We consider the strongly anisotropic spin-1/2 $XXZ$ model on the sawtooth-chain lattice with ferromagnetic longitudinal interaction $J^{zz}=ΔJ$ and aniferromagnetic transversal interaction $J^{xx}=J^{yy}=J>0$. At $Δ=-1/2$ the lowest one-magnon excitation band is dispersionless (flat) leading to a massively degenerate set of ground states. Interestingly, this model admits a three-coloring representation of the ground-state manifold [H.~J.~Changlani et at., Phys. Rev. Lett. {\bf 120}, 117202 (2018)]. We characterize this ground-state manifold and elaborate the low-temperature thermodynamics of the system. We illustrate the manifestation of the flat-band physics of the anisotropic model by comparison with two isotropic flat-band Heisenberg sawtooth chains. Our analytical consideration is complemented by exact diagonalization and finite-temperature Lanczos method calculations.
We present a combined experimental and theoretical study of the mineral atacamite Cu$_2$Cl(OH)$_3$. Density functional theory yields a Hamiltonian describing anisotropic sawtooth chains with weak 3D connections. Experimentally, we fully characterize the antiferromagnetically ordered state. Magnetic order shows a complex evolution with the magnetic field, while, starting at 31.5 T, we observe a plateau-like magnetization at about $M_{\rm sat}/2$. Based on complementary theoretical approaches, we show that the latter is unrelated to the known magnetization plateau of a sawtooth chain. Instead, w…
Antikink dispersion of the asymmetric $J_1$-$J_2$ sawtooth spin-1/2 anisotropic Heisenberg antiferromagnetic chain has been derived. Value of spin-gap is obtained by estimating the minimum of dispersion relation variationally. The exact doubly-degenerate ground state energy has been derived at the symmetric point, $J_1=J_2$, for the whole anisotropic regime. Analytic form of dispersion relations of three different antikink states is obtained and their validity in the parameter space is discussed. The value of spin-gap, specific heat and susceptibility are estimated numerically by diagonalizing…
Electric-field driven flat bands in the distorted sawtooth chain via the Katsura-Nagaosa-Balatsky mechanism
Yerevan State University（埃里温国立大学）；CANDLE, Synchrotron Research Institute（CANDLE 同步辐射研究所）；Institute of Applied Problems of Physics（应用物理问题研究所）；University of Augsburg（奥格斯堡大学）；Andronikashvili Institute of Physics, Javakhishvili Tbilisi State University（贾瓦希什维利第比利斯国立大学安德罗尼卡什维利物理研究所）
On flat bands in the $J_1$-$J_2$-$J_3$ XXZ sawtooth chain
Yerevan State University（埃里温国立大学）；CANDLE, Synchrotron Research Institute（CANDLE 同步辐射研究所）；Universität Magdeburg（马格德堡大学）；Max-Planck-Institut für Physik Komplexer Systeme（马克斯·普朗克复杂系统物理研究所）；University of Augsburg（奥格斯堡大学）；Andronikashvili Institute of Physics, Javakhishvili Tbilisi State University（贾瓦希什维利第比利斯国立大学安德罗尼卡什维利物理研究所）；Center for Theoretical Physics of Complex Systems, Institute for Basic Science（基础科学院复杂系统理论物理中心）；Korea University of Science and Technology（韩国科学技术院）
Thermal DMRG is investigated with emphasis of employability in molecular magnetism studies. To this end magnetic observables at finite temperature are evaluated for two one-dimensional quantum spin systems: a Heisenberg chain with nearest-neighbor antiferromagnetic interaction and a frustrated sawtooth (delta) chain. It is found that thermal DMRG indeed accurately approximates magnetic observables for the chain as well as for the sawtooth chain, but in the latter case only for sufficiently high temperatures. We speculate that the reason is due to the peculiar structure of the low-energy spectr…
We apply the rotation-invariant Green's function method (RGM) to study the spin $S=1/2$ Heisenberg model on a one-dimensional sawtooth lattice, which has two nonequivalent sites in the unit cell. We check the RGM predictions for observable quantities by comparison with the exact-diagonalization and finite-temperature-Lanczos calculations. We discuss the thermodynamic and dynamic properties of this model in relation to the mineral atacamite Cu$_2$Cl(OH)$_3$ complementing the RGM outcomes by results of other approaches.
