly doped quantum spin liquids (QSLs) on the kagome lattice. While a number of distinct conducting phases, including high temperature superconductivity, have been theoretically anticipated, a tendency toward fractionalized insulating charge‐density‐wave (CDW) states is instead found. In agreement with earlier work [Jiang, Devereaux, and Kivelson, Phys. Rev. Lett . 2017, 119 , 067002], results for the t ‐ J model reveal that, starting from a fully gapped QSL, light doping leads to CDW long‐range order with a pattern that depends on lattice geometry and doping concentration such that there is one doped‐hole per CDW unit cell, while the spin–spin correlations remain short‐ranged. Alternatively, this state can be viewed as a stripe crystal or Wigner crystal of spinless holons, rather than of doped holes. From here, by studying generalized versions of the t ‐ J model, these results are extended to light doping of other types of QSLs, including critical and chiral QSLs. These results suggest that doping these QSLs also leads to insulating states with long‐range CDW order. While the superconducting correlations are short‐ranged, they can be significantly enhanced by second‐neighbor electron hopping. The relevance of these numerical results to Kagome materials is also discussed.
Abstract The authors review recent density‐matrix renormalization group studies of lightly doped quantum spin liquids (QSLs) on the kagome lattice. While a number of distinct conducting phases, including high temperature superconductivity, have been theoretically anticipated, a tendency toward fractionalized insulating charge‐density‐wave (CDW) states is instead found. In agreement with earlier work [Jiang, Devereaux, and Kivelson, Phys. Rev. Lett . 2017, 119 , 067002], results for the t ‐ J model reveal that, starting from a fully gapped QSL, light doping leads to CDW long‐range order with a pattern that depends on lattice geometry and doping concentration such that there is one doped‐hole per CDW unit cell, while the spin–spin correlations remain short‐ranged. Alternatively, this state can be viewed as a stripe crystal or Wigner crystal of spinless holons, rather than of doped holes. From here, by studying generalized versions of the t ‐ J model, these results are extended to light doping of other types of QSLs, including critical and chiral QSLs. These results suggest that doping these QSLs also leads to insulating states with long‐range CDW order. While the superconducting correlations are short‐ranged, they can be significantly enhanced by second‐neighbor electron hopping. The relevance of these numerical results to Kagome materials is also discussed.
It has long been believed that doped quantum spin liquids (QSLs) can give rise to fascinating quantum phases, including the possibility of high-temperature superconductivity (SC) as proposed by P. W. Anderson's resonating valence bond (RVB) scenario. The Kagome lattice t-J model is known to exhibit spin liquid behavior at half-filling, making it an ideal system for studying the properties of doped QSL. In this study, we employ the fermionic projected entangled simplex state (PESS) method to investigate the ground state properties of the Kagome lattice t-J model with t/J=3.0. Our results reveal a phase transition from charge density wave (CDW) states to uniform states around a critical doping level δc≈0.27. Within the CDW phase, we observe different types of Wigner crystal (WC) formulated by doped holes that are energetically favored. As we enter the uniform phase, a non-Fermi liquid (NFL) state emerges within the doping range 0.27<δ<0.32, characterized by an exponential decay of all correlation functions. With further hole doping, we discover the appearance of a pair density wave (PDW) state within a narrow doping region 0.32<δ<1/3. We also discuss the potential experimental implications of our findings.
We address the problem of a lightly doped spin liquid through a large-scale density-matrix renormalization group study of the t-J model on a kagome lattice with a small but nonzero concentration δ of doped holes. It is now widely accepted that the undoped (δ=0) spin-1/2 Heisenberg antiferromagnet has a spin-liquid ground state. Theoretical arguments have been presented that light doping of such a spin liquid could give rise to a high temperature superconductor or an exotic topological Fermi liquid metal. Instead, we infer that the doped holes form an insulating charge-density wave state with one doped hole per unit cell, i.e., a Wigner crystal. Spin correlations remain short ranged, as in the spin-liquid parent state, from which we infer that the state is a crystal of spinless holons, rather than of holes. Our results may be relevant to kagome lattice herbertsmithite upon doping.
The doped quantum spin liquid on the kagome lattice provides a fascinating platform to explore exotic quantum states, such as the reported holon Wigner crystal at low doping. By extending the doping range to δ=0.027 - 0.36, we study the kagome-lattice t-J model using the state-of-the-art density matrix renormalization group calculation. On the Ly=3 cylinder (Ly is the number of unit cells along the circumference direction), we establish a quantum phase diagram with increasing doping level. In addition to the charge density wave (CDW) states at lower doping, we find an emergent Fermi-liquid-like phase by melting the holon Wigner crystal at δ≈0.15, which is characterized by suppression of charge density oscillation and power-law decay of various correlation functions. On the wider Ly=4 cylinder, the bond-dimension extrapolated correlation functions also support such a Fermi-liquid-like state, suggesting its stability with increasing system size. In a narrow doping range near δ=1/3 on the Ly=3 cylinder, we find a state with an exponential decay of single-particle correlation but the other correlation functions preserving the features in the Fermi-liquid-like phase, which may be a precursor of a superconducting state. Nevertheless, this peculiar state near δ=1/3 disappears on the Ly=4 cylinder, implying a possible lattice size dependence. Our results reveal a quantum melting from a holon Wigner crystal to a Fermi-liquid-like state with increasing hole density, and suggest a doping regime to explore superconductivity for future study.
Abstract The doped quantum spin liquid on the kagome lattice provides a fascinating platform to explore exotic quantum states, such as the reported holon Wigner crystal at low doping. By extending the doping range to δ = 0.027–0.36, we studied the kagome-lattice t - J model using state-of-the-art density matrix renormalization group calculations. On the L y = 3 cylinder ( L y is the number of unit cells along the circumferential direction), we established a quantum phase diagram with an increasing doping level. In addition to the charge density wave states at lower doping levels, we found an emergent Fermi-liquid-like phase by melting the holon Wigner crystal at δ ≈ 0.15, which is characterized by the suppression of charge density oscillation and power-law decay of various correlation functions. For a wider L y = 4 cylinder, the bond-dimension extrapolated correlation functions also support such a Fermi-liquid-like state, suggesting its stability with increasing system size. In a narrow doping range near δ = 1/3 for the L y = 3 cylinder, we find a state with an exponential decay of the single-particle correlation, but the other correlation functions preserve the features in the Fermi-liquid-like phase, which may be a precursor of a superconducting state. Nevertheless, this peculiar state near δ = 1/3 disappears for the L y = 4 cylinder, implying a possible lattice-size dependence. Our results reveal quantum melting from a holon Wigner crystal to a Fermi-liquid-like state with increasing hole density and suggest a doping regime to explore superconductivity in future studies.
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 and spin interaction J2. On the Ly=3 cylinder (Ly is the number of unit cells along the circumference direction), we establish a quantum phase diagram with tuning t2>0 and J2>0, showing an emergent Fermi-liquid-like phase driven by increased t2 and 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 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.
Fermi-liquid-like phase driven by next-nearest-neighbor couplings in a lightly doped kagome-lattice t-J 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 t-J model in the presence of the next-nearest-neighbor electron hopping t2 and spin interaction J2. On the Ly=3 cylinder (Ly is the number of unit cells along the circumference direction), we establish a quantum phase diagram with tuning t2>0 and J2>0, showing an emergent Fermi-liquid-like phase driven by increased t2 and J2, 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=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.