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Register a new userThe second-order reduced density matrix method and the two-dimensional Hubbard model
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The second-order reduced density matrix method (the RDM method) has performed well in determining energies and properties of atomic and molecular systems, achieving coupled-cluster singles and doubles with perturbative triples (CC SD(T)) accuracy without using the wave-function. One question that arises is how well does the RDM method perform with the same conditions that result in CCSD(T) accuracy in the strong correlation limit. The simplest and a theoretically important model for strongly correlated electronic systems is the Hubbard model. In this paper, we establish the utility of the RDM method when employing the $P$, $Q$, $G$, $T1$ and $T2^prime$ conditions in the two-dimension al Hubbard model case and we conduct a thorough study applying the $4times 4$ Hubbard model employing a coefficients. Within the Hubbard Hamilt onian we found that even in the intermediate setting, where $U/t$ is between 4 and 10, the $P$, $Q$, $G$, $T1$ and $T2^prime$ conditions re produced good ground state energies.
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Competing inhomogeneous orders are a central feature of correlated electron materials including the high-temperature superconductors. The two- dimensional Hubbard model serves as the canonical microscopic physical model for such systems. Multiple orders have been proposed in the underdoped part of the phase diagram, which corresponds to a regime of maximum numerical difficulty. By combining the latest numerical methods in exhaustive simulations, we uncover the ordering in the underdoped ground state. We find a stripe order that has a highly compressible wavelength on an energy scale of a few Kelvin, with wavelength fluctuations coupled to pairing order. The favored filled stripe order is different from that seen in real materials. Our results demonstrate the power of modern numerical methods to solve microscopic models even in challenging settings.
The nonequilibrium dynamics of strongly-correlated fermions in lattice systems have attracted considerable interest in the condensed matter and ultracold atomic-gas communities. While experiments have made remarkable progress in recent years, there remains a need for the further development of theoretical tools that can account for both the nonequilibrium conditions and strong correlations. For instance, time-dependent theoretical quantum approaches based on the density matrix renormalization group (DMRG) methods have been primarily applied to one-dimensional setups. Recently, two-dimensional quantum simulations of the expansion of fermions based on nonequilibrium Green functions (NEGF) have been presented [Schluenzen et al., Phys. Rev. B 93, 035107 (2016)] that showed excellent agreement with the experiments. Here we present an extensive comparison of the NEGF approach to numerically accurate DMRG results. The results indicate that NEGF are a reliable theoretical tool for weak to intermediate coupling strengths in arbitrary dimensions and make long simulations possible. This is complementary to DMRG simulations which are particularly efficient at strong coupling.
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 = 7.55 t and Uc2 = 9.65 t (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 that this phase corresponds to a metallic phase. The local spin density induced by an applied pinning magnetic field for U > Uc2 exhibits a three sublattice feature, which is compatible with the Neel ordered state realized in the strong coupling limit. For Uc1 < U < Uc2, a response to the applied pinning magnetic field is comparable to that in the metallic phase but a relatively large spin correlation length is found with neither valence bond nor chiral magnetic order, suggesting a paramagnetic nature which resembles gapless spin liquid. The calculation also finds that the pair- ing correlation function monotonically decreases with increasing U and thus the superconductivity is unlikely in the intermediate phase.
We present the continued fraction method (CFM) as a new microscopic approximation to the spectral density of the Hubbard model in the correlated metal phase away from half filling. The quantity expanded as a continued fraction is the single particle Green function. Leading spectral moments are taken into account through a set of real expansion coefficients, as known from the projection technique. The new aspect is to add further stages to the continued fraction, with complex coefficients, thus defining a terminator function. This enables us to treat the entire spectral range of the Green function on equal footing and determine the energy scale of the Fermi liquid quasiparticles by minimizing the total energy. The solution is free of phenomenological parameters and remains well defined in the strong coupling limit, near the doping controlled metal-insulator transition. Our results for the density of states agree reasonably with several variants of the dynamical mean field theory. The CFM requires minimal numerical effort and can be generalized in several ways that are interesting for applications to real materials.
We investigate the phases of the ionic Hubbard model in a two-dimensional square lattice using determinant quantum Monte Carlo (DQMC). At half-filling, when the interaction strength or the staggered potential dominate we find Mott and band insulators, respectively. When these two energies are of the same order we find a metallic region. Charge and magnetic structure factors demonstrate the presence of antiferromagnetism only in the Mott region, although the externally imposed density modulation is present everywhere in the phase diagram. Away from half-filling, other insulating phases are found. Kinetic energy correlations do not give clear signals for the existence of a bond-ordered phase.
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