Role of Frustration and Dimensionality in the Hubbard Model on the Stacked Square Lattice: Variational Cluster Approach

TL;DR

This study uses the variational cluster approach to explore how frustration and dimensionality affect magnetic phases in the Hubbard model on a stacked square lattice, revealing complex phase transitions and the disappearance of paramagnetic states.

Contribution

It provides a detailed phase diagram of the Hubbard model considering frustration and interlayer coupling, highlighting the nature of magnetic transitions and the conditions for paramagnetic Mott insulating states.

Findings

Antiferromagnetic order appears at small interlayer hopping and low frustration.

Paramagnetic Mott insulator exists between magnetic phases for certain parameters.

Transitions between magnetic and paramagnetic states are of second and first order, depending on conditions.

Abstract

Using variational cluster approach, we study influence of frustration and dimensionality on magnetic properties in the ground state of Hubbard model on a stacked square lattice in the large $U$ region (U/t=10), by changing the next-nearest-neighbor hopping, $t^{\prime}$, and the interlayer hopping, $t_{\perp}$. For small $t_{\perp}<t^{\ast}_{\perp}$ with $t^{\ast}_{\perp}/t{\approx}0.44$, antiferromagnetic long-range order appears at small $t^{\prime}<t^{\prime}_{c_{1}}$, and collinear magnetic long-range order at large $t^{\prime}>t^{\prime}_{c_{2}}$. They are separated by a paramagnetic Mott insulating state which appears in the parameter region $t^{\prime}_{c_{1}}<t^{\prime}<t^{\prime}_{c_{2}}$. For large $t_{\perp}>t^{\ast}_{\perp}$, the paramagnetic Mott insulating state disappears and a direct transition between antiferromagnetic state and collinear magnetic state occurs at $t^{\prime}=t^{\prime}_{c_{3}}$. We also find that the transition from the antiferromagnetic state to the paramagnetic Mott insulating state is of the second-order and that from the collinear magnetic state to the paramagnetic Mott insulating or the antiferromagnetic state is of the first-order.