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Register a new userGapless spin-liquid phase in an extended spin 1/2 triangular Heisenberg model
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We numerically study the Heisenberg models on triangular lattices by extending it from the simplest equilateral lattice with only the nearest-neighbor exchange interaction. We show that, by including an additional weak next-nearest-neighbor interaction, a quantum spin-liquid phase is stabilized against the antiferromagnetic order. The spin gap (triplet excitation gap) and spin correlation at long distances decay algebraically with increasing system size at the critical point between the antiferromagnetic phase and the spin-liquid phase. This algebraic behavior continues in the spin-liquid phase as well, indicating the presence of an unconventional critical (algebraic spin-liquid) phase characterized by the dynamical and anomalous critical exponents $z+etasim1$. Unusually small triplet and singlet excitation energies found in extended points of the Brillouin zone impose constraints on this algebraic spin liquid.
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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.
We study the spin-$1/2$ Heisenberg model on the triangular lattice with the antiferromagnetic first ($J_1$) and second ($J_2$) nearest-neighbor interactions using density matrix renormalization group. By studying the spin correlation function, we find a $120^{circ}$ magnetic order phase for $J_2 lesssim 0.07 J_1$ and a stripe antiferromagnetic phase for $J_2 gtrsim 0.15 J_1$. Between these two phases, we identify a spin liquid region characterized by the exponential decaying spin and dimer correlations, as well as the large spin singlet and triplet excitation gaps on finite-size systems. We find two near degenerating ground states with distinct properties in two sectors, which indicates more than one spin liquid candidates in this region. While the sector with spinon is found to respect the time reversal symmetry, the even sector without a spinon breaks such a symmetry for finite-size systems. Furthermore, we detect the signature of the fractionalization by following the evolution of different ground states with inserting spin flux into the cylinder system. Moreover, by tuning the anisotropic bond coupling, we explore the nature of the spin liquid phase and find the optimal parameter region for the gapped $Z_2$ spin liquid.
We study the spin liquid candidate of the spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet on the triangular lattice by means of density matrix renormalization group (DMRG) simulations. By applying an external Aharonov-Bohm flux insertion in an infinitely long cylinder, we find unambiguous evidence for gapless $U(1)$ Dirac spin liquid behavior. The flux insertion overcomes the finite size restriction for energy gaps and clearly shows gapless behavior at the expected wave-vectors. Using the DMRG transfer matrix, the low-lying excitation spectrum can be extracted, which shows characteristic Dirac cone structures of both spinon-bilinear and monopole excitations. Finally, we confirm that the entanglement entropy follows the predicted universal response under the flux insertion.
We use the state-of-the-art tensor network state method, specifically, the finite projected entangled pair state (PEPS) algorithm, to simulate the global phase diagram of spin-$1/2$ $J_1$-$J_2$ Heisenberg model on square lattices up to $24times 24$. We provide very solid evidences to show that the nature of the intermediate nonmagnetic phase is a gapless quantum spin liquid (QSL), whose spin-spin and dimer-dimer correlations both decay with a power law behavior. There also exists a valence-bond solid (VBS) phase in a very narrow region $0.56lesssim J_2/J_1leq0.61$ before the system enters the well known collinear antiferromagnetic phase. We stress that our work gives rise to the first solid PEPS results beyond the well established density matrix renormalization group (DMRG) through one-to-one direct benchmark for small system sizes. Thus our numerical evidences explicitly demonstrate the huge power of PEPS for solving long-standing 2D quantum many-body problems. The physical nature of the discovered gapless QSL and potential experimental implications are also addressed.
The spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices are investigated via the finite projected entangled pair states (PEPS) method. Using the recently developed gradient optimization method combining with Monte Carlo sampling techniques, we are able to obtain the ground states energies that are competitive to the best results. The calculations show that there is no Neel order, dimer order and plaquette order in the region of 0.42 $lesssim J_2/J_1lesssim$ 0.6, suggesting a single spin liquid phase in the intermediate region. Furthermore, the calculated staggered spin, dimer and plaquette correlation functions all have power law decay behaviours, which provide strong evidences that the intermediate nonmagnetic phase is a single gapless spin liquid state.
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