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Register a new userQuantum Spin Liquid with Emergent Chiral Order in the Triangular-lattice Hubbard Model
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The interplay between spin frustration and charge fluctuation gives rise to an exotic quantum state in the intermediate-interaction regime of the half-filled triangular-lattice Hubbard (TLU) model, while the nature of the state is under debate. Using the density matrix renormalization group with SU(2)$_{rm{spin}} otimes $U(1)$_{rm{charge}}$ symmetries implemented, we study the TLU model defined on the long cylinder geometry with circumference $W=4$. A gapped quantum spin liquid, with on-site interaction $9 lesssim U / t lesssim 10.75$, is identified between the metallic and the antiferromagnetic Mott insulating phases. In particular, we find that this spin liquid develops a robust long-range spin scalar-chiral correlation as the system length $L$ increases, which unambiguously unveils the spontaneous time-reversal symmetry breaking. In addition, the large degeneracy of the entanglement spectrum supports symmetry fractionalization and spinon edge modes in the obtained ground state. The possible origin of chiral order in this intermediate spin liquid and its relation to the rotonlike excitations have also been discussed.
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We demonstrate that the insulating one-band Hubbard model on the pyrochlore lattice contains, for realistic parameters, an extended quantum spin-liquid phase. This is a three-dimensional spin liquid formed from a highly degenerate manifold of dimer-based states, which is a subset of the classical dimer coverings obeying the ice rules. It possesses spinon excitations, which are both massive and deconfined, and on doping it exhibits spin-charge separation. We discuss the realization of this state in effective S = 1/2 pyrochlore materials with and without spin-orbit coupling.
The Hubbard model and its strong-coupling version, the Heisenberg one, have been widely studied on the triangular lattice to capture the essential low-temperature properties of different materials. One example is given by transition metal dichalcogenides, as 1T$-$TaS$_2$, where a large unit cell with $13$ Ta atom forms weakly-coupled layers with an isotropic triangular lattice. By using accurate variational Monte Carlo calculations, we report the phase diagram of the $t-t^prime$ Hubbard model on the triangular lattice, highlighting the differences between positive and negative values of $t^prime/t$; this result can be captured only by including the charge fluctuations that are always present for a finite electron-electron repulsion. Two spin-liquid regions are detected: one for $t^prime/t<0$, which persists down to intermediate values of the electron-electron repulsion, and a narrower one for $t^prime/t>0$. The spin-liquid phase appears to be gapless, though the variational wave function has a nematic character, in contrast to the Heisenberg limit. We do not find any evidence for non-magnetic Mott phases in the proximity of the metal-insulator transition, at variance with the predictions (mainly based upon strong-coupling expansions in $t/U$) that suggest the existence of a weak-Mott phase that intrudes between the metal and the magnetically ordered insulator.
We study the interplay of competing interactions in spin-$1/2$ triangular Heisenberg model through tuning the first- ($J_1$), second- ($J_2$), and third-neighbor ($J_3$) couplings. Based on large-scale density matrix renormalization group calculation, we identify a quantum phase diagram of the system and discover a new {it gapless} chiral spin liquid (CSL) phase in the intermediate $J_2$ and $J_3$ regime. This CSL state spontaneously breaks time-reversal symmetry with finite scalar chiral order, and it has gapless excitations implied by a vanishing spin triplet gap and a finite central charge on the cylinder. Moreover, the central charge grows rapidly with the cylinder circumference, indicating emergent spinon Fermi surfaces. To understand the numerical results we propose a parton mean-field spin liquid state, the $U(1)$ staggered flux state, which breaks time-reversal symmetry with chiral edge modes by adding a Chern insulator mass to Dirac spinons in the $U(1)$ Dirac spin liquid. This state also breaks lattice rotational symmetries and possesses two spinon Fermi surfaces driven by nonzero $J_2$ and $J_3$, which naturally explains the numerical results. To our knowledge, this is the first example of a gapless CSL state with coexisting spinon Fermi surfaces and chiral edge states, demonstrating the rich family of novel phases emergent from competing interactions in triangular-lattice magnets.
Broad interest in quantum spin liquid (QSL) phases was triggered by the notion that they can be viewed as insulating phases with preexisting electron-pairs, such that upon light doping they might automatically yield superconductivity. Yet despite intense efforts, definitive evidence is lacking. We address the problem of a lightly doped QSL through a large-scale density-matrix renormalization group study of the $t$-$J$ model on the triangular lattice with a small but non-zero concentration of doped holes. The ground state is consistent with a Luther-Emery liquid with power-law superconducting and charge-density-wave correlations associated with partially-filled charge stripes. In particular, the superconducting correlations are dominant on both four-leg and six-leg cylinders at all hole doping concentrations. Our results provide direct evidences that doping a QSL can naturally lead to robust superconductivity.
The existence of a gapped chiral spin liquid has been recently suggested in the vicinity of the metal-insulator transition of the Hubbard model on the triangular lattice, by intensive density-matrix renormalization group (DMRG) simulations [A. Szasz, J. Motruk, M.P. Zaletel, and J.E. Moore, Phys. Rev. X ${bf 10}$, 021042 (2020)]. Here, we report the results obtained within the variational Monte Carlo technique based upon Jastrow-Slater wave functions, implemented with backflow correlations. As in DMRG calculations, we consider $N$-leg cylinders. In highly-frustrated cases, i.e., in the presence of a next-nearest neighbor hopping with $N=4$, a chiral spin liquid emerges between the metal and the insulator with magnetic quasi-long-range order. Within our approach, the chiral state is gapped and breaks the reflection symmetry. By contrast, for the less frustrated case with $N=6$, the chiral spin liquid is not the state with the lowest variational energy and the results are very similar to the one obtained on two-dimensional clusters [L.F. Tocchio, A. Montorsi, and F. Becca, Phys. Rev. B ${bf 102}$, 115150 (2020)].
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