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Physical review. B./Physical review. B

Fermi-liquid-like phase driven by next-nearest-neighbor couplings in a lightly doped kagome-lattice t − J model

Xu-Yan Jia, Fan Yang, D. N. Sheng, Shou-Shu Gong

Published Nov 24, 2025• 1 citation
Publisher

Abstract

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 ${t}_{2}$ and spin interaction ${J}_{2}$. On the ${L}_{y}=3$ cylinder (${L}_{y}$ is the number of unit cells along the circumference direction), we establish a quantum phase diagram with tuning ${t}_{2}>0$ and ${J}_{2}>0$, showing an emergent Fermi-liquid-like phase driven by increased ${t}_{2}$ and ${J}_{2}$, 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 ${L}_{y}=4$ 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.

DOI
10.1103/vy2r-62kw

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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\ensuremath-Jt\text{\ensuremath{-}}Jt\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.
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.
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=0.027δ= 0.027δ=0.027 - 0.360.360.36, we study the kagome-lattice ttt-JJJ model using the state-of-the-art density matrix renormalization group calculation. 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 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≈0.15δ\approx 0.15δ≈0.15, which is characterized by suppression of charge density oscillation and power-law decay of various correlation functions. On the wider Ly=4L_y = 4Ly​=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=1/3δ= 1/3δ=1/3 on the Ly=3L_y = 3Ly​=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=1/3δ= 1/3δ=1/3 disappears on the Ly=4L_y = 4Ly​=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.
Abstract We present a systematic investigation of the stability of the phase diagram of the spinless Falicov–Kimball model on two-dimensional non-bipartite lattices, the triangular and kagome lattices, using Markov-chain Monte Carlo simulations. Three filling or chemical potential conditions are examined: fixed chemical potentials ( μf=μc=U/2\mu _f = \mu _c = U/2μf​=μc​=U/2 μ f = μ c = U / 2 ), “generalized” half-filling ( nˉf=1/3\bar{n}_f = 1/3nˉf​=1/3 n ¯ f = 1 / 3 , nˉc=2/3\bar{n}_c = 2/3nˉc​=2/3 n ¯ c = 2 / 3 ), and conventional half-filling ( nˉf=nˉc=1/2\bar{n}_f = \bar{n}_c = 1/2nˉf​=nˉc​=1/2 n ¯ f = n ¯ c = 1 / 2 ). For each condition, the effects of a perturbatively small next-nearest-neighbor hopping are studied. On the triangular lattice, Anderson insulator, Mott insulator, and charge-density wave (CDW) phases are found in all cases, with the CDW driven by Coulomb interaction-mediated nesting. Evidence for a charge-liquid regime is found in the region between the weakly correlated regime and the CDW, characterized by competing charge-ordering wavevectors and the absence of universal scaling behavior, whose extent shrinks progressively from the grand-canonical to the conventional half-filling condition. On the kagome lattice, the CDW phase is completely absent; instead, an insulating ground state, plausibly of the Mott type, is found, with signatures of a possible quantum phase transition at zero temperature. Our results establish the crucial role of lattice geometry and particle-hole symmetry breaking in shaping the phase diagram of correlated electron systems. Graphical abstract The 2d triangular lattice (left) and the 2d kagome lattice (right) with their unit cells highlighted. Bottom: The corresponding phase diagram of the Falicov-Kimball model (FKM) on each lattice, illustrating the non-Fermi liquid (nFL), charge-density wave (CDW), Anderson insulator (AI) and Mott insulator (MI) regimes.
Unravelling competing orders emergent in doped Mott insulators and their interplay with unconventional superconductivity is one of the major challenges in condensed matter physics. To explore the possible superconducting state in a doped Mott insulator, we study the square-lattice t-J model with both the nearest-neighbor and next-nearest-neighbor electron hoppings and spin interactions. By using the state-of-the-art density matrix renormalization group calculation with imposing charge U(1) and spin SU(2) symmetries on the six-leg cylinders, we establish a quantum phase diagram including three phases: a stripe charge density wave phase, a superconducting phase without static charge order, and a superconducting phase coexistent with a weak charge stripe order. Crucially, we demonstrate that the superconducting phase has a power-law pairing correlation that decays much slower than the charge density and spin correlations, which is a quasi-1D descendant of the uniform d-wave superconductor in two dimensions. These findings reveal that enhanced charge and spin fluctuations with optimal doping is able to produce robust d-wave superconductivity in doped Mott insulators, providing a foundation for connecting theories of superconductivity to models of strongly correlated systems.
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.