Kagome metals exhibit a rich interplay of topology, electronic correlations, and lattice dynamics. Recent discoveries of Kagome materials with a flat band near the Fermi level have revealed a variety of correlated electronic phases. However, elucidating their microscopic origin remains challenging, as realistic descriptions require accounting for multiple orbitals and competing interactions on an equal footing. To disentangle correlation effects from material-specific details and identify the essential physics of the flat-band regime, we study the single-orbital Kagome-Hubbard model at flat-band fillings using dynamical mean-field theory. We find strong signatures of flat-band ferromagnetism, consistent with exact and mean-field ground-state results. Moreover, we uncover an unconventional quasi-ordered phase in which a partially filled spin-polarized flat band pinned at the Fermi level gives rise to persistent local spin fluctuations down to zero temperature, in striking contrast to the classical behavior expected for a conventional ferromagnet. Our results demonstrate that these anomalous fluctuations are an intrinsic consequence of the flat-band degeneracy and establish a minimal framework for understanding correlation effects in flat-band Kagome systems.
Analog quantum simulation provides a unique toolkit to investigate quantum many-body problems of whose solutions may be incredibly challenging. In particular, using ultracold fermionic atoms in optical lattices it realizes the Fermi Hubbard model, which is a fundamental model in condensed matter physics exhibiting properties relevant to many intriguing strongly-correlated systems. However, most quantum simulators of the Hubbard model have so far restricted to the square geometries. In addition, access to low temperatures where the exotic quantum phases are predicted to develop has still remained elusive. In this thesis, we engineer a novel optical lattice with dynamically tunable geometries and significantly reduced technical noises. We extend for the first time the study of quantum magnetism into the exotic phases in a Fermi Hubbard system with tunable geometric frustration. As we continuously tune our system from a square to a triangular lattice geometry, we observe a transition from a Néel antiferromagnet to a 120-degree spin spiral state. We then study, again for the first time, how doping affects a frustrated quantum magnet. To our surprise, we found an emergent ferromagnetic state with strong particle doping, which is absent on the hole-doped side and is in stark contrast with the particle-hole symmetric doping dependence in a square lattice. To shed light on the role of itinerant dopants in the emergence of these new magnetic properties, we furthermore leverage the unique single-particle resolution capabilities of our platform to probe higher-order density and spin correlations. These measurements hint at a new type of magnetism induced by kinetic frustration, which manifests as local antiferromagnetic correlations around hole dopants and and ferromagnetic correlations around particle dopants. Unlike magnetism induced by exchange or superexchange interactions, the energy associated with this mechanism is the kinetic energy, closely related to the famous rigorous results by Nagaoka. Furthermore, the dynamical tunability of the lattice allows adibatic engineering of quantum states in optical lattices. We discuss the preliminery efforts to prepare strongly-correlated states with significantly reduced temperatures, which may pave the way towards low temperature states in the Hubbard model.
Abstract Strongly interacting fermionic systems host a variety of interesting quantum many-body states with exotic excitations. For instance, the interplay of strong interactions and the Pauli exclusion principle can lead to Stoner ferromagnetism, but the fate of this state remains unclear when kinetic terms are added. While in many lattice models the fermions’ dispersion results in delocalization and destabilization of the ferromagnet, flat bands can restore strong interaction effects and ferromagnetic correlations. To reveal this interplay, here we propose to study the Hofstadter–Fermi–Hubbard model using ultracold atoms. We demonstrate, by performing large-scale density-matrix renormalization group simulations, that this model exhibits a lattice analog of the quantum Hall (QH) ferromagnet at magnetic filling factor ν = 1. We reveal the nature of the low energy spin-singlet states around ν ≈ 1 and find that they host quasi-particles and quasi-holes exhibiting spin-spin correlations reminiscent of skyrmions. Finally, we predict the breakdown of flat-band ferromagnetism at large fields. Our work paves the way towards experimental studies of lattice QH ferromagnetism, including prospects to study many-body states of interacting skyrmions and explore the relation to high- T c superconductivity.
On a large class of lattices (such as the sawtooth chain, the kagome and the pyrochlore lattices), the quantum Heisenberg and the repulsive Hubbard models may host a completely dispersionless (flat) energy band in the single-particle spectrum. The flat-band states can be viewed as completely localized within a finite volume (trap) of the lattice and allow for construction of many-particle states, roughly speaking, by occupying the traps with particles. If the flat-band happens to be the lowest-energy one, the manifold of such many-body states will often determine the ground-state and low-temperature physics of the models at hand even in the presence of strong interactions. The localized nature of these many-body states makes possible the mapping of this subset of eigenstates onto a corresponding classical hard-core system. As a result, the ground-state and low-temperature properties of the strongly correlated flat-band systems can be analyzed in detail using concepts and tools of classical statistical mechanics (e.g., classical lattice-gas approach or percolation approach), in contrast to more challenging quantum many-body techniques usually necessary to examine strongly correlated quantum systems. In this review, we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field. The main emphasis is made on recent developments which include results for both spin and electron flat-band models. In particular, for flat-band spin systems, we highlight field-driven phase transitions for frustrated quantum Heisenberg antiferromagnets at low temperatures, chiral flat-band states, as well as the effect of a slight dispersion of a previously strictly flat-band due to nonideal lattice geometry. For electronic systems, we discuss the universal low-temperature behavior of several flat-band Hubbard models, the emergence of ground-state ferromagnetism in the square-lattice Tasaki–Hubbard model and the related Pauli-correlated percolation problem, as well as the dispersion-driven ground-state ferromagnetism in flat-band Hubbard systems. Closely related studies and possible experimental realizations of the flat-band physics are also described briefly.
The noninteracting electronic structures of tight-binding models on bipartite lattices with unequal numbers of sites in the two sublattices have a number of unique features, including the presence of spatially localized eigenstates and flat bands. When a uniform on-site Hubbard interaction
U is turned on, Lieb proved rigorously that at half-filling ($\ensuremath{\rho}=1$) the ground state has a nonzero spin. In this paper we consider a ``
CuO2 lattice'' (also known as ``Lieb lattice,'' or as a decorated square lattice), in which ``
d orbitals'' occupy the vertices of the squares, while ``
p orbitals'' lie halfway between two
d orbitals; both
d and
p orbitals can accommodate only up to two electrons. We use exact determinant quantum Monte Carlo (DQMC) simulations to quantify the nature of magnetic order through the behavior of correlation functions and sublattice magnetizations in the different orbitals as a function of
U and temperature; we have also calculated the projected density of states, and the compressibility. We study both the homogeneous (H) case,
Ud=Up, originally considered by Lieb, and the inhomogeneous (IH) case, ${U}_{d}\ensuremath{\ne}{U}_{p}$. For the H case at half-filling, we found that the global magnetization rises sharply at weak coupling, and then stabilizes towards the strong-coupling (Heisenberg) value, as a result of the interplay between the ferromagnetism of like sites and the antiferromagnetism between unlike sites; we verified that the system is an insulator for all
U. For the IH system at half-filling, we argue that the case ${U}_{p}\ensuremath{\ne}{U}_{d}$ falls under Lieb's theorem, provided they are positive definite, so we used DQMC to probe the cases
Up=0,Ud=U and
Up=U,Ud=0. We found that the different environments of
d and
p sites lead to a ferromagnetic insulator when
Ud=0; by contrast,
Up=0 leads to to a metal without any magnetic ordering. In addition, we have also established that at density $\ensuremath{\rho}=1/3$, strong antiferromagnetic correlations set in, caused by the presence of one fermion on each
d site.
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.