Ground-state phase diagram of the triangular lattice Hubbard model by the density-matrix renormalization group method

Abstract

Two-dimensional density-matrix renormalization group method is employed to examine the ground state phase diagram of the Hubbard model on the triangular lattice at half-filling. The calculation reveals two discontinuities in the double occupancy with increasing the repulsive Hubbard interaction U at Uc1 ∼ 7.8t and Uc2 ∼ 9.9t (t being the hopping integral), indicating that there are three phases separated by first order transitions. The absence of any singularity in physical quantities for 0 ≤ U < Uc1 implies a metallic phase in this regime. For U > Uc2, the local spin density induced by an applied pinning magnetic field exhibits a three sublattice feature, which is compatible with the 120 • Néel ordered state realized in the limit of U → ∞. For Uc1 < U < Uc2, a response to the applied pinning magnetic field is comparable to that in the metallic phase with a relatively large spin correlation length, but showing neither valence bond nor chiral magnetic order, which therefore resembles gapless spin liquid. However, the spin structure factor for the intermediate phase exhibits the maximum at the K and K points in the momentum space, which is not compatible to spin liquid with a large spinon Fermi surface. The calculation also finds that the pairing correlation function monotonically decreases with increasing U and thus the superconductivity is unlikely in the intermediate phase.arXiv:1606.06814v2 [cond-mat.str-el]

Two-temperature scales in the triangular-lattice Heisenberg antiferromagnet

“…Intriguingly, recent T = 0 studies on the fermionic triangular lattice Hubbard model proposed a chiral intermediate phase versus Coulomb repulsion which thus breaks time reversal symmetry [63]. While debated [64], we take this as a strong motivation to also study traces of chiral correlations in the TLH at finite T .…”

Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model

“…We also present data for simulated neutron spectroscopy and spin-lattice relaxation times, and perform direct comparisons to inelastic neutron spectroscopy experiments on the triangular material Ba8CoNb6O24 and to the relaxation times on κ-(ET)2Cu2(CN)3. Finally, we present charge susceptibilities in different areas of parameter space, which should correspond to momentum-resolved electron-loss spectroscopy measurements on triangular compounds., suggests that these compounds are close to a two-dimensional triangular structure and exhibit interesting electron correlation behavior including, potentially, a quantum spin liquid phase [7] in the ground state [8]. These compounds, as well as the low energy physics of the fully isotropic triangular material Ba 8 CoNb 6 O 24 [9], may be described by a half-filled single orbital Hubbard model on a triangular two-dimensional lattice, with an on-site Coulomb interaction strength comparable to or larger than the bandwidth [10].Because of the subtle competition of metallic, ordered, and spin liquid phases in the ground state, this model has been studied extensively with a wide range of numerical tools, including exact diagonalization (ED) [11][12][13], density matrix renormalization group theory (DMRG) [8], variational Monte Carlo (VMC) [14][15][16][17], variational cluster approximation [18][19][20], strong coupling expansions [21], path integral renormalization group techniques [22], and cluster dynamical mean field theory (DMFT) in the cellular [23][24][25][26][27] and dynamical cluster [28,29] variants.…”

“…Introduction. Experimental evidence on several organic materials, including κ-(BEDT-TTF) 2 Cu 2 (CN) 3 [1,2], EtMe 3 Sb[Pd(dmit) 2 ] 2 [3][4][5], and κ-H 3 (Cat-EDT-TTF) 2 [6], suggests that these compounds are close to a two-dimensional triangular structure and exhibit interesting electron correlation behavior including, potentially, a quantum spin liquid phase [7] in the ground state [8]. These compounds, as well as the low energy physics of the fully isotropic triangular material Ba 8 CoNb 6 O 24 [9], may be described by a half-filled single orbital Hubbard model on a triangular two-dimensional lattice, with an on-site Coulomb interaction strength comparable to or larger than the bandwidth [10].…”

“…Because of the subtle competition of metallic, ordered, and spin liquid phases in the ground state, this model has been studied extensively with a wide range of numerical tools, including exact diagonalization (ED) [11][12][13], density matrix renormalization group theory (DMRG) [8], variational Monte Carlo (VMC) [14][15][16][17], variational cluster approximation [18][19][20], strong coupling expansions [21], path integral renormalization group techniques [22], and cluster dynamical mean field theory (DMFT) in the cellular [23][24][25][26][27] and dynamical cluster [28,29] variants. The focus in most of these studies has been on the precise location of the phase boundaries, ordering (or the absence thereof), and on the nature of these phases.…”

Spin-Orbital Density Wave and a Mott Insulator in a Two-Orbital Hubbard Model on a Honeycomb Lattice

“…Meanwhile, our finding of the SODW near MIT at intermediate U is a new result. Our work shows that the phase diagram of SU (4) Hubbard model is distinctly different from SU(2) case [31][32][33][34][35][36][37][38][39], where a magnetic ordered phase often appears in large U limit, a direct phase transition [33][34][35][36][37] or an intermediate phase [31,32,38,39] are found close to the MIT. It is also distinguished from half-filled SU (2N ≥ 4) case, where a direct transition from semimetal to valence bond solid was identified [40,41].…”