In this study, we investigate the magnetoelectric (ME) effect of the newly discovered antiferromagnetic (AFM) compound Ce$_{3}$TiBi$_{5}$ with a hexagonal structure (space group $P6_{3}$/$mcm$). In this system, Ce ions form zig-zag chains that extend along the $c$-axis. We focus on the lack of the local inversion symmetry at the Ce site, although the crystal structure has an inversion center. A theoretical study has predicted that magnetization can be induced by an electric current in the AFM ordering on the zig-zag chain. We conducted magnetization measurements on Ce$_{3}$TiBi$_{5}$ under an applied constant electric current and a static magnetic field around the AFM ordering temperature of $T_{\rm N}$ = 5.0 K. We successfully observed of the current-induced magnetization below $T_{\rm N}$. The magnitude of the current-induced magnetization has a linear electric current dependence and exhibits no magnetic field dependence. This behavior is consistent with the theoretical prediction of the ME effect in the ferrotoroidal ordered state.
We theoretically investigate an antiferromagnetic structure in a hexagonal zigzag-chain compound Ce$_3$TiBi$_5$, which shows a linear magnetoelectric effect in metals and an unfamiliar temperature dependence of magnetic susceptibility. We find a partial magnetic order as a coexistence of a nonmagnetic zigzag chain and staggered antiferromagnetic zigzag chains. The latter accompany in-plane magnetic toroidal dipole moments which are responsible for the observed behaviors. We show that magnetic frustration arising from competing exchange interactions plays an important role to realize such a par…
We investigate the elementary excitations of quasi one-dimensional S=1/2 systems built up from zig-zag chains with general isotropic exchange constants, using exact (Lanczos) diagonalization for 24 spins and series expansions starting from the decoupled dimer limit. For the ideal one-dimensional zig-zag chain we discuss the systematic variation of the basic (magnon) triplet excitation with general exchange parameters and in particular the presence of practically flat dispersions in certain regions of phase space. We extend the dimer expansion in order to include the effects of 3D interactions …
Using the next-nearest neighbor (zig-zag) Hubbard chain as an one dimemensional model, we investigate the influence of interactions on the position of the Fermi wavevectors with the density-matrix renormalization-group technique (DMRG). For suitable choices of the hopping parameters we observe that electron-electron correlations induce very different renormalizations for the two different Fermi wavevectors, which ultimately lead to a complete destruction of one section of the Fermi sea in a quantum critical point.
The topological properties of massive and massless fermionic quasiparticles have been intensively investigated over the past decade in topological materials without magnetism. Recently, the bosonic analogs of such quasiparticles arising from spin waves have been reported in the two-dimensional (2D) honeycomb lattice ferromagnet/antiferromagnet and the 3D antiferromagnet. Here we use time-of-flight inelastic neutron scattering to study spin waves of the S = 1 honeycomb lattice antiferromagnet BaNi2(AsO4)2, which has a zig-zag antiferromagnetic (AF) ground state identical to that of the Kitaev q…
By means of electron spin resonance investigations we revealed the crucial role of the interchain coupling in the spin dynamics of the spin-1/2 Heisenberg antiferromagnetic (AF) chain material copper-pyrazine-dinitrate, Cu(C$_4$H$_4$N$_2$)(NO$_3$)$_2$. We found that the dominating interchain interaction is of a zig-zag type. This interaction gives rise to geometrical frustration effects and strongly influences the character of AF ordering. Combining our experimental findings with the results of a quasiclassical approach we argue that at low temperatures the system orders in an incommensurate s…
We use exact diagonalization and the modified Lanczos method to study the finite energy and finite momentum spectral weight of the longitudinal and transverse spin excitations of the anisotropic zig-zag ladder. We find that the spin excitations form continua of gapless or gapped spinons in the different regions of the phase diagram. The results obtained are consistent with a picture previously proposed that in the anisotropic case there is a transition from a gapped regime to a gapless regime, for small interchain coupling. In this regime we find a sharp low-energy peak in the structure functi…
