Two-leg Ladder Research Articles

Ground-state phase diagram of the frustrated spin- 12 two-leg honeycomb ladder

We investigate a spin-$1/2$ two-leg honeycomb ladder with frustrating next-nearest-neighbor (NNN) coupling along the legs, which is equivalent to two $J_1$-$J_2$ spin chains coupled with $J_\perp$ at odd rungs. The full parameter region of the model is systematically studied using conventional and infinite density-matrix renormalization group as well as bosonization. The rich phase diagram consists of five distinct phases: A Haldane phase, a NNN-Haldane phase and a staggered dimer phase when $J_{\perp} < 0$; a rung singlet phase and a columnar dimer phase when $J_{\perp} > 0$. An interesting reentrant behavior from the dimerized phase into the Haldane phase is found as the frustration $J_2$ increases. The universalities of the critical phase transitions are fully analyzed. Phase transitions between dimerized and disordered phases belong to the two-dimensional Ising class with central charge $c=1/2$. The transition from the Haldane phase to NNN-Haldane phase is of a weak topological first order, while the continuous transition between the Haldane phase and rung singlet phase has central charge $c=2$.

A Developed Two-Leg Ladder Multilevel Converter Structure

The applications of multilevel converters (MCs) in industry have been increased because of their advantages such as high quality output waveform and lower harmonic distortions. This paper proposes an improved two-leg ladder topology for MC. For generating all levels at output voltage waveform, two methods are investigated for selecting the values of dc sources. The suggested structure generates a large number of levels at output voltage waveform with the least number of power electronic components such as insulated gate bipolar transistors, gate driver circuits, dc voltage sources and anti-parallel diodes in comparison with other similar topologies. Also, the magnitude of blocked voltage by switches is low. Power losses analysis on the proposed topology is provided. It is shown that the number of on-state switches in the presented structure is less than other similar topologies, which causes the voltage drop and power losses of proposed topology to be reduced. To show the merits of the proposed structure, comparison results are provided with other structures. To validate the analytical results of proposed topology, an experimental work for a 9-level converter and the simulation results for a 25-level converter are provided. PSCAD/EMTDC software is used for simulation works.

Quantum chaos in spin-1/2 two-leg ladders

In this paper, we study numerically the emergence of quantum chaos in the antiferromagnetic (AF) Heisenberg two-leg spin-1/2 ladder. We investigate the mutual effects of magnetic defects and couplings (rung or leg) on the statistical properties of the energy spectrum using the exact diagonalization technique. The system is chaotic when the leg and rung coupling strengths are equal, and even adding a strong magnetic defect does not change the energy distribution. Introducing two defects also does not change the level spacing distribution. We conclude that the system not strongly depend on the number of defects. However, when one of the couplings (rung or leg) is much larger than the other, level spacing distribution shows a profound dependence on it and a transition from chaotic to the integrable regime is found.

Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and FLEX results

We study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (RPA+FLEX). Our calculations reveal that RPA+FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly-interacting electron-hole excitations across the Fermi surface, at intermediate coupling DMRG shows gapped spin excitations at large momentum transfer that remain gapless within the RPA+FLEX approximation. For the charge response, RPA+FLEX can only reproduce the main features of the DMRG spectra at weak coupling and high doping levels, while it shows an incoherent character away from this limit. Overall, our analysis shows that RPA+FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard $U$ values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.

Quantum phase transitions of a two-leg bosonic ladder in an artificial gauge field

We consider a two leg bosonic ladder in a $U(1)$ gauge field with both interleg hopping and interleg repulsion. As a function of the flux, the interleg interaction converts the commensurate-incommensurate transition from the Meissner to a Vortex phase, into an Ising-type of transition towards a density wave phase. A disorder point is also found after which the correlation functions develop a damped sinusoid behavior signaling a melting of the vortex phase. We discuss the differences on the phase diagram for attractive and repulsive interleg interaction. In particular, we show how repulsion favors the Meissner phase at low-flux and a phase with a second incommensuration in the correlation functions for intermediate flux, leading to a richer phase diagram than in the case of interleg attraction. The effect of the temperature on the chiral current is also discussed.

Electronic structure and magnetic properties of the strong-rung spin-1 ladder compound Rb3Ni2(NO3)7

Small single crystals of Rb$_3$Ni$_2$(NO$_3$)$_7$ were obtained by crystallization from anhydrous nitric acid solution of rubidium nitrate and nickel nitrate hexahydrate. The basic elements of the crystal structure of this new compound are isolated spin-1 two-leg ladders of Ni$^{2+}$-ions connected by (NO$_3$)$^-$ groups. The experimental data show the absence of long range magnetic order at T $\geq 2$~K. LDA+U calculations and the detailed analysis of the experimental data, i.e. of the magnetic susceptibility, the specific heat in magnetic fields up to 9~T, the magnetization, and of the high-frequency electron spin resonance data, enable quantitative estimates of the relevant parameters of the $S=1$ ladders in Rb$_3$Ni$_2$(NO$_3$)$_7$ . The rung-coupling $J_1 = 10.5$~K, the leg-coupling $J_2=1.6$~K, and the uniaxial anisotropy $|A| = 179$~GHz are obtained. The scenario of spin liquid quantum ground state is further corroborated by quantum Monte Carlo simulations of the magnetic susceptibility.

