We study ``frustrated'' hopping models, in which at least one energy band, at the maximum or minimum of the spectrum, is dispersionless. The states of the flat band(s) can be represented in a basis which is fully localized, having support on a vanishing fraction of the system in the thermodynamic limit. In the majority of examples, a dispersive band touches the flat band(s) at a number of discrete points in momentum space. We demonstrate that this band touching is related to states which exhibit non-trivial topology in real space. Specifically, these states have support on one-dimensional loops which wind around the entire system (with periodic boundary conditions). A counting argument is given that determines, in each case, whether there is band touching or not, in precise correspondence to the result of straightforward diagonalization. When they are present, the topological structure protects the band touchings in the sense that they can only be removed by perturbations which {\sl also} split the degeneracy of the flat band.
We show that correlated hopping of triplets, which is often the dominant source of kinetic energy in dimer-based frustrated quantum magnets, produces a remarkably strong tendency to form supersolid phases in a magnetic field. These phases are characterized by simultaneous modulation and ordering of the longitudinal and transverse magnetization respectively. Using Quantum Monte Carlo and a semiclassical approach for an effective hard-core boson model with nearest-neighbor repulsion on a square lattice, we prove in particular that a supersolid phase can exist even if the repulsion is not strong …
We numerically demonstrate that a supersolid phase exists in a frustrated hard-core boson system on a triangular lattice over a wide range of interaction strength. In the infinite repulsion (Ising) limit, we establish a mapping to the same problem with unfrustrated hopping, which connects the supersolid to the known results in that case. The weak superfluidity can be destroyed or strongly enhanced by a next nearest neighbor hopping term, which provides valuable information for experimental realization of a supersolid phase on optical lattice.
We study the infinite U Hubbard model with one hole doped away half-filling, in triangular and square lattices with frustrated hoppings that invalidate Nagaoka's theorem, by means of the density matrix renormalization group. We find that these kinetically frustrated models have antiferromagnetic ground states with classical local magnetization in the thermodynamic limit. We identify the mechanism of this kinetic antiferromagnetism with the release of the kinetic energy frustration as the hole moves in the established antiferromagnetic background. This release can occurs in two different ways: …
We study the Mott transition in a frustrated Hubbard model with next-nearest neighbor hopping at half-filling. The interplay between interaction, dimensionality and geometric frustration closes the one-dimensional Mott gap and gives rise to a metallic phase with Fermi surface pockets. We argue that they emerge as a consequence of remnant one-dimensional Umklapp scattering at the momenta with vanishing interchain hopping matrix elements. In this pseudogap phase, enhanced d-wave pairing correlations are driven by antiferromagnetic fluctuations. Within the adopted cluster dynamical mean-field the…
We investigate the ground-state phase diagram of the half-filled one-dimensional Hubbard model with next-nearest-neighbor hopping using the Density-Matrix Renormalization Group technique as well as an unrestricted Hartree-Fock approximation. We find commensurate and incommensurate disordered magnetic insulating phases and a spin-gapped metallic phase in addition to the one-dimensional Heisenberg phase. At large on-site Coulomb repulsion $U$, we make contact with the phase diagram of the frustrated Heisenberg chain, which has spin-gapped phases for sufficiently large frustration. For weak $U$, …
Recently, the field of strongly correlated electrons has begun an intense search for a correlation induced topological insulating phase. An example is the quadratic band touching point which arises in a checkerboard lattice at half-filling, and in the presence of interactions gives rise to topological Mott insulators. In this work, we perform a mean-field theory computation to show that such a system shows instability to topological insulating phases even away from half-filling (chemical potential $μ= 0 $). The interaction parameters consist of on-site repulsion ($ U $), nearest-neighbour repu…
Quantum antiferromagnets with geometrical frustration exhibit rich many-body physics but are hard to simulate by means of classical computers. Although quantum-simulation studies for analyzing such systems are thus desirable, they are still limited to high temperature regions, where interesting quantum effects are smeared out. Here, we propose a feasible protocol to perform analog quantum simulation of frustrated antiferromagnetism with strong quantum fluctuations by using ultracold Bose gases in optical lattices at negative absolute temperatures. Specifically, we show from numerical simulatio…