The spin-1/2 antiferromagnetic zig-zag ladder is studied by exact diagonalization of small systems in the regime of weak inter-chain coupling. A gapless phase with quasi long-range spiral correlations has been predicted to occur in this regime if easy-plane (XY) anisotropy is present. We find in general that the finite zig-zag ladder shows three phases: a gapless collinear phase, a dimer phase and a spiral phase. We study the level crossings of the spectrum,the dimer correlation function, the structure factor and the spin stiffness within these phases, as well as at the transition points. As t…
We analyze the effects of a trimerized modulation in a quantum spin $S=\frac12$ zig-zag ladder at the magnetization plateau $M=1/3$. Such periodicity is argued to be stemmed from lattice deformations by phonons. The interplay between frustration and exchange modulation is well described by an effective triple sine-Gordon field theory close to the homogeneous ladder and by block-spin perturbation theory in the weakly coupled trimers regime. The characteristic triple degeneracy of the ground state for homogeneous ladders gives place to modulation driven quantum phase transitions, leading to a ri…
We develop a low-energy effective theory for spin-1/2 frustrated two-leg Heisenberg spin ladders. We obtain a new type of interchain coupling that breaks parity symmetry. In the presence of an XXZ-type anisotropy, this interaction gives rise to a novel ground state, characterized by incommensurate correlations. In the case of a single ladder, this state corresponds to a spin nematic phase. For a frustrated quasi-one-dimensional system of infinitely many weakly coupled chains, this state develops true three dimensional spiral order. We apply our theory to recent neutron scattering experiments o…
We study hard-core bosons with unfrustrated nearest-neighbor hopping $t$ and repulsive interaction $V$ on a zig-zag ladder. As a function of the boson density $ρ$ and $V/t$, the ground state displays different quantum phases. A standard one-component Tomonaga-Luttinger liquid is stable for $ρ<1/3$ (and $ρ>2/3$) at any value of $V/t$. At commensurate densities $ρ=1/3$, $1/2$, and $2/3$ insulating (crystalline) phases are stabilized for a sufficiently large interaction $V$. For intermediate densities $1/3<ρ<2/3$ and large $V/t$, the ground state shows a clear evidence of a bound state of two bos…
Ultra-cold dipolar spinor fermions in zig-zag type optical lattices can mimic spin-orbital models relevant in solid-state systems, as transition-metal oxides with partially filled d-levels, with the interesting advantage of reviving the quantum nature of orbital fluctuations. We discuss two different physical systems in which these models may be simulated, showing that the interplay between lattice geometry and spin-orbital quantum dynamics produces a wealth of novel quantum phases.
Momentum-Space Entanglement Signatures and Spinon Breakdown in the $J_1$-$J_2$ Zig-Zag Heisenberg Chain
Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ctd.qmat, Universität Würzburg（维尔茨堡大学理论与天体物理研究所及维尔茨堡-德累斯顿卓越集群ctd.qmat）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究所计算量子物理中心）；Leinweber Institute for Theoretical Physics, Stanford University（斯坦福大学莱因韦伯理论物理研究所）
The COntractor REnormalization group method was devised in 1994 by Morningstar and Weinstein. It was primarily aimed at extracting the physics of lattice quantum field theories (like lattice Quantum Chromodynamics). However, it is a general method of analyzing Hamiltonian lattice systems, e.g. Ising, Heisenberg or Hubbard models. The aim of this work is to show the application of CORE to one-dimensional quantum systems -- the Heisenberg zig-zag model and the Hubbard chain. As a test of the method, the ground state energy of these systems will be calculated.
Neutron diffraction and inelastic spectroscopy is used to characterize the magnetic Hamiltonian of SrHo2O4 and SrDy2O4. Through a detailed computation of the crystal-field levels we find site- dependent anisotropic single-ion magnetism in both materials and diffraction measurements show the presence of strong one-dimensional spin correlations. Our measurements indicate that competing interactions of the zig-zag chain, combined with frustrated interchain interactions, play a crucial role in stabilizing spin-liquid type correlations in this series.