While certain magnetic sublattices have long been known theoretically to give rise to emergent physics via competing magnetic interactions and quantum effects, finding such configurations in real materials is often deeply challenging. Here we report the synthesis and characterization of a new such material, NaCo2(SeO3)2(OH) which crystallizes with a highly frustrated sublattice of sawtooth Co2+ chains. Single crystals of NaCo2(SeO3)2(OH) were synthesized using a low-temperature hydrothermal method. X-ray single crystal structure analysis reveals that the material crystallizes in orthorhombic s…
Complex Magnetic Behavior of the Ce sawtooth chains in CeRhSn$_2$
Charles University, Faculty of Mathematics and Physics（查理大学数学物理学院）；CNRS, ICMCB UMR5026, Bordeaux INP, Bordeaux University（法国国家科学研究中心、ICMCB UMR5026、波尔多国立理工学院、波尔多大学）；Tata Institute of Fundamental Research（塔塔基础研究所）；Indian Institute of Technology, Kanpur（坎普尔印度理工学院）；Institute of Low Temperature and Structure Research, Polish Academy of Sciences（波兰科学院低温结构研究所）；P.J. Šafárik University in Košice（科希策P.J.沙法里克大学）；VŠB-Technical University of Ostrava（俄斯特拉发理工大学）；University of Augsburg（奥格斯堡大学）
The spin-$\frac{1}{2}$ delta-chain (sawtooth chain) with antiferromagnetic Heisenberg basal chain and Ising apical-basal interactions is studied. The basal-apical interactions involve the bond alternation. The limiting cases of the model include the symmetrical delta-chain and the antiferromagnetic chain in the staggered magnetic field. We study ground state properties of the model by the exact diagonalization and density matrix renormalization group methods. The ground state phase diagram as a function of the bond alternation consists of magnetic and various non-magnetic phases. All phases ex…
We study the low-energy properties and, in particular, the magnetization process of a spin-1/2 Heisenberg $J_1-J_2$ sawtooth and frustrated chain (also known as zig-zag ladder) with a spatially anisotropic $g$-factor. We treat the problem both analytically and numerically while keeping the $J_2/J_1$ ratio generic. Numerically, we use complete and Lanczos diagonalization as well as the infinite time-evolving block decimation (iTEBD) method. Analytically we employ (non-)Abelian bosonization. Additionally for the sawtooth chain, we provide an analytical description in terms of flat bands and loca…
Identifying and characterizing new magnetic systems with Co2+ ions can enhance our understanding of quantum behavior since Co2+ can host a pseudospin-1/2 magnetic ground state. Understanding the magnetic ground state and the phase diagrams of such systems are central to the development of new theoretical models to described emergent quantum properties of complex magnetic systems. The sawtooth chain compound, CsCo2MoO4_2OH, is one such complex magnetic system and here, we present a comprehensive series of magnetic and neutron scattering measurements to determine its magnetic phase diagram. The …
The Magnetic Ground State of Atacamite Cu$_2$Cl(OH)$_3$: The Crucial Role of Frustrated Zigzag Chains Revealed by Inelastic Neutron Scattering
University of Wollongong（伍伦贡大学）；Technische Universität Braunschweig（布伦瑞克工业大学）；Forschungszentrum Jülich GmbH（于利希研究中心有限公司）；Australian Nuclear Science and Technology Organisation（澳大利亚核科学与技术组织）；Leibniz Institute for Solid State and Materials Research Dresden（德累斯顿莱布尼茨固体与材料研究所）；Technical University Dresden（德累斯顿工业大学）
The $J_1$-$J_2$ quantum spin sawtooth chain is a paradigmatic one-dimensional frustrated quantum spin system exhibiting unconventional ground-state and finite-temperature properties. In particular, it exhibits a flat energy band of one-magnon excitations accompanied by an enhanced magnetocaloric effect for two singular ratios of the basal interactions $J_1$ and the zigzag interactions $J_2$. In our paper, we demonstrate that one can drive the spin system into a flat-band scenario by applying an appropriate electric field, thus overcoming the restriction of fine-tuned exchange couplings $J_1$ a…
We investigate the origin of the ubiquitous existence of flat bands in the network superstructures of atomic chains, where one-dimensional(1D) atomic chains array periodically. While there can be many ways to connect those chains, we consider two representative ways of linking them, the dot-type and triangle-type links. Then, we construct a variety of superstructures, such as the square, rectangular, and honeycomb network superstructures with dot-type links and the honeycomb superstructure with triangle-type links. These links provide the wavefunctions with an opportunity to have destructive i…
For the Haldane phase, the magnetic field usually tends to break the symmetry and drives the system into a topologically trivial phase. Here, we report a novel reentrance of the Haldane phase at zero temperature in the spin-1 antiferromagnetic Heisenberg model on sawtooth chain. A partial Haldane phase is induced by the magnetic field, which is the combination of the Haldane state in one sublattice and a ferromagnetically ordered state in the other sublattice. Such a partial topological order is a result of the zero-temperature entropy due to quantum fluctuations caused by geometrical frustrat…
