The quantum phases in a spin-1 skewed ladder system formed by alternately fusing five- and seven-membered rings are studied numerically using the exact diagonalization technique up to 16 spins and using the density matrix renormalization group method for larger system sizes. The ladder has a fixed isotropic antiferromagnetic (AF) exchange interaction ($J_2 = 1$) between the nearest-neighbor spins along the legs and a varying isotropic AF exchange interaction ($J_1$) along the rungs. As a function of $J_1$, the system shows many interesting ground states (gs) which vary from different types of nonmagnetic and ferrimagnetic gs. The study of diverse gs properties such as spin gap, spin-spin correlations, spin density and bond order reveal that the system has four distinct phases, namely, the AF phase at small $J_1$; the ferrimagnetic phase with gs spin $S_G = n$ for $1.44 < J_1 < 4.74$ and with $S_G = 2n$ for $J_1 > 5.63$, where $n$ is the number of unit cells; and a reentrant nonmagnetic phase at $4.74 < J_1 < 5.44$. The system also shows the presence of spin current at specific $J_1$ values due to simultaneous breaking of both reflection and spin parity symmetries.
The quantum phases of 2-leg spin-1/2 ladders with skewed rungs are obtained using exact diagonalization of systems with up to 26 spins and by density matrix renormalization group calculations to 500 spins. The ladders have isotropic antiferromagnetic (AF) exchange $J_2 > 0$ between first neighbors in the legs, variable isotropic AF exchange $J_1$ between some first neighbors in different legs, and an unpaired spin per odd-membered ring when $J_1 \gg J_2$. Ladders with skewed rungs and variable $J_1$ have frustrated AF interactions leading to multiple quantum phases: AF at small $J_1$, either F…
We study the quantum phase transitions of frustrated antiferromagnetic Heisenberg spin-1 systems on the 3/4 and 3/5 skewed two leg ladder geometries. These systems can be viewed as arising by periodically removing rung bonds from a zigzag ladder. We find that in large systems, the ground state (gs) of the 3/4 ladder switches from a singlet to a magnetic state for $J_1 \ge 1.82$; the gs spin corresponds to ferromagnetic alignment of effective $S = 2$ objects on each unit cell. The gs of antiferromagnetic exchange Heisenberg spin-1 system on a 3/5 skewed ladder is highly frustrated and has spira…
Quantum Monte Carlo simulations provide one of the more powerful and versatile numerical approaches to condensed matter systems. However, their application to frustrated quantum spin models, in all relevant temperature regimes, is hamstrung by the infamous "sign problem." Here we exploit the fact that the sign problem is basis-dependent. Recent studies have shown that passing to a dimer (two-site) basis eliminates the sign problem completely for a fully frustrated spin model on the two-leg ladder. We generalize this result to all partially frustrated two-leg spin-1/2 ladders, meaning those whe…
Magnetization plateaus are some of the most striking manifestations of frustration in low-dimensional spin systems. We present numerical studies of magnetization plateaus in the fascinating spin-1/2 skewed ladder system obtained by alternately fusing five- and seven-membered rings. This system exhibits three significant plateaus at $m = 1/4$, $1/2$ and $3/4$, consistent with the Oshikawa-Yamanaka-Affleck condition. Our numerical as well as perturbative analysis shows that the ground state can be approximated by three weakly coupled singlet dimers and two free spins, in the absence of a magneti…
We theoretically study a spin-spin correlation enhanced by non-magnetic impurities in a frustrated two-leg spin ladder. The frustration is introduced by the next-nearest-neighbor antiferromagnetic interaction in the leg direction in the antiferromagnetic two-leg spin ladder. The spin-spin correlation function around impurity site is calculated by the density-matrix renormalization-group method. We find that the spin-spin correlation is enhanced around impurity site with the wavenumber reflecting the frustration. As increasing the frustration, the wavenumber is shifted from commensurate to inco…
