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Register a new userRotationally invariant slave-boson and density matrix embedding theory: A unified framework and a comparative study on the 1D and 2D Hubbard Model
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We present detailed benchmark ground-state calculations of the one- and two-dimensional Hubbard model utilizing the cluster extensions of the rotationally invariant slave-boson (RISB) mean-field theory and the density matrix embedding theory (DMET). Our analysis shows that the overall accuracy and the performance of these two methods are very similar. Furthermore, we propose a unified computational framework that allows us to implement both of these techniques on the same footing. This provides us with a new line of interpretation and paves the ways for developing systematically new generalizations of these complementary approaches.
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We examine the performance of the density matrix embedding theory (DMET) recently proposed in [G. Knizia and G. K.-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)]. The core of this method is to find a proper one-body potential that generates a good trial wave function for projecting a large scale original Hamiltonian to a local subsystem with a small number of basis. The resultant ground state of the projected Hamiltonian can locally approximate the true ground state. However, the lack of the variational principle makes it difficult to judge the quality of the choice of the potential. Here we focus on the entanglement spectrum (ES) as a judging criterion; accurate evaluation of the ES guarantees that the corresponding reduced density matrix well reproduces all physical quantities on the local subsystem. We apply the DMET to the Hubbard model on the one-dimensional chain, zigzag chain, and triangular lattice and test several variants of potentials and cost functions. It turns out that ES serves as a more sensitive quantity than the energy and double occupancy to probe the quality of the DMET outcomes. A symmetric potential reproduces the ES of the phase that continues from a noninteracting limit. The Mott transition as well as symmetry-breaking transitions can be detected by the singularities in the ES. However, the details of the ES in the strongly interacting parameter region depends much on these variants, meaning that the present DMET algorithm allowing for numerous variant is insufficient to fully characterize the particular phases that require characterization by the ES.
We employ the cluster slave-spin method to investigate systematically the ground state properties of the Hubbard model on a square lattice with doping $delta$ and coupling strength $U$ being its parameters. In addition to a crossover reflected in the behavior of the antiferromagnetic gap $Delta_{text{AFM}}$, this property can also be observed in the energetics of the cluster slave-spin Hamiltonian -- the antiferromagnetism at small $U$ is due to the potential energy gain while that in the strong coupling limit is driven by the kinetic energy gain, which is consistent with the results from the cluster dynamical mean-field theory calculation and the quantum Monte Carlo simulation. We find the interaction $U_{c}$ for the crossover in the AFM state, separating the weak- and strong- coupling regimes, almost remains unchanged upon doping, and it is smaller than the critical coupling strength $U_{text{Mott}}$ for the first-order metal-insulator Mott transition in the half-filled paramagnetic state. At half-filling, a relationship between the staggered magnetization $M$ and $Delta_{text{AFM}}$ is established in the small $U$ limit to nullify the Hartree-Fock theory, and a first-order Mott transition in the paramagnetic state is substantiated, which is characterized by discontinuities and hystereses at $U_{text{Mott}}=10t$. Finally, an overall phase diagram in the $U$-$delta$ plane is presented, which is composed of four regimes: the antiferromagnetic insulator, the antiferromagnetic metal with the compressibility $kappa>0$ or $kappa<0$, and the paramagnetic metal, as well as three phase transitions: (i) From the antiferromagnetic metal to the paramagnetic metal, (ii) between the antiferromagnetic metal phases with positive and negative $kappa$, and (iii) separating the antiferromagnetic insulating phase from the antiferromagnetic metal phase.
We determine the ground-state phase diagram of the three-band Hubbard model across a range of model parameters using density matrix embedding theory. We study the atomic-scale nature of the antiferromagnetic (AFM) and superconducting (SC) orders, explicitly including the oxygen degrees of freedom. All parametrizations of the model display AFM and SC phases, but the decay of AFM order with doping is too slow compared to the experimental phase diagram, and further, coexistence of AFM and SC orders occurs in all parameter sets. The local magnetic moment localizes entirely at the copper sites. The magnetic phase diagram is particularly sensitive to $Delta_{pd}$ and $t_{pp}$, and existing estimates of the charge transfer gap $Delta_{pd}$ appear too large in so-called minimal model parametrizations. The electron-doped side of the phase diagram is qualitatively distinct from hole-doped side and we find an unusual two-peak structure in the SC in the full model parametrization. Examining the SC order at the atomic scale, within the larger scale $d_{x^2 - y^2}$-wave SC pairing order between Cu-Cu and O-O, we also observe a local $p_{x (y)}$ [or $d_{xz (yz)}$]-symmetry modulation of the pair density on the Cu-O bonds. Our work highlights some of the features that arise in a three-band versus one-band picture, the role of the oxygen degrees of freedom in new kinds of atomic-scale SC orders, and the necessity of re-evaluating current parametrizations of the three-band Hubbard model.
We introduce Extended Density Matrix Embedding Theory (EDMET), a static quantum embedding theory explicitly self-consistent with respect to two-body environmental interactions. This overcomes the biggest practical and conceptual limitation of more traditional one-body embedding methods, namely the lack of screening and treatment of long-range correlations. This algebraic zero-temperature embedding augments the correlated cluster with a minimal number of bosons from the random phase approximation, and admits an analytic approach to build a self-consistent Coulomb-exchange-correlation kernel. For extended Hubbard models with non-local interactions, this leads to the accurate description of phase transitions, static quantities and dynamics. We also move towards {em ab initio} systems via the Parriser--Parr--Pople model of conjugated coronene derivatives, finding good agreement with experimental optical gaps.
In this Letter we study the periodic Anderson model, employing both the slave-boson and the X-boson approaches in the mean field approximation. We investigate the breakdown of the slave-boson at intermediate temperatures when the total occupation number of particles Nt = Nf + Nc is keep constant, where Nf and Nc are respectively the occupation numbers of the localized and conduction electrons, and we show that the high-temperature limit of the slave-boson is Nf = Nc = Nt /2. We also compare the results of the two approaches in the Kondo limit and we show that at low-temperatures the X-boson exhibits a phase transition, from the Kondo heavy fermion (K-HF) regime to a local moment magnetic regime (LMM).
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