We study the ground state properties of the geometrically frustrated Hubbard model on the anisotropic checkerboard lattice with nearest-neighbor hopping $t$ and next nearest-neighbor hopping $t'$. By using the path-integral renormalization group method, we study the phase diagram in the parameter space of the Hubbard interaction $U$ and the frustration-control parameter $t'/t$. Close examinations of the effective hopping, the double occupancy, the momentum distribution and the spin/charge correlation functions allow us to determine the phase diagram at zero temperature, where the plaquette-sin…
Frustration and quantum entanglement are two exotic quantum properties in quantum many-body systems. However, despite several efforts, an exact relation between them remains elusive. In this work, we explore the relationship between frustration and quantum entanglement in a physical model describing strongly correlated ultracold bosonic atoms in optical lattices. In particular, we consider the one-dimensional Bose-Hubbard model comprising both nearest-neighbor ($t_{1}$) and frustrated next-nearest neighbor ($t_{2}$) hoppings and examine how the interplay of onsite interaction ($U$) and hopping…
In this work we solve the sign problem of a frustrated quantum impurity model consisting of three quantum spin-half chains interacting through an anti-ferromagnetic Heisenberg interaction at one end. We first map the model into a repulsive Hubbard model of spin-half fermions hopping on three independent one dimensional chains that interact through a triangular hopping at one end. We then convert the fermion model into an inhomogeneous one dimensional model and express the partition function as a weighted sum over fermion worldline configurations. By imposing a pairing of fermion worldlines in …
We study a model of hard-core bosons with frustrated nearest-neighbor hopping ($t$) and repulsion ($V$) on the triangular lattice. We argue for a supersolid ground state in the large repulsion ($V\gg|t|$) limit where a dimer representation applies, by constructing a unitary mapping to the well understood unfrustrated hopping case. This generalized 'Marshall sign rule' allows us to establish the precise nature of the supersolid order by utilizing a recently proposed dimer variational wavefunction, whose correlations can be efficiently calculated using the Grassman approach. By continuity, a sup…
We investigate the zero-temperature quantum phases of a quasi-one-dimensional zigzag chain of dipoles that are polarized in a plane by an external electric field. Since the Hamiltonian contains nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping and interaction terms, this model allows frustration which induces phases that can be interesting and unusual. By using the density matrix renormalization group (DMRG) algorithm, we produce a complex phase diagram. This is an extension of an earlier work by Wang et. al. [Phys. Rev. A 96, 043615 (2017)].
Being dispersionless, flat bands on periodic lattices are solely characterized by their macroscopically degenerate eigenstates: compact localized states (CLSs) in real space and Bloch states in reciprocal space. Based on this property, this work presents a straightforward method to build flat-band tight-binding models with short-range hoppings \emph{on any periodic lattice}. The method consists in starting from a CLS and engineering families of Bloch Hamiltonians as quadratic (or linear) functions of the associated Bloch state. The resulting tight-binding models not only exhibit a flat band, b…
We study the Hubbard model on the AB-stacked bilayer honeycomb lattice with a repulsive onsite interaction U in second order perturbation theory and in self-consistent random phase approximation. We determine the changes in the antiferromagnetic magnetic ordering tendencies due to the real and imaginary parts of the selfenergy at the band crossing points. In particular we present an estimate for the threshold value U* below which the magnetic order is endangered by the splitting of the quadratic band touching points into four Dirac points by an interaction-induced interlayer skew hopping. For …
We investigate the effect of next nearest-neighbour hopping on the zero temperature Drude weight or superfluidity in mesoscopic one-dimensional systems of (a) single particle with quasidisorder (Aubry-André model) and (b) hardcore bosons with nearest-neighbour interaction. We show that there is an interaction-induced enhancement of the Drude weight when the next nearest-neighbour hopping is frustrated for the many-body system. The observed non-monotonic behaviour of the Drude weight occurs because the repulsive interactions first suppress the frustration in the system, leading to a rise in the…
Motivated by the recent experimental realizations of hyperbolic lattices in circuit quantum electrodynamics and in classical electric-circuit networks, we study flat bands and band-touching phenomena in such lattices. We analyze noninteracting nearest-neighbor hopping models on hyperbolic analogs of the kagome and dice lattices with heptagonal and octagonal symmetry. We show that two characteristic features of the energy spectrum of those models, namely the fraction of states in the flat band as well as the number of touching points between the flat band and the dispersive bands, can both be c…