Two-leg spin-1/2 ladder systems consisting of a ferromagnetic leg and an antiferromagnetic leg are considered where the spins on the legs interact through antiferromagnetic rung couplings $J_1$. These ladders can have two geometrical arrangements either zigzag or normal ladder and these systems are frustrated irrespective of their geometry. This frustration gives rise to incommensurate spin density wave, dimer and spin fluid phases in the ground state. The magnetization in the systems decreases linearly with $J^2_1$, and the systems show an incommensurate phase for $0.0<J_1<1.0$. The spin-spin…
The magnetization curve in a frustrated two-leg spin-ladder system is theoretically studied using both analytical and numerical methods. This spin system is mapped onto a hard-core boson system, which is composed of bond-operators describing the triplon excitation. By the analytical method using the mean-field theory on the bond-operators, we show that cusp singularities emerge in the magnetization curve as a function of a magnetic field due to the strong frustration. This originates from a change of number of Fermi points in the bosonic dispersion relation with the applied field. It is analog…
Frustrated spin ladders show magnetization plateaux depending on the rung-exchange interaction and frustration defined by the ratio of first and second neighbor exchange interactions in each chain. This paper is the first report on its magnetic phase diagram. Using the variational matrix-product state method, we accurately determine phase boundaries. Several kinds of magnetization plateaux are induced by the frustration and the strong correlation among quasi-particles on a lattice. The appropriate description of quasi-particles and their relevant interactions are changed by a magnetic field. W…
Entanglement entropy (EE) of a state is a measure of correlation or entanglement between two parts of a composite system and it may show appreciable change when the ground state (GS) undergoes a qualitative change in a quantum phase transition (QPT). Therefore, the EE has been extensively used to characterise the QPT in various correlated Hamiltonians. Similarly fidelity also shows sharp changes at a QPT. We characterized the QPT of frustrated antiferromagnetic Heisenberg spin-1/2 systems on 3/4, 3/5 and 5/7 skewed ladders using the EE and fidelity analysis. It is noted that all the non-magnet…
Based on exact diagonalization data for finite quantum Heisenberg antiferromagnets on two frustrated lattices (two-leg ladder and bilayer) and analytical arguments we map low-energy degrees of freedom of the spin models in a magnetic field on classical lattice-gas models. Further we use transfer-matrix calculations and classical Monte Carlo simulations to give a quantitative description of low-temperature thermodynamics of the quantum spin models. The classical lattice-gas model yields an excellent description of the quantum spin models up to quite large temperatures. The main peculiarity of t…
The magnetic phase diagram of a plaquette dimerized antiferromagnetic system is studied by using a combination of numerical and analytical techniques. For the strongly frustrated regime, series expansions and bond operators techniques are employed to analyze zero magnetization plateau, whereas low energy effective models are used to study the complete magnetization process. The interplay between frustration and dimerization gives rise to a rich plateaus structure that is captured by effective models and corroborated by numerical density matrix renormalization group simulations, in particular t…
The quasi-spin correlations in a frustrated quantum spin ladder with one-half magnetization are theoretically studied by using the density-matrix renormalization-group method and the quasi-spin transformation. In this model, the frustration induces a gapless-to-gapful phase transition with a strong rung coupling. The gapful state is observed as the one-half magnetization plateau in the magnetization curve. In the magnetization-plateau state, we find that the quasi-spin dimer has a large expectation value with long-ranged correlations. This result does not only comes in useful to clarify the ma…
Magnetization plateaux emerging in quantum spin systems due to spontaneously breaking of translational symmetry have been reported both theoretically and experimentally. The broken symmetry can induce reconstruction of elementary excitations such as Goldstone and Higgs modes, whereas its microscopic mechanism and reconstructed quasi-particle in magnetization-plateau phases have remained unclear so far. Here we theoretically study magnetic excitations in the magnetization-plateau phases of a frustrated spin ladder by using dynamical density-matrix renormalization-group method. Additionally, ana…
