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Register a new userCollective charge excitations and the metal-insulator transition in the square lattice Hubbard-Coulomb model
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In this article, we discuss the non-trivial collective charge excitations (plasmons) of the extended square-lattice Hubbard model. Using a fully non-perturbative approach, we employ the hybrid Monte Carlo algorithm to simulate the system at half-filling. A modified Backus-Gilbert method is introduced to obtain the spectral functions via numerical analytic continuation. We directly compute the single-particle density of states which demonstrates the formation of Hubbard bands in the strongly-correlated phase. The momentum-resolved charge susceptibility is also computed on the basis of the Euclidean charge density-density correlator. In agreement with previous EDMFT studies, we find that at large strength of the electron-electron interaction, the plasmon dispersion develops two branches.
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The charge response in the barium vanadium sulfide (BaVS3) single crystals is characterized by dc resistivity and low frequency dielectric spectroscopy. A broad relaxation mode in MHz range with huge dielectric constant ~= 10^6 emerges at the metal-to-insulator phase transition TMI ~= 67 K, weakens with lowering temperature and eventually levels off below the magnetic transition Tchi ~= 30 K. The mean relaxation time is thermally activated in a manner similar to the dc resistivity. These features are interpreted as signatures of the collective charge excitations characteristic for the orbital ordering that gradually develops below TMI and stabilizes at long-range scale below Tchi.
We take advantage of recent improvements in the grand canonical Hybrid Monte Carlo algorithm, to perform a precision study of the single-particle gap in the hexagonal Hubbard model, with on-site electron-electron interactions. After carefully controlled analyses of the Trotter error, the thermodynamic limit, and finite-size scaling with inverse temperature, we find a critical coupling of $U_c/kappa=3.834(14)$ and the critical exponent $z u=1.185(43)$. Under the assumption that this corresponds to the expected anti-ferromagnetic Mott transition, we are also able to provide a preliminary estimate $beta=1.095(37)$ for the critical exponent of the order parameter. We consider our findings in view of the $SU(2)$ Gross-Neveu, or chiral Heisenberg, universality class. We also discuss the computational scaling of the Hybrid Monte Carlo algorithm, and possible extensions of our work to carbon nanotubes, fullerenes, and topological insulators.
We examine the metal-insulator transition in a half-filled Hubbard model of electrons with random and all-to-all hopping and exchange, and an on-site non-random repulsion, the Hubbard $U$. We argue that recent numerical results of Cha et al. (arXiv:2002.07181) can be understood in terms of a deconfined critical point between a disordered Fermi liquid and an insulating spin glass. We find a deconfined critical point in a previously proposed large $M$ theory which generalizes the SU(2) spin symmetry to SU($M$), and obtain exponents for the electron and spin correlators which agree with those of Cha et al. We also present a renormalization group analysis, and argue for the presence of an additional metallic spin glass phase at half-filling and small $U$.
In contrast to the Hubbard model, the extended Hubbard model, which additionally accounts for non-local interactions, lacks systemic studies of thermodynamic properties especially across the metal-insulator transition. Using a variational principle, we perform such a systematic study and describe how non-local interactions screen local correlations differently in the Fermi-liquid and in the insulator. The thermodynamics reveal that non-local interactions are at least in parts responsible for first-order metal-insulator transitions in real materials.
We have investigated the half-filling two-orbital Hubbard model on a triangular lattice by means of the dynamical mean-field theory (DMFT). The densities of states and optical conductivity clearly show the occurence of metal-insulating transition (MIT) at U$_{c}$, U$_{c}$=18.2, 16.8, 6.12 and 5.85 for J=0, 0.01U, U/4 and U/3, respectively. The distinct continuities of double occupation of electrons, local square moments and local susceptibility of the charge, the spin and the orbital at J > 0 suggest that the MIT is the first-order; however at J=0, the MIT is the second-order in the half-filling two-orbital Hubbard model on triangular lattices. We attribute the first-order nature of the MIT to the low symmetry of the systems with finite Hunds coupling J.
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