Spin-orbital quantum liquid on the honeycomb lattice

In addition to low-energy spin fluctuations, which distinguish them from band insulators, Mott insulators often possess orbital degrees of freedom when crystal-field levels are partially filled. While in most situations spins and orbitals develop long-range order, the possibility for the ground state to be a quantum liquid opens new perspectives. In this paper, we provide clear evidence that the SU(4) symmetric Kugel-Khomskii model on the honeycomb lattice is a quantum spin-orbital liquid. The absence of any form of symmetry breaking - lattice or SU(N) - is supported by a combination of semiclassical and numerical approaches: flavor-wave theory, tensor network algorithm, and exact diagonalizations. In addition, all properties revealed by these methods are very accurately accounted for by a projected variational wave-function based on the \pi-flux state of fermions on the honeycomb lattice at 1/4-filling. In that state, correlations are algebraic because of the presence of a Dirac point at the Fermi level, suggesting that the symmetric Kugel-Khomskii model on the honeycomb lattice is an algebraic quantum spin-orbital liquid. This model provides a good starting point to understand the recently discovered spin-orbital liquid behavior of Ba_3CuSb_2O_9. The present results also suggest to choose optical lattices with honeycomb geometry in the search for quantum liquids in ultra-cold four-color fermionic atoms.Comment: 10 pages, 7 figure

Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state

Conflicting predictions have been made for the ground state of the SU(3) Heisenberg model on the honeycomb lattice: Tensor network simulations found a plaquette order [Zhao et al, Phys. Rev. B 85, 134416 (2012)], where singlets are formed on hexagons, while linear flavor-wave theory (LFWT) suggested a dimerized, color ordered state [Lee and Yang, Phys. Rev. B 85, 100402 (2012)]. In this work we show that the former state is the true ground state by a systematic study with infinite projected-entangled pair states (iPEPS), for which the accuracy can be systematically controlled by the so-called bond dimension $D$. Both competing states can be reproduced with iPEPS by using different unit cell sizes. For small $D$ the dimer state has a lower variational energy than the plaquette state, however, for large $D$ it is the latter which becomes energetically favorable. The plaquette formation is also confirmed by exact diagonalizations and variational Monte Carlo studies, according to which both the dimerized and plaquette states are non-chiral flux states.Comment: 11 pages, 12 figures, small changes, added more reference

Chiral spin liquids in triangular lattice SU(N) fermionic Mott insulators with artificial gauge fields

We show that, in the presence of a $\pi/2$ artificial gauge field per plaquette, Mott insulating phases of ultra-cold fermions with $SU(N)$ symmetry and one particle per site generically possess an extended chiral phase with intrinsic topological order characterized by a multiplet of $N$ low-lying singlet excitations for periodic boundary conditions, and by chiral edge states described by the $SU(N)_1$ Wess-Zumino-Novikov-Witten conformal field theory for open boundary conditions. This has been achieved by extensive exact diagonalizations for $N$ between $3$ and $9$, and by a parton construction based on a set of $N$ Gutzwiller projected fermionic wave-functions with flux $\pi/N$ per triangular plaquette. Experimental implications are briefly discussed.Comment: 5+2 pages, 4 figures, 2 table

Logarithmic delocalization of end spins in the S=3/2 antiferromagnetic Heisenberg chain

Using the DMRG method we calculate the surface spin correlation function, $C_L(l)=$, in the spin $S=3/2$ antiferromagnetic Heisenberg chain. For comparison we also investigate the $S=1/2$ chain with S=1 impurity end spins and the S=1 chain. In the half-integer spin models the end-to-end correlations are found to decay to zero logarithmically, $C_L(1)\sim (\log L)^{-2d}$, with $d=0.13(2)$. We find no surface order, in clear contrast with the behavior of the S=1 chain, where exponentially localized end spins induce finite surface correlations. The lack of surface order implies that end spins do not exist in the strict sense. However, the system possesses a logarithmically weakly delocalizing boundary excitation, which, for any chain lengths attainable numerically or even experimentally, creates the illusion of an end spin. This mode is responsible for the first gap, which vanishes asymptotically as $\Delta_1 \approx (\pi v_S d)/(L\ln L)$, where $v_S$ is the sound velocity and $d$ is the logarithmic decay exponent. For the half-integer spin models our results on the surface correlations and on the first gap support universality. Those for the second gap are less conclusive, due to strong higher-order corrections.Comment: 10 pages, 8 figure

Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice

We provide numerical evidence in favor of spontaneous chiral symmetry breaking and the concomitant appearance of an Abelian chiral spin liquid for three-component fermions on the triangular lattice described by an SU(3) symmetric Hubbard model with hopping amplitude $-t$ ($t>0$) and on-site interaction $U$. This chiral phase is stabilized in the Mott phase with one particle per site in the presence of a uniform $\pi$-flux per plaquette, and in the Mott phase with two particles per site without any flux. Our approach relies on effective spin models derived in the strong-coupling limit in powers of $t/U$ for general SU$(N)$ and arbitrary uniform charge flux per plaquette, which are subsequently studied using exact diagonalizations and variational Monte Carlo simulations for $N=3$, as well as exact diagonalizations of the SU($3$) Hubbard model on small clusters. Up to third order in $t/U$, and for the time-reversal symmetric cases (flux $0$ or $\pi$), the low-energy description is given by the $J$-$K$ model with Heisenberg coupling $J$ and real ring exchange $K$. The phase diagram in the full $J$-$K$ parameter range contains, apart from three already known, magnetically long-range ordered phases, two previously unreported phases: i) a lattice nematic phase breaking the lattice rotation symmetry and ii) a spontaneous time-reversal and parity symmetry breaking Abelian chiral spin liquid. For the Hubbard model, an investigation that includes higher-order itinerancy effects supports the presence of a phase transition inside the insulating region, occurring at $(t/U)_{\rm c}\approx 0.07$ [$(U/t)_{\rm c} \approx 13$] between the three-sublattice magnetically ordered phase at small $t/U$ and this Abelian chiral spin liquid.Comment: 21 pages, 23 figure

Surface critical behavior of two-dimensional dilute Ising models

Ising models with nearest-neighbor ferromagnetic random couplings on a square lattice with a (1,1) surface are studied, using Monte Carlo techniques and star-tiangle transformation method. In particular, the critical exponent of the surface magnetization is found to be close to that of the perfect model, beta_s=1/2. The crossover from surface to bulk critical properties is discussed.Comment: 6 pages in RevTex, 3 ps figures, to appear in Journal of Stat. Phy

Numerical study of the critical behavior of the Ashkin-Teller model at a line defect

We consider the Ashkin-Teller model on the square lattice, which is represented by two Ising models ($\sigma$ and $\tau$) having a four-spin coupling of strength, $\epsilon$, between them. We introduce an asymmetric defect line in the system along which the couplings in the $\sigma$ Ising model are modified. In the Hamiltonian version of the model we study the scaling behavior of the critical magnetization at the defect, both for $\sigma$ and for $\tau$ spins by density matrix renormalization. For $\epsilon>0$ we observe identical scaling for $\sigma$ and $\tau$ spins, whereas for $\epsilon<0$ one model becomes locally ordered and the other locally disordered. This is different of the critical behavior of the uncoupled model ($\epsilon=0$) and is in contradiction with the results of recent field-theoretical calculations.Comment: 6 pages, 4 figure

Griffiths-McCoy singularities in random quantum spin chains: Exact results through renormalization

The Ma-Dasgupta-Hu renormalization group (RG) scheme is used to study singular quantities in the Griffiths phase of random quantum spin chains. For the random transverse-field Ising spin chain we have extended Fisher's analytical solution to the off-critical region and calculated the dynamical exponent exactly. Concerning other random chains we argue by scaling considerations that the RG method generally becomes asymptotically exact for large times, both at the critical point and in the whole Griffiths phase. This statement is checked via numerical calculations on the random Heisenberg and quantum Potts models by the density matrix renormalization group method.Comment: 4 pages RevTeX, 2 figures include