Two-site Dynamical Mean-field Theory Research Articles

Quantum-classical simulation of two-site dynamical mean-field theory on noisy quantum hardware

We report on a quantum–classical simulation of the single-band Hubbard model using two-site dynamical mean-field theory (DMFT). Our approach uses IBM’s superconducting qubit chip to compute the zero-temperature impurity Green’s function in the time domain and a classical computer to fit the measured Green’s functions and extract their frequency domain parameters. We find that the quantum circuit synthesis (Trotter) and hardware errors lead to incorrect frequency estimates, and subsequently to an inaccurate quasiparticle weight when calculated from the frequency derivative of the self-energy. These errors produce incorrect hybridization parameters that prevent the DMFT algorithm from converging to the correct self-consistent solution. To avoid this pitfall, we compute the quasiparticle weight by integrating the quasiparticle peaks in the spectral function. This method is much less sensitive to Trotter errors and allows the algorithm to converge to self-consistency for a half-filled Mott insulating system after applying quantum error mitigation techniques to the quantum simulation data.

Mott Transition in the Mass Imbalanced Ionic Hubbard Model at Half Filling

The Mott - Hubbard metal - insulator transition in the half-filled mass imbalanced ionic Hubbard model is investigated using the two-site dynamical mean field theory. We find that for a fixed mass imbalanced parameter r the critical interaction Uc increases when the ionic energy \(\Delta\) is increased. In the other hand, for a fixed \(\Delta\), \(U_c\) decreases with increasing the mass imbalance. We also show the existence of BI phase in the system for the case \(\Delta \ne 0\), \(U=0\) and calculate the staggered charge density \(n_B − n_A\) as a function of the interaction for different values of the mass imbalance. Our results in the limiting cases (\(r = 1\); \(\Delta \ne 0\) or/and \(\Delta = 0\); \(r\ne 1\)) are in good agreement with those obtained from full dynamical mean field theory.

Two-component Fermions in Optical Lattice with Spatially Alternating Interactions

We investigate two-component mass-imbalanced fermions in an optical lattice with spatially modulated interactions by using two-site dynamical mean field theory. At half-filling and zero temperature, the phase diagram of the system is analytically obtained, in which the metallic region is reduced with increasing the mass imbalance. The ground-state properties of the fermionic system are discussed from the behaviors of both the spin-dependent quasi-particle weight at the Fermi level and the double occupancy for each sublattice as functions of the local interaction strengths for various values of the mass imbalance.

Critical behavior near the Mott transition in the half-filled asymmetric Hubbard model

We study the half-filled asymmetric Hubbard model within the two-site dynamical mean field theory. At zero temperature, explicit expressions of the critical interaction Uc for the Mott transition and the local self-energy are analytically derived. Critical behavior of the quasiparticle weights and the double occupancy are obtained analytically as functions of the on-site interaction U and the hopping asymmetry r. Our results are in good agreement with the ones obtained by much more sophisticated theory.

Mott transition in the dynamic Hubbard model within slave boson mean-field approach

At zero temperature, the Kotliar–Ruckenstein slave boson mean-field approach is applied to the dynamic Hubbard model. In this paper, the influences of the dynamics of the auxiliary boson field on the Mott transition are investigated. At finite boson frequency, the Mott-type features of the Hubbard model is found to be enhanced by increasing the pseudospin coupling parameter g. For sufficiently large pseudospin coupling g, the Mott transition occurs even for modest values of the bare Hubbard interaction U. The lack of electron–hole symmetry is highlighted through the quasiparticle weight. Our results are in good agreement with the ones obtained by two-site dynamical mean-field theory and determinant quantum Monte Carlo simulation.

Coherent potential approximation study of the Mott transition in optical lattice system with site-dependent interactions

We study the Mott transition in the half-filled Hubbard model with spatially alternating interactions by means of the coherent potential approximation. The phase boundary between metallic and insulating phases at zero temperature is derived and the nature of the Mott states is also considered. Our results are in good agreement with the ones recently obtained by the two-site dynamical mean-field theory.

LOCAL ENTANGLEMENT ENTROPY AT THE MOTT METAL-INSULATOR TRANSITION IN INFINITE DIMENSIONS

We study the critical behavior of the single-site entanglement entropy S at the Mott metal-insulator transition in infinite-dimensional Hubbard model. For this model, the entanglement between a single site and rest of the lattice can be evaluated exactly, using the dynamical mean-field theory (DMFT). Both the numerical solution using exact diagonalization and the analytical one using two-site DMFT gives S - Sc∝ α log2[(1/2 - Dc)/Dc](U - Uc), with Dcthe double occupancy at Ucand α < 0 being different on two sides of the transition.

Metal–Insulator Transition in Optical Lattice System with Site-Dependent Interactions

We investigate the half-filled Hubbard model with spatially alternating interactions by means of the two-site dynamical mean-field theory. It is found that a single Mott transition occurs when two kinds of interactions are increased. This implies that the different interactions are essentially irrelevant at the critical point. The nature of the Mott states is also addressed.

Erratum: Two-site dynamical mean field theory for the dynamic Hubbard model [Phys. Rev. B82, 155122 (2010)

Received 28 October 2010DOI:https://doi.org/10.1103/PhysRevB.82.209904©2010 American Physical Society

Electron-Hole Asymmetry in the Dynamic Hubbard Model

The two-site dynamical mean field theory (DMFT) is applied to the dynamic Hubbard model. This model takes into account a correction to the Coulomb interaction due to particle double occupancy by using an Ising-like degree of freedom to represent an associated boson field. At finite boson frequency, the appearance of a Mott gap is found to be enhanced even though it shows a metallic phase with the same bare on-site interaction U in the conventional Hubbard model. A lack of electron-hole symmetry is observed through the quasi-particle weight versus particle density.

