14 research outputs found
Bose-Hubbard model on two-dimensional line graphs
We construct a basis for the many-particle ground states of the positive
hopping Bose-Hubbard model on line graphs of finite 2-connected planar
bipartite graphs at sufficiently low filling factors. The particles in these
states are localized on non-intersecting vertex-disjoint cycles of the line
graph which correspond to non-intersecting edge-disjoint cycles of the original
graph. The construction works up to a critical filling factor at which the
cycles are close-packed.Comment: 9 pages, 5 figures, figures and conclusions update
Schwinger boson study of the -- kagome Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions
Schwinger boson mean field theory is a powerful approach to study frustrated
magnetic systems which allows to distinguish long range magnetic orders from
quantum spin liquid phases, where quantum fluctuations remain strong up to zero
temperature. In this work, we use this framework to study the Heisenberg model
on the Kagome lattice with up to third nearest neighbour interaction and
Dzyaloshinskii-Moriya (DM) antisymmetric exchange. This model has been argued
to be relevant for the description of transition metal dichalcogenide bilayers
in certain parameter regimes, where spin liquids could be realized. By means of
the projective symmetry group classification of possible ans\"atze, we study
the effect of the DM interaction at first nearest neighbor and then compute the
- phase diagram at different DM angles. We find a new phase
displaying chiral spin liquid characteristics up to spin , indicating an
exceptional stability of the state
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Chiral Spin Liquid Phase of the Triangular Lattice Hubbard Model: A Density Matrix Renormalization Group Study
Motivated by experimental studies that have found signatures of a quantum spin liquid phase in organic crystals whose structure is well described by the two-dimensional triangular lattice, we study the Hubbard model on this lattice at half filling using the infinite-system density matrix renormalization group (iDMRG) method. On infinite cylinders with finite circumference, we identify an intermediate phase between observed metallic behavior at low interaction strength and Mott insulating spin-ordered behavior at strong interactions. Chiral ordering from spontaneous breaking of time-reversal symmetry, a fractionally quantized spin Hall response, and characteristic level statistics in the entanglement spectrum in the intermediate phase provide strong evidence for the existence of a chiral spin liquid in the full two-dimensional limit of the model
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Performance of the rigorous renormalization group for first-order phase transitions and topological phases
Expanding and improving the repertoire of numerical methods for studying quantum lattice models is an ongoing focus in many-body physics. While the density matrix renormalization group (DMRG) has been established as a practically useful algorithm for finding the ground state in one-dimensional systems, a provably efficient and accurate algorithm remained elusive until the introduction of the rigorous renormalization group (RRG) by Landau [Nat. Phys. 11, 566 (2015)1745-247310.1038/nphys3345]. In this paper, we study the accuracy and performance of a numerical implementation of RRG at first-order phase transitions and in symmetry-protected topological phases. Our study is motivated by the question of when RRG might provide a useful complement to the more established DMRG technique. In particular, despite its general utility, DMRG can give unreliable results near first-order phase transitions and in topological phases, since its local update procedure can fail to adequately explore (near-)degenerate manifolds. The rigorous theoretical underpinnings of RRG, meanwhile, suggest that it should not suffer from the same difficulties. We show this optimism is justified, and that RRG indeed determines well-ordered, accurate energies even when DMRG does not. Moreover, our performance analysis indicates that in certain circumstances seeding DMRG with states determined by coarse runs of RRG may provide an advantage over simply performing DMRG