Two-leg ladder systems with dipole–dipole Fermion interactions

The ground-state phase diagram of a two-leg fermionic dipolar ladder with inter-site interactions is studied using density matrix renormalization group (DMRG) techniques. We use a state-of-the-art implementation of the DMRG algorithm and finite size scaling to simulate large system sizes with high accuracy. We also consider two different model systems and explore stable phases in half and quarter filling factors. We find that in the half filling, the charge and spin gaps emerge in a finite value of the dipole–dipole and on-site interactions. In the quarter filling case, s-wave superconducting state, charge density wave, homogenous insulating and phase separation phases occur depend on the interaction values. Moreover, in the dipole–dipole interaction, the D-Mott phase emerges when the hopping terms along the chain and rung are the same, whereas, this phase has been only proposed for the anisotropic Hubbard model. In the half filling case, on the other hand, there is either charge-density wave or charged Mott order phase depends on the orientation of the dipole moments of the particles with respect to the ladder geometry.

Quantum phases of strongly interacting bosons on a two-leg Haldane ladder

We study the ground-state physics of a single-component Haldane model on a hexagonal two-leg ladder geometry with a particular focus on strongly interacting bosonic particles. We concentrate our analysis on the regime of less than one particle per unit-cell. As a main result, we observe several Meissner-like and vortex-fluid phases both for a superfluid as well as a Mott-insulating background. Furthermore, we show that for strongly interacting bosonic particles an unconventional vortex-lattice phase emerges, which is stable even in the regime of hardcore bosons. We discuss the mechanism for its stabilization for finite interactions by a means of an analytical approximation. We show how the different phases may be discerned by measuring the nearest- and next-nearest-neighbor chiral currents as well as their characteristic momentum distributions.

Topological insulation in a ladder model with particle-hole and reflection symmetries

A two-legged ladder model, one dimensional, exhibiting the parity anomaly is constructed. The model belongs to the C and CI symmetry classes, depending on the parameters, but, due to reflection, it exhibits topological insulation. The model consists of two superimposed Creutz models with onsite potentials. The topological invariants of each Creutz model sum to give the mirror winding number, with winding numbers which are nonzero individually but equal and opposite in the topological phase, and both zero in the trivial phase. We demonstrate the presence of edge states and quantized Hall response in the topological region. Our model exhibits two distinct topological regions, distinguished by the different types of reflection symmetries.

Sequential structural and antiferromagnetic transitions in BaFe2Se3 under pressure

The discovery of superconductivity in the two-leg ladder compound BaFe$_2$S$_3$ has established the 123-type iron chalcogenides as a novel and interesting subgroup of the iron-based superconductors family. However, in this 123 series, BaFe$_2$Se$_3$ is an exceptional member, with a magnetic order and crystalline structure different from all others. Recently, an exciting experiment reported the emergence of superconductivity in BaFe$_2$Se$_3$ at high pressure [J.-J. Ying, et al., Phys. Rev. B 95, 241109 (R) (2017)]. In this publication, we report a first principles study of BaFe$_2$Se$_3$. Our analysis unveils a variety of qualitative differences between BaFe$_2$S$_3$ and BaFe$_2$Se$_3$, including in the latter an unexpected chain of transitions with increasing pressure. First, by gradually reducing the tilting angle of iron ladders, the crystalline structure smoothly transforms from Pnma to Cmcm at ~6 GPa. Second, the system becomes metallic at 10.4 GPa. Third, its unique ambient pressure Block antiferromagnetic ground state is replaced by the more common CX antiferromagnetic order at ~12 GPa, the same magnetic state of the 123-S ladder. This transition is found at a pressure very similar to the experimental superconducting transition. Finally, all magnetic moments vanish at 30 GPa. This reported theoretical diagram of the complete phase evolution is important because of the technical challenges to capture many physical properties in high-pressure experiments. The information obtained in our calculations suggest different characteristics for superconductivity in BaFe$_2$Se$_3$ and BaFe$_2$S$_3$: in 123-S pairing occurs when magnetic moments vanish, while in 123-Se the transition region from Block- to CX-type magnetism appears to catalyze superconductivity. Finally, an additional superconducting dome above ~30 GPa is expected to occur.