A geometrically frustrated lattice may host frustrated electron spin or charge states that spawn exotic quantum phases. We show that a newly synthesized metal-organic framework of Cu-Hexaaminobenzene [Cu$_3$(HAB)$_2$] exhibits a multi spectra of unusual quantum phases long sought after in condensed matter physics. On one hand, the Cu$^{2+}$ ions form an ideal $S$-1/2 antiferromagnetic kagome lattice. On the other hand, the conjugated-electrons from the organic ligands give rise to completely dispersionless energy bands around the Fermi level, reproducing a frustrated $π_x$-$π_y$ hopping model …
We revisit the effect of local interactions on the quadratic band touching (QBT) of Bernal stacked bilayer graphene models using renormalization group (RG) arguments and quantum Monte Carlo simulations of the Hubbard model. We present an RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased quantum Monte Carlo simulations of the Hubbard mo…
Groundstate magnetism of the one-band Hubbard model on the frustrated square lattice where both nearest-neighbour $t_1$ and next-nearest-neighbour $t_2$ hoppings are considered at half-filling are revisited within mean field approximation. Two new magnetic phases are detected at intermediate strength of Hubbard $U$ and relative strong frustration of $t_2/t_1$, named double-stripe and plaquette antiferromagnetic states, both of which are metallic and stable even at finite temperature and electron doping. The nature of the phase transitions between different phases and the properties of the two …
The pyrochlore iridate In$_2$Ir$_2$O$_7$ is a strong $J_{\mathrm{eff}} = 1/2$ Mott insulator with frustrated magnetism. Despite the large trigonal crystal field, a small admixture of $J_{\mathrm{eff}} = 3/2$ component in the $J_{\mathrm{eff}} = 1/2$ bands and a small splitting of $J_{\mathrm{eff}} = 3/2$ bands are observed as compared with other pyrochlore iridates A$_2$Ir$_2$O$_7$ (A: trivalent cation). We argue that the reduced inter-site hopping between the $J_{\mathrm{eff}} = 1/2$ and the $J_{\mathrm{eff}} = 3/2$ manifold plays a predominant role in the distinct behavior of In$_2$Ir$_2$O$_…
Field-selected seven-site topological magnons in a classical frustrated triangular-lattice K-$Γ$-$Γ'$ magnet
College of Physics Science and Technology, Yangzhou University（扬州大学物理科学与技术学院）；National Laboratory of Solid State Microstructures and School of Physics, Nanjing University（南京大学固体微结构物理国家重点实验室和物理学院）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）；Jiangsu Key Laboratory of Quantum Information Science and Technology, Nanjing University（南京大学江苏省量子信息科学技术重点实验室）
We study the anisotropic two-dimensional Hubbard model at and near half filling within a functional renormalization group method, focusing on the structure of momentum-dependent correlations which grow strongly upon approaching a critical temperature from above. We find that a finite nearest-neighbor interchain hopping is not sufficient to introduce a substantial momentum dependence of single-particle properties along the Fermi surface. However, when a sufficiently large second-nearest neighbor inter-chain hopping is introduced, the system is frustrated and we observe the appearance of so-call…
Frustrated transition metal compounds in which spin-orbit coupling (SOC) and electron correlation work together have attracted much attention recently. In the case of 5$d$ transition metals, where SOC is large, $j_\text{eff}=1/2$ bands near the Fermi level are thought to encompass the essential physics of the material, potentially leading to a concrete realization of exotic magnetic phases such as the Kitaev spin liquid. Here we derive a spin model on a triangular lattice based on $j_\text{eff} = 1/2$ pseudospins that interact via antiferromagnetic Heisenberg ($J$) and Kitaev ($K$) exchanges, …
We study hardcore bosons on a triangular ladder at half filling in the presence of a frustrating hopping term and a competing nearest neighbor repulsion $V$ which promotes crystallization. Using the finite-size density-matrix renormalization group method, we obtain the phase diagram which contains three phases: a uniform superfluid (SF), an insulating charge density wave (CDW) crystal and a bond ordered insulator (BO). We find that the transitions from SF to CDW and SF to BO are continuous in nature, with critical exponents varying continously along the phase boundaries, while the transition f…
Electronic flat bands in momentum space, arising from strong localization of electrons in real space, are an ideal stage to realize strong correlation phenomena. In certain lattices with built-in geometrical frustration, electronic confinement and flat bands can naturally arise from the destructive interference of electronic hopping pathways. Such lattice-borne flat bands are often endowed with nontrivial topology if combined with spin-orbit coupling, while their experimental realization in condensed matter system has been elusive so far. Here, we report the direct observation of topological f…
On the basis of the "molecular-orbital" representation which describes generic flat-band models, we propose a systematic way to construct a class of flat-band models with finite-range hoppings that have topological natures. In these models, the topological natures are encoded not into the flat band itself but into the dispersive bands touching the flat band. Such a band structure may become a source of exotic phenomena arising from the combination of flat bands, topology and correlations.