Controlling the forbidden gap of graphene nano-ribbons (GNR) is a major challenge that has to be attained if this attractive material has to be used in micro- and nano-electronics. Using an unambiguous notation {m,n}-GNR, where m (n) is the number of six carbon rings in the arm-chair (zig-zag) directions, we investigate how varies the HOMO-LUMO gap when the size of the GNR is varied by increasing either m or n, while keeping the other variable fixed. It is shown that no matter whether charge- or spin-density-waves solutions are considered, the gap varies smoothly when n is kept fixed whereas i…
Recent theoretical studies raised the possibility of a realization of spin nematic states in the S=1 triangular lattice compound NiGa_2S_4. We study the bilinear-biquadratic spin 1 chain in a zig-zag geometry by means of the density matrix renormalization group method and exact diagonalization. We present the phase diagram focusing on antiferromagnetic interactions. Adjacent to the known Haldane-double Haldane and the extended critical phase with dominant spin nematic correlations we find a trimerized phase with a nonvanishing energy gap. We discuss results for different order parameters, ener…
The zig-zag symmetry transition is a phase transition in 1D quantum wires, in which a Wigner lattice of electrons transitions to two staggered lattices. Previous studies model this transition as a Luttinger liquid coupled to a Majorana fermion. The model exhibits interesting RG flows, involving quenching of velocities in subsectors of the theory. We suggest an extension of the model which replaces the Majorana fermion by a more general CFT; this includes an experimentally realizable case with two Majorana fermions. We analyse the RG flow both in field theory and using AdS/CFT techniques in the…
Structural and thermodynamic properties of single-crystalline UNi$_{1-x}$Ge$_2$ with $x$\,=\,0.66 have been investigated by measuring magnetization, specific heat, and thermal expansion over a wide range of temperatures and magnetic fields. The measurements revealed the emergence of a long-range antiferromagnetic ordering of uranium magnetic moments below the N{é}el temperature $T_{\rm N}$\,=\,45.5\,K and the existence of two easy axes in the studied compound, namely $b$ and $c$, which correspond to the planes of the uranium zig-zag chains. Magnetic field applied along these two crystallograph…
We analyze the phase diagram of a system of spin-1/2 Heisenberg antiferromagnetic chains interacting through a zig-zag coupling, also called zig-zag ladders. Using bosonization techniques we study how a spin-gap or more generally plateaux in magnetization curves arise in different situations. While for coupled XXZ chains, one has to deal with a recently discovered chiral perturbation, the coupling term which is present for normal ladders is restored by an external magnetic field, dimerization or the presence of charge carriers. We then proceed with a numerical investigation of the phase diagra…
We present a study of the entanglement properties of the F-AF zig-zag Heisenberg chain done by means of the Density Matrix Renormalization Group method. In particular, we have selected the concurrence as measure of entanglement and checked its capability to signal the presence of quantum phase transitions within the previously found ergodicity phase diagram [E. Plekhanov, A. Avella, and F. Mancini, Phys. Rev. B \textbf{74}, 115120 (2006)]. By analyzing the behavior of the concurrence, we have been able not only to determine the position of the transition lines within the phase diagram of the s…
Theoretical studies have predicted the existence of topological magnons in honeycomb compounds with zig-zag antiferromagnetic (AFM) order. Here we report the discovery of zig-zag AFM order in the layered and non-centrosymmetric honeycomb nickelate Ni$_2$Mo$_3$O$_8$ through a combination of magnetization, specific heat, x-ray and neutron diffraction and electron paramagnetic resonance measurements. It is the first example of such order in an integer-spin non-centrosymmetric structure ($P$$_6$3$mc$). Further, each of the two distinct sites of the bipartite honeycomb lattice has a unique crystal …
We report nuclear quadrupole resonance (NQR) studies on the chain Cu sites of PrBa$_{2}$Cu$_{4}$O$_{8}$, a quasi-one-dimensional conductor with a nearly quarter-filled band. The nuclear spin-lattice relaxation rate $1/T_{1}$ shows a pronounced peak near 100 K caused by fluctuations of electric field gradient (EFG). Similar peak was observed for the spin-echo decay rate $1/T_{2}$, however, at a different temperature near 50 K. These results and broadening of the NQR spectrum at low temperatures indicate that slow charge fluctuations of either electronic or ionic origin freeze gradually at low t…
This response on a Comment on Reference 2 discusses the space group Fmm2 determination of the low temperature structure of NaV2O5. We show that while conventional crystallography is consistent with 'zig-zag' charge ordering of half of the ladders, recent spectroscopic measurements suggest that the symmetry is lower than Fmm2. We suggest space group C2, consistent with full 'zig-zag' charge ordering of all the ladders.
