Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuantum trimer models and topological SU(3) spin liquids on the kagome lattice
252
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We construct and study quantum trimer models and resonating SU(3)-singlet models on the kagome lattice, which generalize quantum dimer models and the Resonating Valence Bond wavefunctions to a trimer and SU(3) setting. We demonstrate that these models carry a Z_3 symmetry which originates in the structure of trimers and the SU(3) representation theory, and which becomes the only symmetry under renormalization. Based on this, we construct simple and exact parent Hamiltonians for the model which exhibit a topological 9-fold degenerate ground space. A combination of analytical reasoning and numerical analysis reveals that the quantum order ultimately displayed by the model depends on the relative weight assigned to different types of trimers -- it can display either Z_3 topological order or form a symmetry-broken trimer crystal, and in addition possesses a point with an enhanced U(1) symmetry and critical behavior. Our results accordingly hold for the SU(3) model, where the two natural choices for trimer weights give rise to either a topological spin liquid or a system with symmetry-broken order, respectively. Our work thus demonstrates the suitability of resonating trimer and SU(3)-singlet ansatzes to model SU(3) topological spin liquids on the kagome lattice.
rate research
Read More
We review recent density-matrix renormalization group (DMRG) 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 we find instead a tendency toward fractionalized insulating charge-density-wave (CDW) states. In agreement with earlier work (Jiang, Devereaux, and Kivelson, Phys. Rev. Lett. ${bf 119}$, 067002 (2017)), 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 doped holes. From here, by studying generaliz
We introduce a simple model of SO($N$) spins with two-site interactions which is amenable to quantum Monte-Carlo studies without a sign problem on non-bipartite lattices. We present numerical results for this model on the two-dimensional triangular lattice where we find evidence for a spin nematic at small $N$, a valence-bond solid (VBS) at large $N$ and a quantum spin liquid at intermediate $N$. By the introduction of a sign-free four-site interaction we uncover a rich phase diagram with evidence for both first-order and exotic continuous phase transitions.
We study the nearest neighbor $XXZ$ Heisenberg quantum antiferromagnet on the kagome lattice. Here we consider the effects of several perturbations: a) a chirality term, b) a Dzyaloshinski-Moriya term, and c) a ring-exchange type term on the bowties of the kagome lattice, and inquire if they can suppport chiral spin liquids as ground states. The method used to study these Hamiltonians is a flux attachment transformation that maps the spins on the lattice to fermions coupled to a Chern-Simons gauge field on the kagome lattice. This transformation requires us to consistently define a Chern-Simons term on the kagome lattice. We find that the chirality term leads to a chiral spin liquid even in the absence of an uniform magnetic field, with an effective spin Hall conductance of $sxy = frac{1}{2}$ in the regime of $XY$ anisotropy. The Dzyaloshinkii-Moriya term also leads a similar chiral spin liquid but only when this term is not too strong. An external magnetic field also has the possibility of giving rise to additional plateaus which also behave like chiral spin liquids in the $XY$ regime. Finally, we consider the effects of a ring-exchange term and find that, provided its coupling constant is large enough, it may trigger a phase transition into a chiral spin liquid by the spontaneous breaking of time-reversal invariance.
We consider the $(2+1)$-d $SU(2)$ quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the Kagome lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges (which transform non-trivially under the $mathbb{Z}(2)$ center of the $SU(2)$ gauge group) are confined to each other by fractionalized strings with a delocalized $mathbb{Z}(2)$ flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the 3-d Ising universality class separates two confining phases; one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.
We perform an extensive density matrix renormalization group (DMRG) study of the ground-state phase diagram of the spin-1/2 J_1-J_2 Heisenberg model on the kagome lattice. We focus on the region of the phase diagram around the kagome Heisenberg antiferromagnet, i.e., at J_2=0. We investigate the static spin structure factor, the magnetic correlation lengths, and the spin gaps. Our results are consistent with the absence of magnetic order in a narrow region around J_2approx 0, although strong finite-size effects do not allow us to accurately determine the phase boundaries. This result is in agreement with the presence of an extended spin-liquid region, as it has been proposed recently. Outside the disordered region, we find that for ferromagnetic and antiferromagnetic J_2 the ground state displays signatures of the magnetic order of the sqrt{3}timessqrt{3} and the q=0 type, respectively. Finally, we focus on the structure of the entanglement spectrum (ES) in the q=0 ordered phase. We discuss the importance of the choice of the bipartition on the finite-size structure of the ES.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