We consider analytically and numerically an anisotropic spin-$\frac{1}{2}$ delta-chain (sawtooth chain) in which exchange interactions between apical and basal spins are ferromagnetic and those between basal spins are antiferromagnetic. In the limit of strong anisotropy of exchange interactions this model can be considered as the Ising delta chain with macroscopic degenerate ground state perturbed by transverse quantum fluctuations. These perturbations lift the ground state degeneracy and the model reduces to the basal XXZ spin chain in the magnetic field induced by static apical spins. We sho…
Localized magnons states, due to flat bands in the spectrum, is an intensely studied phenomenon and can be found in many frustrated magnets of different spatial dimensionality. The presence of Dzyaloshinskii-Moriya (DM) interactions may change radically the behavior in such systems. In this context, we study a paradigmatic example of a one-dimensional frustrated antiferromagnet, the sawtooth chain in the presence of DM interactions. Using both path integrals methods and numerical Density Matrix Renormalization Group, we revisit the physics of localized magnons and determine the consequences of…
We consider the three-body problem in a generic multiband lattice, and analyze the dispersion of the trimer states that are made of two spin-$\uparrow$ fermions and a spin-$\downarrow$ fermion due to an onsite attraction in between. Based on a variational approach, we first obtain the exact solution in the form of a set of coupled integral equations, and then reduce it to an eigenvalue problem. As an illustration we apply our theory to the sawtooth lattice, and numerically show that energetically-stable trimers are allowed in a two-band setting, which is in sharp contrast with the single-band …
We theoretically demonstrate that interacting symmetry-protected topological (SPT) phases can be realized with ultracold spinful bosonic atoms loaded on the lattices which have a flat band at the bottom of the band structure. Ground states of such systems are not conventional Mott insulators in the sense that the ground states possess not only spin fluctuations but also non-negligible charge fluctuations. The SPT phases in such systems are determined by both spin and charge fluctuations at zero temperature. We find that the many-body ground states of such systems can be exactly obtained in som…
We start with a variational approach and derive a set of coupled integral equations for the bound states of $N$ identical spin-$\uparrow$ fermions and a single spin-$\downarrow$ fermion in a generic multiband Hubbard Hamiltonian with an attractive onsite interaction. As an illustration we apply our integral equations to the one-dimensional sawtooth lattice up to $N \le 3$, i.e., to the $(3+1)$-body problem, and reveal not only the presence of tetramer states in this two-band model but also their quasi-flat dispersion when formed in a flat band. Furthermore, for $N = \{4, 5, \cdots, 10 \}$, our…
Quantum geometry has been identified as an important ingredient for the physics of quantum materials and especially of flat-band systems, such as moiré materials. On the other hand, the coupling between light and matter is of key importance across disciplines and especially for Floquet and cavity engineering of solids. Here we present fundamental relations between light-matter coupling and quantum geometry of Bloch wave functions, with a particular focus on flat-band and moiré materials, in which the quenching of the electronic kinetic energy could allow one to reach the limit of strong light-…
In contrast to strongly frustrated classical systems, their quantum counterparts typically have a non-degenerate ground state. A counterexample is the celebrated Heisenberg sawtooth spin chain with ferromagnetic zigzag bonds $J_1$ and competing antiferromagnetic basal bonds $J_2$. At a quantum phase transition point $|J_2/J_1|=1/2$, this model exhibits a flat one-magnon excitation band leading to a massively degenerate ground-state manifold which results in a large residual entropy. Thus, for the spin-half model, the residual entropy amounts to exactly one half of its maximum value $\lim_{T\to…
Fe$^{3+}$ $S = 5/2$ ions form saw-tooth like chains along the $a$ axis of the oxo-selenite Fe$_2$O(SeO$_3$)$_2$ and an onset of long-range magnetic order is observed for temperatures below $T_C = 105$ K. This order leads to distinct fingerprints in phonon mode linewidths and energies as resolved by Raman scattering. In addition, new excitations with small linewidths emerge below $T = 150$ K, and are assigned to two-magnon scattering processes with the participation of flat-band and high energy magnon branches. From this a set of exchange coupling constants is estimated. The specific ratio of t…
We systematically study the effect of disorder and interactions on a quasi-one dimensional diamond chain possessing flat bands. Disorder localizes all the single particle eigenstates, while at low disorder strengths we obtain weak flat-band based localization (FBL), at high disorder strengths, we see conventional Anderson localization (AL). The compactly localized (CL) eigenstates of flat bands show a persisting oscillatory recurrence in the study of single-particle wavepacket dynamics. For low disorder a damped oscillatory recurrence behavior is observed which is absent for high disorder. Non…