The single ion properties of the zig-zag chain compound SrTm$_2$O$_4$ have been investigated using heat capacity, magnetic susceptibility, magnetization, inelastic neutron scattering, and polarized muon spectroscopy. Two crystal field models are employed to estimate the single ion properties; a Density Function Theory based model and an effective charge model based on the Hutchings point charge model. The latter describes our experimental results well. This model estimates an easy-axis anisotropy for one of the Tm$^{3+}$ sites and an easy-plane anisotropy for the second site. It also predicts …
The phase diagram of a frustrated spin-$S$ zig-zag ladder is studied through different numerical and analytical methods. We show that for arbitrary $S$, there is a family of Hamiltonians for which a fully-dimerized state is an exact ground state, being the Majumdar-Ghosh point a particular member of the family. We show that the system presents a transition between a dimerized phase to a Néel-like phase for $S=1/2$, and spiral phases can appear for large $S$. The phase diagram is characterized by means of a generalization of the usual Mean Field Approximation (MFA). The novelty in the present i…
Temperature-driven sodium-ion dynamical-to-static crossover in the zig-zag ordered phase of Na$_{0.5}$CoO$_2$
Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院人工结构与量子控制教育部重点实验室）；School of Physical Science and Technology, Lanzhou University（兰州大学物理科学与技术学院）；International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院物质科学量子创新中心）；Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所北京凝聚态物理国家实验室）
Despite the exciting implications of the Kitaev spin-Hamiltonian, finding and confirming the quantum spin liquid state has proven incredibly difficult. Recently the applicability of the model has been expanded through the development of a microscopic description of a spin-1 Kitaev interaction. Here we explore a candidate spin-1 honeycomb system, KNiAsO$_4$ , which meets many of the proposed criteria to generate such an interaction. Bulk measurements reveal an antiferromagnetic transition at $\sim$ 19 K which is generally robust to applied magnetic fields. Neutron diffraction measurements show …
A large number of symmetry-protected topological (SPT) phases have been hypothesized for strongly interacting spin-1/2 systems in one dimension. Realizing these SPT phases, however, often demands fine-tunings hard to reach experimentally. And the lack of analytical solutions hinders the understanding of their many-body wave functions. Here we show that two kinds of SPT phases naturally arise for ultracold polar molecules confined in a zigzag optical lattice. This system, motivated by recent experiments, is described by a spin model whose exchange couplings can be tuned by an external field to …
Static magnetic susceptibility χ, ac susceptibility χ_{ac} and specific heat C versus temperature T measurements on polycrystalline samples of In2VO5 and χand C versus T measurements on the isostructural, nonmagnetic compound In2TiO5 are reported. A Curie-Wiess fit to the χ(T) data above 175 K for In2VO5 indicates ferromagnetic exchange between V^{4+} (S = 1/2) moments. Below 150 K the χ(T) data deviate from the Curie-Weiss behavior but there is no signature of any long range magnetic order down to 1.8 K. There is a cusp at 2.8 K in the zero field cooled (ZFC) χ(T) data measured in a magnetic …
An exact solvable 'zig-zag' ladder model of degenerated spinless fermions is proposed and solved exactly by the means of the Bethe ansatz. An effective attractive hard-core interaction and direct Coulomb repulsion of fermions on the nearest-neighbor sites of different chains induce a new phase state of the ladder. We give a detailed analysis of the exact phase diagram at zero temperature, that is characterized by two phases at the filling exceeding 2/3: itinerant and 'frozen' fermions, for which two different species reside in spatially separate regions. The critical exponents describing asymp…
The spin-1/2 zig-zag Heisenberg ladder (J_1 - J_2 model) is considered. A new representation for the model is found and a saddle point approximation over the spin-liquid order parameter < \vec σ_{n-1}(\vec σ_{n}\times \vec σ_{n+1}) > is performed. Corresponding effective action is derived and analytically analyzed. We observe the presence of phase transitions at values J_2/J_1=0.231 and J_2/J_1=1/2.
