[Paper Review] Dynamical Cluster Approximation Study of Electron Localization in the Extended Hubbard Model

Hanna Terletska, Sergei Iskakov+2 more|arXiv (Cornell University)|May 19, 2021

Physics of Superconductivity and Magnetism88 references22 citations

TL;DR

This study employs the dynamical cluster approximation (DCA) on a 2×2 cluster to investigate electron localization in the extended Hubbard model, revealing that nearest-neighbor repulsion V induces screening of the onsite interaction U, shifting the Mott transition to larger U values. The work distinguishes between Mott localization (driven by U) and charge-ordering (CO) localization (driven by V), showing CO insulators are weakly correlated with band-like gaps, while Mott insulators exhibit strong correlations and reduced double occupancy.

ABSTRACT

We perform a detailed study of the phase transitions and mechanisms of electron localization in the extended Hubbard model using the dynamical cluster approximation on a $2 imes 2$ cluster. We explore the interplay of charge order and Mott physics. We find that a nearest-neighbor Coulomb interaction $V$ causes "screening" effects close to the Mott phase transition, pushing the phase boundary to larger values of $U$. We also demonstrate the different effects of $V$ on correlations in metallic and insulating regimes and document the different correlation aspects of charge order and Mott states.

Motivation & Objective

• To understand the interplay between Mott localization and charge ordering (CO) in the extended Hubbard model with non-local interactions.
• To investigate how nearest-neighbor Coulomb repulsion V modifies the Mott metal-insulator transition and electron localization mechanisms.
• To clarify the distinct correlation effects in metallic and insulating regimes under varying U and V.
• To determine whether CO insulators are strongly correlated or band-like, contrasting them with Mott insulators.

Proposed method

• The extended Hubbard model is formulated with onsite U and nearest-neighbor V interactions on a 2D square lattice, with t = 1 as the energy unit.
• The dynamical cluster approximation (DCA) is used to map the lattice problem onto a 2×2 cluster embedded in a self-consistently determined effective medium.
• DCA enforces self-consistency between the cluster Green’s function and the coarse-grained lattice Green’s function over Nc/N momentum patches.
• The continuous-time auxiliary field (CT-AUX) quantum solver is applied to the cluster problem, generalized to handle non-local V interactions.
• Key observables such as double occupancy, self-energy, and spectral functions are computed to analyze correlation effects and phase transitions.

Experimental results

Research questions

• RQ1 How does the nearest-neighbor interaction V affect the phase boundary of the Mott metal-insulator transition in the extended Hubbard model?
• RQ2 What are the distinct correlation signatures of Mott localization versus charge-ordering (CO) localization?
• RQ3 How does V influence double occupancy and self-energy in metallic and insulating phases?
• RQ4 Is the CO insulator phase strongly correlated or band-like, and how does it differ from the Mott insulator?
• RQ5 To what extent does V screen the onsite interaction U, leading to a shift in the Mott transition?

Key findings

• The inclusion of V causes a screening effect that effectively reduces the onsite interaction U, shifting the Mott transition to larger U values.
• In the metallic regime, increasing V reduces correlations, evidenced by a decreasing self-energy and increasing double occupancy.
• In the insulating regime, the CO phase is weakly correlated with a band-like gap, contrasting with the strongly correlated Mott insulator characterized by a reduced quasi-particle peak and increased self-energy.
• The CO insulator phase exhibits a larger gap than the Mott insulator and is not driven by strong local correlations, indicating a fundamentally different localization mechanism.
• The V-induced phase transition to CO occurs at Vc = U/z in the mean-field limit, but DCA reveals non-mean-field corrections due to dynamic fluctuations.
• Double occupancy increases with V in the CO phase, while it decreases with U in the Mott phase, highlighting the opposite role of U and V in electron localization.