Two-site dynamical mean field theory for the dynamic Hubbard model

At zero temperature, two-site dynamical mean field theory is applied to the Dynamic Hubbard model. The Dynamic Hubbard model describes the orbital relaxation that occurs when two electrons occupy the same site, by using a two-level boson field at each site. At finite boson frequency, the appearance of a Mott gap is found to be enhanced even though it shows a metallic phase with the same bare on-site interaction $U$ in the conventional Hubbard model. The lack of electron-hole symmetry is highlighted through the quasi-particle weight and the single particle density of states at different fillings, which qualitatively differentiates the dynamic Hubbard model from other conventional Hubbard-like models.

Optical Spectra and Exciton in Correlated Insulators in Electron–Hole Systems

We study the optical properties of an electron–hole two-band Hubbard model with interactions of electron–electron (hole–hole) repulsion U and electron–hole attraction U '. In the case of two types of correlated insulators at half filling, viz. , the Mott–Hubbard type and the biexciton type, interband linear absorption/gain spectra including excitonic effects are calculated analytically using two-site dynamical mean-field theory and ladder approximation. We show that an exciton-like peak structure emerges because of an “exciton” in the sea of correlated fermions when U ' is larger than a certain critical value. The binding energy of the photoinduced excitonic bound state and the spectral intensity are evaluated as a function of U '. The emergence and absence of the exciton-like peak suggests that there are two different insulating mechanisms in the Mott–Hubbard insulating state of the electron–hole system: one is attributable to only U and the other is attributable to both U and U '; the latter is called t...

Superfluid-insulator transition of two-band fermionic atom systems in optical lattices

We study the multiband effects on ultracold fermionic atoms in optical lattices by two-site dynamical mean-field theory. We find that the density wave state becomes stable for a small orbital splitting region. As the orbital splitting is increased, the transition from the density wave state to the superfluid state occurs. By systematically changing the orbital splitting and the attractive interaction, we obtain the phase diagram at half-filling.

Multiband effects on fermionic atoms in optical lattices

The superfluid-insulator transition of two-band fermionic atom systems in optical lattices is investigated by the two-site dynamical mean-field theory. Because of the spin-flip and pair-hopping interactions, orbital fluctuations are enhanced, leading to the suppression of the Mott insulating state. The numerical results are discussed in comparison with the effective boson model.

Multiband-driven superfluid-insulator transition of fermionic atoms in optical lattices: A dynamical mean-field-theory study

The superfluid-insulator transition of fermionic atoms in optical lattices is investigated by two-site dynamical mean-field theory. It is shown that the Mott transition occurs as a result of multiband effects. The quasiparticle weight in the superfluid state decreases significantly as the system approaches the Mott transition point. By changing the interaction and the orbital splitting, we obtain the phase diagram at half filling. The numerical results are discussed in comparison with the effective boson model.

Optical spectra and exciton Mott transition in correlated electron–hole systems

Optical properties in the insulating states of three-dimensional electron–hole systems are studied using a two-band Hubbard model with both repulsion U and attraction U ′ . For two types of insulators, the Mott–Hubbard type and the biexciton type at half-filling, in particular, interband absorption spectra are calculated analytically within the two-site dynamical mean-field theory and ladder approximation. We show that an excitonic peak structure appears due to an “exciton” in the sea of correlated fermions when U ′ is larger than a certain critical value.

Phase diagram and quasiparticle properties of the Hubbard model within cluster two-site dynamical mean-field theory

We present a cluster dynamical mean-field treatment of the Hubbard model on a square lattice to study the evolution of magnetism and quasiparticle properties as the electron filling and interaction strength are varied. Our approach for solving the dynamical mean-field equations is an extension of Potthoff's "two-site" method [Phys. Rev. B. 64, 165114 (2001)] where the self-consistent bath is represented by a highly restricted set of states. As well as the expected antiferromagnetism close to half filling, we observe distortions of the Fermi surface. The proximity of a van Hove point and the incipient antiferromagnetism lead to the evolution from an electron-like Fermi surface away from the Mott transition, to a hole-like one near half-filling. Our results also show a gap opening anisotropically around the Fermi surface close to the Mott transition (reminiscent of the pseudogap phenomenon seen in the cuprate high-Tc superconductors). This leaves Fermi arcs which are closed into pockets by lines with very small quasiparticle residue.

Two-site dynamical mean-field theory

It is shown that a minimum realization of the dynamical mean-field theory (DMFT) can be achieved by mapping a correlated lattice model onto an impurity model in which the impurity is coupled to an uncorrelated bath that consists of a single site only. The two-site impurity model can be solved exactly. The mapping is approximate. The self-consistency conditions are constructed in a way that the resulting ``two-site DMFT'' reduces to the previously discussed linearized DMFT for the Mott transition. It is demonstrated that a reasonable description of the mean-field physics is possible with a minimum computational effort. This qualifies the simple two-site DMFT for a systematic study of more complex lattice models which cannot be treated by the full DMFT in a feasible way. To show the strengths and limitations of the new approach, the single-band Hubbard model is investigated in detail. The predictions of the two-site DMFT are compared with results of the full DMFT. Internal consistency checks are performed which concern the Luttinger sum rule, other Fermi-liquid relations and thermodynamic consistency.