Spin-gap spectroscopy in a bosonic flux ladder

Ultracold bosonic atoms trapped in a two-leg ladder pierced by a magnetic field provide a minimal and quasi-one-dimensional instance to study the interplay between orbital magnetism and interactions. Using time-dependent matrix-product-state simulations, we investigate the properties of the so-called ‘Meissner’ and ‘vortex’ phases which appear in such a system, focusing on the experimentally accessible observables. We discuss how to experimentally monitor the phase transition, and show that the response to the modulation of the density imbalance between the two legs of the ladder is qualitatively different in the two phases. We argue that this technique can be used as a tool for many-body spectroscopy, allowing us to quantitatively measure the spin gap in the Meissner phase. We finally discuss its experimental implementation.

Ground-state magnetic properties of spin ladder-shaped quantum nanomagnet: Exact diagonalization study

The paper presents a computational study of the ground-state properties of a quantum nanomagnet possessing the shape of a finite two-legged ladder composed of 12 spins S=1/2. The system is described with isotropic quantum Heisenberg model with nearest-neighbour interleg and intraleg interactions supplemented with diagonal interleg coupling between next nearest neighbours. All the couplings can take arbitrary values. The description of the ground state is based on the exact numerical diagonalization of the Hamiltonian. The ground-state phase diagram is constructed and analysed as a function of the interactions and the external magnetic field. The ground-state energy and spin-spin correlations are extensively discussed. The cases of ferro- and antiferromagnetic couplings are compared and contrasted.

Tabby graphene: Dimensional magnetic crossover in fluorinated graphite

Tabby is a pattern of short irregular stripes, usually related to domestic cats. We have produced Tabby patterns on graphene by attaching fluorine atoms running as monoatomic chains in crystallographic directions. Separated by non-fluorinated sp2 carbon ribbons, sp3-hybridized carbon atoms bonded to zigzag fluorine chains produce sp2-sp3 interfaces and spin-polarized edge states localized on both sides of the chains. We have compared two kinds of fluorinated graphite samples C2Fx, with x near to 1 and x substantially below 1. The magnetic susceptibility of C2Fx (x < 1) shows a broad maximum and a thermally activated spin gap behaviour that can be understood in a two-leg spin ladder model with ferromagnetic legs and antiferromagnetic rungs; the spin gap constitutes about 450 K. Besides, stable room-temperature ferromagnetism is observed in C2Fx (x < 1) samples: the crossover to a three-dimensional magnetic behaviour is due to the onset of interlayer interactions. Similarly prepared C2Fx (x ≈ 1) samples demonstrate features of two-dimensional magnetism without signs of high-temperature magnetic ordering, but with transition to a superparamagnetic state below 40 K instead. The magnetism of the Tabby graphene is stable until 520 K, which is the temperature of the structural reconstruction of fluorinated graphite.

Possible high- Tc superconductivity due to incipient narrow bands originating from hidden ladders in Ruddlesden-Popper compounds

We introduce a concept of hidden ladders for the bilayer Ruddlesden-Popper type compounds: While the crystal structure is bilayer, $d_{xz}$ ($d_{yz}$) orbitals in the relevant $t_{2g}$ sector of the transition metal form a two-leg ladder along $x$ ($y$), since the $d_{xz}$ ($d_{yz}$) electrons primarily hop along the leg direction $x$ ($y$) on top of the rung $z$ direction. We predict that Sr$_3$Mo$_2$O$_7$ and Sr$_3$Cr$_2$O$_7$ are candidates for the hidden-ladder material with a right position of $E_F$, from a first-principles band calculation. Based on the analysis of Eliashberg equation for these systems, we propose a possible occurrence of high temperature superconductivity in these materials arising from the interband pair scattering processes between the wide and "incipient" narrow bands on the ladder.

Magnetic dimerization in the frustrated spin ladder Li2Cu2O(SO4)2

The magnetic properties of ${\mathrm{Li}}_{2}{\mathrm{Cu}}_{2}\mathrm{O}{({\mathrm{SO}}_{4})}_{2}$ are investigated in the framework of density functional theory. In its high-temperature tetragonal structure, this compound appears as a rare material realization of a frustrated spin-1/2 two-leg ladder, where magnetic frustration arises from competing nearest and next-nearest interactions along the legs. Through a large magnetoelastic coupling, the triclinic distortion occurring around 125 K is shown to induce the formation of a staggered dimer structure, lifting most of the magnetic frustration.

