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arXiv:2306.06697 · Physical review. B./Physical review. B

Strong ferromagnetic fluctuations in a doped checkerboard lattice

Yue Pan, Runyu Ma, Tianxing Ma

Published Jun 16, 2023• 6 citations
arXivHTMLPDF

Abstract

Using the determinant quantum Monte Carlo method, we study the magnetic susceptibility in the parameter space of the on-site interaction $U$, temperature $T$, electron filling $\ensuremath{\langle}n\ensuremath{\rangle}$, and the frustration control parameter ${t}^{\ensuremath{'}}$ within the Hubbard model on a two-dimensional checkerboard lattice. It is shown that the system exhibits stable and strong ferromagnetic fluctuations about the electron filling $\ensuremath{\langle}n\ensuremath{\rangle}\ensuremath{\ge}1.2$ for different ${t}^{\ensuremath{'}}$, and the ferromagnetic susceptibility is strongly enhanced by the increasing interaction and decreasing temperature. We also discuss the sign problem to clarify which parameter region is accessible and reliable. Our findings not only demonstrate important implications for modulating magnetism in the checkerboard lattice, but will also provide a theoretical platform for a flat-band model that demonstrates a variety of physical properties.

DOI
10.1103/physrevb.107.245126

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We study a ferromagnetic instability in a single-band Hubbard model on the hypercubic lattice away from half filling. Using dynamical mean-field theory with the continuous-time quantum Monte Carlo simulations based on the segment algorithm, we calculate the magnetic susceptibility in the weak and strong coupling regions systematically. We then find how ferromagnetic fluctuations are enhanced when the interaction strength and density of holes are varied. The efficiency of the double flip updates in the Monte Carlo simulations is also addressed.
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Using quantum Monte Carlo techniques we study the magnetic susceptibility of the Hubbard model on a two-dimensional square lattice for values of the coupling U/t ranging from 4 to 20, and as a function of temperature and doping. For U/t=4 the magnetic susceptibility has a maximum at half filling and decreases with doping, in qualitative agreement with recent random-phase-approximation calculations. However, for U/t=10 the susceptibility increases with hole doping near half filling resembling the experimental results obtained for ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Srx{\mathrm{Sr}}_{\mathit{x}}Srx​CuO4{\mathrm{CuO}}_{4}CuO4​. At low electronic density the temperature dependence of the susceptibility is compatible with that of a Fermi liquid.
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We explore the magnetic properties of a two-dimensional Hubbard model on an inhomogeneous square lattice, which provides a platform for tuning the bandwidth of the flat band. In its limit, this inhomogeneous square lattice turns into a Lieb lattice, and it exhibits abundant properties due to the flat band structure at the Fermi level. By using the determinant quantum Monte Carlo simulation, we calculate the spin susceptibility, double occupancy, magnetization, spin structure factor, and effective pairing interaction of the system. It is found that the antiferromagnetic correlation is suppressed by the inhomogeneous strength and that the ferromagnetic correlation is enhanced. Both the antiferromagnetic correlation and ferromagnetic correlation are enhanced as the interaction increases. It is also found that the effective ddd-wave pairing interaction is suppressed by the increasing inhomogeneity. In addition, we also study the thermodynamic properties of the inhomogeneous square lattice, and the calculation of specific heat provides good support for our point. Our intensive numerical results provide a rich magnetic phase diagram over both the inhomogeneity and interaction.