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arXiv:1912.05053 · AIP conference proceedings

Ferromagnetically ordered metal in the single-band hubbard model

Akihisa Koga, Yusuke Kamogawa, Joji Nasu

Published Jan 1, 2021• 1 citation
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Abstract

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.

DOI
10.1063/5.0036968

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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.
We study a ferromagnetic instability in a doped single-band Hubbard model by means of dynamical mean-field theory with the continuous-time quantum Monte Carlo simulations. Examining the effect of the strong correlations in the system on the hypercubic and Bethe lattice, we find that the ferromagnetically ordered state appears in the former, while it does not in the latter. We also reveal that the ferromagnetic order is more stable in the case that the noninteracting density of states (DOS) exhibits a slower decay in the high-energy region. The present results suggest that, in the strong-coupling regime, the high-energy part of DOS plays an essential role for the emergence of the ferromagnetically ordered state, in contrast to the Stoner criterion justified in the weak-interaction limit.
We investigate an SU(3) Fermi-Hubbard model on a hypercubic lattice at finite temperatures, combining dynamical mean-field theory with continuous-time quantum Monte Carlo simulations. Taking strong correlations into account carefully, we find a ferromagnetically ordered state, in which one of the three components becomes dominant, when holes are doped away from one-third filling. Furthermore, we demonstrate that this ferromagnetically ordered phase undergoes a first-order transition to a paramagnetic state. We clarify the stability of the ferromagnetically ordered state against interaction strength, hole doping, and temperatures. The relevance of generalized Nagaoka ferromagnetism is also addressed, by comparing the results on the Bethe lattice.
We study the ferromagnetic instability in an SU(NNN) Fermi-Hubbard model on the hypercubic lattice. Combining dynamical mean-field theory with continuous-time quantum Monte Carlo simulations, we find that, in the strong-coupling regime at low temperatures, ferromagnetically ordered (FM) states develop away from the commensurate fillings. In the particle-doped SU(333) system near one-third filling, the FM state is accompanied by a spontaneous flavor-selective Mott state, where two of the three flavors are Mott insulating while the remaining flavor is metallic. Since particles in the metallic flavor can almost freely move on the lattice without correlation effects, the ordered state is stabilized by the kinetic-energy gain of the doped particles. This is similar to the generalized Nagaoka ferromagnetism discussed in the one-hole-doped system at one-third filling. In the SU(444) case, we find that six distinct types of FM states appear as the particle density varies. The results uncover the nature of the FM state in the SU(NNN) Fermi-Hubbard systems and highlight the rich magnetic behavior enabled by enlarged internal symmetries.
We investigate the sampling efficiency in a segment-based continuous-time hybridization-expansion quantum Monte Carlo solver within dynamical mean-field theory for the doped SU(3) Fermi-Hubbard model. Focusing on the low-temperature and strong-coupling regime, where a ferromagnetic state appears upon hole doping away from one-third filling, we compare several update schemes. Adding the double-flip update to the basic local update yields the smallest integrated autocorrelation time of the majority-flavor occupation in the ferromagnetic regime, whereas adding the flavor-permutation update is the most effective in the paramagnetic regime. We further clarify the origin of this difference by analyzing the characteristic occupation changes caused by accepted updates.
Using the determinant quantum Monte Carlo method, we study the magnetic susceptibility in the parameter space of the on-site interaction UUU, temperature TTT, 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.
We perform a numerical study using both determinantal and constrain path Monte Carlo methods to investigate the magnetic and pairing properties of the single-band Hubbard model on the triangular lattice. We find that the system in the filling region ⟨n⟩=1.5−−1.85⟨n⟩=1.5--1.85⟨n⟩=1.5−−1.85 shows a short-ranged ferromagnetic correlation, and the on-site Coulomb interaction tends to strengthen ferromagnetic fluctuation slightly. It is shown that the large density of states near the Van Hove singularity point plays an important role in the enhancement of ferromagnetic fluctuation. In the ferromagnetic region, we observe that the fff-wave pairing correlation tends to increase faster than other pairing correlations. However, it is subtle to stabilize the fff-wave pairing since the effective pairing interaction was found to be very small.