Layered kagome-lattice 3d transition metals are emerging as an exciting platform to explore the frustrated lattice geometry and quantum topology. However, the typical kagome electronic bands, characterized by sets of the Dirac-like band capped by a phase-destructive flat band, have not been clearly observed, and their orbital physics are even less well investigated. Here, we present close-to-textbook kagome bands with orbital differentiation physics in CoSn, which can be well described by a minimal tight-binding model with single-orbital hopping in Co kagome lattice. The capping flat bands wit…
It was known that by a duality transformation, interaction bosons at filling factor $ f=p/q $ hopping on a lattice can be mapped to interacting vortices hopping on the dual lattice subject to a fluctuating{\em dual} " magnetic field" whose average strength through a dual plaquette is equal to the boson density $ f=p/q $.So the kinetic term of the vortices is the same as the Hofstadter problem of electrons moving in a lattice in the presence of $ f=p/q $ flux per plaquette. Motivated by this mapping, we study the Hofstadter bands of vortices hopping in the presence of magnetic flux $ f=p/q $ pe…
The spin ice materials Ho$_{2}$Ti$_{2}$O$_{7}$ and Dy$_{2}$Ti$_{2}$O$_{7}$ are by now perhaps the best-studied classical frustrated magnets. A crucial step towards the understanding of their low temperature behaviour -- both regarding their unusual dynamical properties and the possibility of observing their quantum coherent time evolution -- is a quantitative understanding of the spin-flip processes which underpin the hopping of magnetic monopoles. We attack this problem in the framework of a quantum treatment of a single-ion subject to the crystal, exchange and dipolar fields from neighbourin…
Massachusetts Institute of Technology（麻省理工学院）；Flatiron Institute（平顿研究所）；University of British Columbia（不列颠哥伦比亚大学）；Canadian Light Source, Inc.（加拿大光源公司）；Lund University（隆德大学）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Max Planck Institute for Solid State Research（马克斯·普朗克固态研究所）；Universität Würzburg（维尔茨堡大学）；Ludwig- Maximilians-Universität München（慕尼黑路德维希-马克西米利安大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；CEA（法国原子能和替代能源委员会）；Institut de Physique Théorique（理论物理研究所）；University of Tokyo（东京大学）；University of Stuttgart（斯图加特大学）；Collège de France（法兰西公学院）；Université PSL（巴黎文理研究大学）；Ecole Polytechnique（巴黎综合理工学院）；IP Paris（巴黎理工学院）；Université de Genève（日内瓦大学）
The interplay between Kondo effect, indirect magnetic interaction and geometrical frustration is studied in the Kondo lattice on the one-dimensional zigzag ladder. Using the density-matrix renormalization group (DMRG), the ground state and various short- and long-range spin- and density-correlation functions are calculated for the model at half-filling as a function of the antiferromagnetic Kondo interaction down to $J=0.3t$ where $t$ is the nearest-neighbor hopping on the zigzag ladder. Geometrical frustration is shown to lead to at least two critical points: Starting from the strong-$J$ limi…
We have performed extensive density matrix renormalization group (DMRG) studies of the Hubbard model on a honeycomb ladder. The band structure (with Hubbard U=0) exhibits an unusual quadratic band touching at half filling, which is associated with a quantum Lifshitz transition from a band insulator to a metal. %SAK as a function of a third-neighbor hopping parameter. For one electron per site, non-zero $U$ drives the system into an insulating state in which there is no pair-binding between added electrons; this implies that superconductivity driven directly by the repulsive electron-electron i…
We find unconventional Mott insulators in a quasi-2D version of the Shastry-Sutherland model in a magnetic field. In our realization on a 4-leg tube geometry, these are stabilized by correlated hopping of localized magnetic excitations. Using perturbative continuous unitary transformations (pCUTs, plus classical approximation or exact diagonalization) and the density matrix renormalisation group method (DMRG), we identify prominent magnetization plateaus at magnetizations M=1/8, M=3/16, M=1/4, and M=1/2. While the plateau at M=1/4 can be understood in a semi-classical fashion in terms of diago…
The hallmark of topological phases is their robust boundary signature whose intriguing properties---such as the one-way transport on the chiral edge of a Chern insulator and the sudden disappearance of surface states forming open Fermi arcs on the surfaces of Weyl semimetals---are impossible to realize on the surface alone. Yet, despite the glaring simplicity of non-interacting topological bulk Hamiltonians and their concomitant energy spectrum, the detailed study of the corresponding surface states has essentially been restricted to numerical simulation. In this work, however, we show that ex…
Using the example of the sawtooth chain, we argue that the t-J model shares important features with the Hubbard model on highly frustrated lattices. The lowest single-fermion band is completely flat (for a specific choice of the hopping parameters $t_{i,j}$ in the case of the sawtooth chain), giving rise to single-particle excitations which can be localized in real space. These localized excitations do not interact for sufficient spatial separations such that exact many-electron states can also be constructed. Furthermore, all these excitations acquire zero energy for a suitable choice of the …
Obstructed Cooper pairs in flat band systems -- weakly-coherent superfluids and exact spin liquids
Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院凝聚态理论研究所）；Department of Physics, Columbia University（哥伦比亚大学物理系）；Institut für Quantenmaterialien und Technologien, Karlsruher Institut für Technologie（卡尔斯鲁厄理工学院量子材料与技术研究所）
