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arXiv:2209.01048 · Physical review. B./Physical review. B

Thermodynamic, magnetic, and transport properties of the repulsive Hubbard model on the kagome lattice

Andressa R. Medeiros-Silva, Natanael C. Costa, Thereza Paiva

Published Jan 20, 2023• 12 citations
arXivHTMLPDF

Abstract

Over the past few decades, magnetic frustration has been under intense debate due to its unusual properties. For instance, frustration in the kagome lattice suppresses long-range spin correlations, and it is expected to be a candidate for a spin liquid system. Therefore, with the advent of experiments with ultracold atoms, the interest in frustrated geometries has increased. Given this, in the present work we investigate the repulsive Hubbard model on the kagome lattice using unbiased quantum Monte Carlo simulations. We examine its thermodynamic properties, as well as the magnetic and transport response of the system at finite temperatures and different values of the repulsive interaction. From these results, we discuss the possible occurrence of adiabatic cooling, a quite important feature in ultracold systems, and the presence of a metal-to-insulator transition at a finite interaction strength. Our findings may guide future experiments in ultracold fermionic atoms on the kagome lattice.

DOI
10.1103/physrevb.107.035134

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Over the past few decades, magnetic frustration has been under intense debate due to its unusual properties. For instance, frustration in the kagome lattice suppresses long-range spin correlations, and it is expected to be a candidate for a spin liquid system. Therefore, with the advent of experiments with ultracold atoms, the interest in frustrated geometries has increased. Given this, in the present work we investigate the repulsive Hubbard model on the kagome lattice using unbiased quantum Monte Carlo simulations. We examine its thermodynamic properties, as well as the magnetic and transport response of the system at finite temperatures and different values of the repulsive interaction. From these results, we discuss the possible occurrence of adiabatic cooling, a quite important feature in ultracold systems, and the presence of a metal-to-insulator transition at a finite interaction strength. Our findings may guide future experiments in ultracold fermionic atoms on the kagome lattice.
The Kagome lattice Fermi-Hubbard model is one of the most physically rich, and at the same time most challenging, models to study in strongly-correlated physics. Among its special features are geometric frustration and a flat energy band that create conditions favorable to ferromagnetism near the band insulating limit. Here, we utilize two exact finite-temperature methods, the numerical linked-cluster expansion and the determinant quantum Monte Carlo, to study the extent as well as doping and interaction dependence of ferromagnetic correlations and other thermodynamic properties of the model. We find that repulsive interactions enhance ferromagnetic correlations at high electron densities and that increasing the interaction strength, extends the region with strong ferromagnetic correlations towards half filling, smoothly connecting it to Nagaoka ferromagnetism near the Mott insulating region. We also use the charge compressibility to obtain an accurate estimate for the critical interaction strength for the metal-insulator transition at half filling. These results improve our understanding of the magnetic tendencies of the model away from half filling and pave the way for further studies, including with ultracold atoms in optical lattices.
We study magnetic, transport, and thermodynamic properties of the half-filled two-dimensional (2D)(2D)(2D) Hubbard model with layered distributed repulsive interactions using unbiased finite temperature quantum Monte Carlo simulations. Antiferromagnetic long-ranged correlations at T=0T=0T=0 are confirmed by means of the magnetic structure factor and the onset of short-ranged ones is at a minimum temperature, which can be obtained by peaks in susceptibility and specific heat following a random-phase-approximation (RPA) prediction. We also show that transport is affected in the large interaction limit and is enhanced in the nonrepulsive layers suggesting a change of dimensionality induced by increased interactions. Lastly, we show that by adiabatically switching the interactions in layered distributed patterns reduces the overall temperature of the system with a potential application in cooling protocols in cold atoms systems.
The aim of this thesis is the investigation of electronic correlations in the intermediate region between the metallic and insulating phase of the frustrated Kagome lattice. Most previous studies address the ground state of the Heisenberg model on the Kagome lattice, and therefore only the purely insulating phase. However, we go a step further by studying the Hubbard model on the Kagome lattice and thus including metallic contributions. We solve the Hubbard model with the determinant quantum Monte Carlo (DQMC) method and compare to results of the dynamical mean field theory (DMFT). First we study the half-filled system across the range of the Mott-Hubbard metal-insulator transition, and then the electron doped system, where the chemical potential is in the center of the flat band. In various post-processing steps we calculate the k-integrated spectral functions, the k-resolved spectral functions, the equal-time magnetic structure factors and the dynamic magnetic structure factors.
Finite-temperature properties of the frustrated Hubbard model are theoretically examined by using the recently proposed thermal pure quantum state, which is an unbiased numerical method for finite-temperature calculations. By performing systematic calculations for the frustrated Hubbard model, we show that the geometrical frustration controls the characteristic energy scale of the metal-insulator transitions. We also find that entropy remains large even at moderately high temperature around the region where the quantum spin liquid is expected to appear at zero temperature. We propose that this is a useful criterion whether the target systems have a chance to be the quantum spin liquid or the non-magnetic insulator at zero temperature.
The interplay of disorder and strong correlations in quantum many-body systems remains an open question. That is despite much progress made in recent years with ultracold atoms in optical lattices to better understand phenomena such as many-body localization or the effect of disorder on Mott metal-insulator transitions. Here, we utilize the numerical linked-cluster expansion technique, extended to treat disordered quantum lattice models, and study exact thermodynamic properties of the disordered Fermi-Hubbard model on the square and cubic geometries. We consider box distributions for the disorder in the onsite energy, the interaction strength, as well as the hopping amplitude and explore how energy, double occupancy, entropy, heat capacity, and magnetic correlations of the system in the thermodynamic limit evolve as the strength of disorder changes. We compare our findings with those obtained from determinant quantum Monte Carlo simulations and discuss the relevance of our results to experiments with cold fermionic atoms in optical lattices.
We study the phase diagram of the two-dimensional repulsive Hubbard model with spin-dependent anisotropic hopping at half filling. The system develops Ising antiferromagnetic long-range order already at infinitesimal repulsive interaction strength in the ground state. Outside the perturbative regime, unbiased predictions for the critical temperatures of the Ising antiferromagnet are made for representative interaction values by a variety of state-of-the-art quantum Monte Carlo methods, including the diagrammatic Monte Carlo, continuous-time determinantal Monte Carlo, and path-integral Monte Carlo methods. Our findings are relevant to ultracold atom experiments in the ppp orbital or with spin-dependent optical lattices.