To establish the microscopic model of the compound BiCu$_2$PO$_6$ is a challenging task. Inelastic neutron scattering experiments showed that the dispersion of this material is non-degenerate suggesting the existence of anisotropic interactions. Here we present a quantitative description of the excitation spectrum for BiCu$_2$PO$_6$ on the one-particle level. The solution of the isotropic frustrated spin ladder by continuous unitary transformations is the starting point of our approach. Further couplings such as isotropic interladder couplings and anisotropic interactions are included on the m…
Low-dimensional quantum magnets at finite temperatures present a complex interplay of quantum and thermal fluctuation effects in a restricted phase space. While some information about dynamical response functions is available from theoretical studies of the one-triplet dispersion in unfrustrated chains and ladders, little is known about the finite-temperature dynamics of frustrated systems. Experimentally, inelastic neutron scattering studies of the highly frustrated two-dimensional material SrCu$_2$(BO$_3$)$_2$ show an almost complete destruction of the one-triplet excitation band at a temper…
We have measured temperature and magnetic-field dependences of the thermal conductivity of single crystals of the frustrated two-leg spin-ladder system BiCu2PO6 in magnetic fields up to 14 T. It has been found that the temperature dependence of the thermal conductivity along every principal crystallographic axis shows two peaks in zero field but that the magnitude of the thermal conductivity along the b-axis parallel to spin ladders, $κ$b, is significantly larger than those of the thermal conductivity along the a-axis, $κ$a, and along the c-axis, $κ$c, at high temperatures above 7 K. These res…
Although the frustrated spin chain (zigzag chain) is a Drosophila of frustrated magnetism, the understanding of a pair of coupled zigzag chains (frustrated spin ladder) in a magnetic field is incomplete. We address this problem through nuclear magnetic resonance (NMR) experiments on $\text{BiCu}_2\text{PO}_6$ in magnetic fields up to 45 T, revealing a field-induced spiral magnetic structure. Conjointly, we present advanced numerical calculations showing that even moderate rung coupling dramatically simplifies the phase diagram below half-saturation magnetization by stabilizing a field-induced …
We report experimental and theoretical evidence that Rb$_2$Cu$_2$Mo$_3$O$_{12}$ has a nonmagnetic tetramer ground state of a two-leg ladder comprising antiferromagnetically coupled frustrated spin-$1/2$ chains and exhibits a Haldane spin gap of emergent spin-1 pairs. Three spin excitations split from the spin-1 triplet by a Dzyaloshinskii-Moriya interaction are identified in inelastic neutron-scattering and electron spin resonance spectra. A tiny magnetic field generates ferroelectricity without closing the spin gap, indicating a novel class of ferroelectricity induced by a vector spin chirali…
We perform a systematic investigation on the ground state of an asymmetric two-leg spin ladder (where exchange couplings of the legs are unequal) with ferromagnetic (FM) nearest-neighbor interaction and diagonal anti-ferromagnetic frustration using the Density Matrix Renormalization Group (DMRG) method. When the ladder is strongly asymmetric with moderate frustration, a magnetic canted state is observed between a FM state and a singlet dimerized state. The phase boundaries are dependent on the asymmetric strength $α_{a}$. On the other hand, when the asymmetric strength is intermediate, a so-ca…
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；University of Geneva（日内瓦大学）；ETH Zürich（苏黎世联邦理工学院）；Institut Laue-Langevin（劳厄-朗之万研究所）；ISIS Neutron and Muon Source, Rutherford Appleton Laboratory（鲁瑟福阿普尔顿实验室 ISIS 中子与μ子源）
An overview on the phase diagram of the frustrated two-leg ladder model
利用密度矩阵重整化群，我们研究了具有Heisenberg相互作用的两足阶梯的一般相图。我们确认，所有的反铁磁带隙态属于相同的普适类的Halfoxin相。在三维相图中，我们确定了一个连续的表面与奇异的字符串-序参量或其一阶导数，对应于两个Haldron相位之间的过渡具有不同的拓扑顺序。这个过渡曲面的某些部分是临界的，带隙为零，弦序参量为零。在互补部分，跃迁是一阶的，具有有限的间隙和弦序。这个表面与铁磁区域的边界是临界端线，当表面是临界的时，并且在其他任何地方是三线。该边界的一部分与D. V. Dmitriev、V. Ya Krivnov和A.A. Ovchinnikov [Phys.Rev.B56，5985（1997）]。