Signatures of pairing in the magnetic excitation spectrum of strongly correlated two-leg ladders

Magnetic interactions are widely believed to play a crucial role in the microscopic mechanism leading to high critical temperature superconductivity. It is therefore important to study the signatures of pairing in the magnetic excitation spectrum of simple models known to show unconventional superconducting tendencies. Using the Density Matrix Renormalization Group technique, we calculate the dynamical spin structure factor $S({\bf k},\omega)$ of a generalized $t-U-J$ Hubbard model away from half-filling in a two-leg ladder geometry. The addition of $J$ enhances pairing tendencies. We analyze quantitatively the signatures of pairing in the magnetic excitation spectra. We found that the superconducting pair-correlation strength, that can be estimated independently from ground state properties, is closely correlated with the integrated low-energy magnetic spectral weight in the vicinity of $(\pi,\pi)$. In this wave-vector region, robust spin incommensurate features develop with increasing doping. The branch of the spectrum with rung direction wave-vector $k_{rung}=0$ does not change substantially with doping where pairing dominates, and thus plays a minor role. We discuss the implications of our results for neutron scattering experiments, where the spin excitation dynamics of hole-doped quasi-one dimensional magnetic materials can be measured, and also address implications for recent resonant inelastic X-ray scattering experiments.

Majorana spin liquids, topology, and superconductivity in ladders

We theoretically address spin chain analogs of the Kitaev quantum spin model on the honeycomb lattice. The emergent quantum spin liquid phases or Anderson resonating valence bond (RVB) states can be understood, as an effective model, in terms of p-wave superconductivity and Majorana fermions. We derive a generalized phase diagram for the two-leg ladder system with tunable interaction strengths between chains allowing us to vary the shape of the lattice (from square to honeycomb ribbon or brickwall ladder). We evaluate the winding number associated with possible emergent (topological) gapless modes at the edges. In the Az phase, as a result of the emergent Z2 gauge fields and pi-flux ground state, one may build spin-1/2 (loop) qubit operators by analogy to the toric code. In addition, we show how the intermediate gapless B phase evolves in the generalized ladder model. For the brickwall ladder, the $B$ phase is reduced to one line, which is analyzed through perturbation theory in a rung tensor product states representation and bosonization. Finally, we show that doping with a few holes can result in the formation of hole pairs and leads to a mapping with the Su-Schrieffer-Heeger model in polyacetylene; a superconducting-insulating quantum phase transition for these hole pairs is accessible, as well as related topological properties.

Orbital order and fluctuations in the two-leg ladder materials BaFe2X3 ( X=S and Se) and CsFe2Se3

The electronic structure of BaFe$_2X_3$ ($X$ = S and Se) and CsFe$_2$Se$_3$ in which two-leg ladders are formed by the Fe sites are studied by means of x-ray absorption and resonant inelastic x-ray scattering spectroscopy. The x-ray absorption spectra at the Fe L edges for BaFe$_2X_3$ exhibit two components, indicating that itinerant and localized Fe 3$d$ sites coexist. Substantial x-ray linear dichroism (XLD) is observed in polarization dependent spectra, indicating the existence of orbital order or fluctuation in the Fe-ladder even above the N\'{e}el temperature $T_N$. Direct exchange interaction along the legs of the Fe-ladder stabilizes the orbital and antiferromagnetic orders in BaFe$_2$S$_3$, while the ferromagnetic molecular orbitals are realized between the rungs in CsFe$_2$Se$_3$.

Efficiency of fermionic quantum distillation

We present a time-dependent density-matrix renormalization group investigation of the quantum distillation process within the Fermi--Hubbard model on a quasi-1D ladder geometry. The term distillation refers to the dynamical, spatial separation of singlons and doublons in the sudden expansion of interacting particles in an optical lattice, i.e., the release of a cloud of atoms from a trapping potential. Remarkably, quantum distillation can lead to a contraction of the doublon cloud, resulting in an increased density of the doublons in the core region compared to the initial state. As a main result, we show that this phenomenon is not limited to chains that were previously studied. Interestingly, there are additional dynamical processes on the two-leg ladder such as density oscillations and selftrapping of defects that lead to a less efficient distillation process. An investigation of the time evolution starting from product states provides an explanation for this behaviour. Initial product states are also considered, since in optical lattice experiments such states are often used as the initial setup. We propose configurations that lead to a fast and efficient quantum distillation.

Optimal inhomogeneity for pairing in Hubbard systems with next-nearest-neighbor hopping

Previous studies have shown that bipartite Hubbard systems with inhomogeneous hopping amplitudes can exhibit higher pair-binding energies than the uniform model. Here we examine whether this result holds for systems with a more generic band structure. To this end, we use exact diagonalization and the density matrix renormalization group method to study the 4x4 Hubbard cluster and the two-leg Hubbard ladder with checkerboard-modulated nearest-neighbor hopping, t, and next-nearest-neighbor (diagonal) hopping, t_d. We find that the strongest pairing continues to occur at an intermediate level of inhomogeneity. While the maximal pair-binding energy is enhanced by a positive t_d/t, it is suppressed and appears at weaker repulsion strengths and smaller hole concentrations when t_d/t is negative. We point out a possible connection between the pairing maximum and the magnetic properties of the system.