The quantum phase transitions induced by a magnetic field are theoretically studied in a frustrated two-leg spin ladder. Using the density-matrix renormalization-group method, we find some magnetic phase transitions and plateaux in two different cases of strong and weak rung couplings. With the strong rung coupling, the three magnetization plateaux are found at 1/3, 1/2, and 2/3 due to the frustration. Those can be understood in terms of a quasi-spinon reconstructed from the singlet and the triplets of spins on a rung. The plateau at 1/2 corresponds to the valence bond solid of the quasi-spino…
Quantum antiferromagnets have proven to be some of the cleanest realizations available for theoretical, numerical, and experimental studies of quantum fluctuation effects. At finite temperatures, however, the additional effects of thermal fluctuations in the restricted phase space of a low-dimensional system have received much less attention, particularly the situation in frustrated quantum magnets, where the excitations may be complex collective (bound or even fractionalized) modes. We investigate this problem by studying the thermodynamic properties of the frustrated two-leg S=1/2 spin ladde…
Magnetic excitations of the recently discovered frustrated spin-1/2 two-leg ladder system Li$_2$Cu$_2$O(SO$_4$)$_2$ are investigated using inelastic neutron scattering, magnetic susceptibility and infrared absorption measurements. Despite the presence of a magnetic dimerization concomitant with the tetragonal-to-triclinic structural distortion occurring below 125 K, neutron scattering experiments reveal the presence of dispersive triplet excitations above a spin gap of $Δ= 10.6$ meV at 1.5 K, a value consistent with the estimates extracted from magnetic susceptibility. The likely detection of …
We study the ground-state phase diagram of a spin-$\frac{1}{2}$ frustrated XXZ ladder, in which two antiferromagnetic chains are coupled by competing rung and diagonal interactions, $J_\perp$ and $J_\times$. Previous studies on the isotropic model have revealed that a fluctuation-induced effective dimer attraction between the legs stabilizes the columnar dimer (CD) phase in the highly frustrated regime $J_\perp\approx 2J_\times$, especially for ferromagnetic $J_{\perp, \times}<0$. By means of effective field theory and numerical analyses, we extend this analysis to the XXZ model, and obtain a …
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…
In frustrated magnetic systems, the competition amongst interactions can introduce extremely high degeneracy and prevent the system from readily selecting a unique ground state. In such cases, the magnetic order is often exquisitely sensitive to the balance among the interactions, allowing tuning among novel magnetically ordered phases. In antlerite, Cu$_3$SO$_4$(OH)$_4$, Cu$^{2+}$ ($S=1/2$) quantum spins populate three-leg zigzag ladders in a highly frustrated quasi-one-dimensional structural motif. We demonstrate that at zero applied field, in addition to its recently reported low-temperatur…
Singlet quantum phases and magnetization of the frustrated spin-1/2 ladder with ferromagnetic (F) exchange in legs and alternating F-AF exchange in rungs
We study the antiferromagnetic spin-half Heisenberg ladder in the presence of an additional frustrating rung spin which is motivated and relevant also for the description of real two-dimensional materials such as the two-dimensional trimer magnet Ba$_4$Ir$_3$O$_{10}$. We study the zero-temperature phase diagram, where we combine numerical and analytical methods into an overall consistent description. All numerical simulations are also accompanied by studies of the dynamical spin structure factor obtained via the density matrix renormalization group. Overall, we find in the regime of strong run…
The effect of disorder is studied on the field-induced quantum phase transition in the frustrated spin-ladder compound H8C4SO2Cu2(Cl[1-x]Brx)4 using bulk magnetic and thermodynamic measurements. The parent material (x=0) is a quantum spin liquid, which in applied fields is known to form a magnon condensate with long-range helimagnetic order. We show that bond randomness introduced by a chemical substitution on the non-magnetic halogene site destroys this phase transition at very low concentrations, already for x=0.01. The extreme fragility of the magnon condensate is attributed to random frust…
