Two-leg Ladder Research Articles

Vortex and Meissner phases of strongly interacting bosons on a two-leg ladder

We establish the phase diagram of the strongly-interacting Bose-Hubbard model defined on a two-leg ladder geometry in the presence of a homogeneous flux. Our work is motivated by a recent experiment [Atala et al., Nature Phys. 10, 588 (2014)], which studied the same system, in the complementary regime of weak interactions. Based on extensive density matrix renormalization group simulations and a bosonization analysis, we fully explore the parameter space spanned by filling, inter-leg tunneling, and flux. As a main result, we demonstrate the existence of gapless and gapped Meissner and vortex phases, with the gapped states emerging in Mott-insulating regimes. We calculate experimentally accessible observables such as chiral currents and vortex patterns.

Meissner to vortex phase transition in a two-leg ladder in artificial gauge field

We consider a two-leg boson ladder in artificial gauge field with hard-core intraleg and negligible interleg interactions. Using numerical simulations based on the Density Matrix Renormalization Group (DMRG) algorithm, combined with a bosonization approach, we study its commensurate-incommensurate transition to a vortex phase at a critical flux. We discuss the finite-size scaling behavior of the longitudinal current near the transition. For weak interchain boson hopping, the finite size scaling is in agreement with the predictions from bosonization.

Chiral Mott insulators, Meissner effect, and Laughlin states in quantum ladders

We introduce generic bosonic models exemplifying that chiral Meissner currents can persist in insulating phases of matter. We first consider interacting bosons on a two-leg ladder. The total density sector can be gapped in a bosonic Mott insulator at odd-integer filling, while the relative density sector remains superfluid due to interchain hopping. Coupling the relative density to gauge fields yields a pseudospin Meissner effect. We show that the same phase arises if the bosons are replaced by spinful fermions confined in Cooper pairs, and find a dual fermionic Mott insulator with spinon currents. We prove that by tuning the mean density the Mott insulator with Meissner currents turns into a low-dimensional bosonic $\nu = \frac{1}{2}$ Laughlin state for strong enough repulsive interactions across the ladder rungs. We finally discuss extensions to multileg ladders and bilayers in which spinon superfluids with Meissner currents become possible. We propose two experimental realizations, one with ultracold atoms in the setup of Atala et al., Nat. Phys. \textbf{8}, 588 (2014) and another with Josephson junction arrays. We also address a Bose-Fermi mixture subject to a magnetic field in connection with the pseudo-gap phase of high-Tc cuprates.

Electronic Structure Reconstruction across the Antiferromagnetic Transition in TaFe1.23Te3 Spin Ladder

Employing the angle-resolved photoemission spectroscopy we study the electronic structure of TaFe1.23Te3, a two-leg spin ladder compound with a novel antiferromagnetic ground state. Quasi-two-dimensional (2D) Fermi surface is observed, with sizable inter-ladder hopping. Moreover, instead of observing an energy gap at the Fermi surface in the antiferromagnetic state, we observe the shifts of various bands. Combining these observations with density-functional-theory calculations, we propose that the large scale reconstruction of the electronic structure, caused by the interactions between the coexisting itinerant electrons and local moments, is most likely the driving force of the magnetic transition. Thus TaFe1.23Te3 serves as a simpler platform that contains similar ingredients to the parent compounds of iron-based superconductors.

Mott transition in a two-leg Bose-Hubbard ladder under an artificial magnetic field

We consider the Bose-Hubbard model on a two-leg ladder under an artificial magnetic field, and investigate the superfluid-to-Mott insulator transition in this setting. Recently, this system has been experimentally realized [M.Atala \textit{et al.}, Nature Physics \textbf{10}, 588--593 (2014)], albeit in a parameter regime that is far from the Mott transition boundary. Depending on the strength of the magnetic field, the single-particle spectrum has either a single ground state or two degenerate ground states. The transition between these two phases is reflected in the many-particle properties. We first investigate these phases through the Bogoliubov approximation in the superfluid regime and calculate the transition boundary for weak interactions. For stronger interactions the system is expected to form a Mott insulator. We calculate the Mott transition boundary as a function of the magnetic field and interleg coupling with mean-field theory, strong-coupling expansion and density matrix renormalization group (DMRG). Finally, using the DMRG, we investigate the particle-hole excitation gaps of this system at different filling factors and find peaks at simple fractions indicating the possibility of correlated phases.

Coexistence of localized and itinerant electrons inBaFe2X3(X=Sand Se) revealed by photoemission spectroscopy

We report a photoemission study at room temperature on BaFe2X3 (X = S and Se) and CsFe2Se3 in which two-leg ladders are formed by the Fe sites. The Fe 2p core-level peaks of BaFe2X3 are broad and exhibit two components, indicating that itinerant and localized Fe 3d sites coexist similar to KxFe2-ySe2. The Fe 2p core-level peak of CsFe2Se3 is rather sharp and is accompanied by a charge-transfer satellite. The insulating ground state of CsFe2Se3 can be viewed as a Fe2+ Mott insulator in spite of the formal valence of +2.5. The itinerant versus localized behaviors can be associated with the stability of chalcogen p holes in the two-leg ladder structure.

Two-leg fermionic Hubbard ladder system in the presence of state-dependent hopping

We study a two-leg fermionic Hubbard ladder model with a state-dependent hopping. We find that, contrary to the case without a state-dependent hopping, for which the system has a superfluid nature regardless of the sign of the interaction at incommensurate filling, in the presence of such a hopping a spin-triplet superfluid, spin- density wave and charge-density wave phases emerge. We examine our results in the light of recent experiments on periodically-driven optical lattices in cold atoms. We give protocols allowing us to realize the spin-triplet superfluid elusive in the cold atoms.

Variational Study on Loop Currents in Bose Hubbard model with Staggered Flux

In view of strongly interacting bosons in an optical lattice with a large gauge field, we study phase transitions in a two-dimensional Bose-Hubbard model with a staggered flux, on the basis of variational Monte Carlo calculations. Inthe trial states,besides typical onsite and intersite correlation factors, we introduce a configuration-dependent phase factor,which was recently found essential for treating current-carrying states. It is found that this phase factor is qualitativelyvitalfordescribing a Mott insulating (MI) state in the present model. Thereby, the Peierls phasesattached in relevant hopping processes are cancelled out. As a result, local currents completely suppressed in MI states, namely, a chiral Mott state does not appear for the square lattice, in contrast tothecorresponding two-leg ladder model. In addition, we discuss other features of the first-order superfluid-MI transition in this model.

Magnetism in Two-leg Ladder Compound Ba6Fe8S15 with Mixed Oxidation State of Iron

The magnetic properties of two-leg ladder compound Ba6Fe8S15 were studied to clarify the magnetic state at low temperatures. The 57Fe Mössbauer spectra above 120K indicate the existence of only a single quadrupole doublet, which is consistent with the evidence of one crystallographic Fe site. Below 120K, however, the spectra characterized by two kinds of magnetic hyperfine patterns were observed, indicating an existence of complicated magnetic order. These spectra observed down to 4.2K were analyzed using one-site model of iron where only the hyperfine field is different from each pattern.

Topological pair-density-wave superconducting states.

We show that the pair-density-wave (PDW) superconducting state emergent in extended Heisenberg-Hubbard models in two-leg ladders is topological in the presence of an Ising spin symmetry and supports a Majorana zero mode (MZM) at an open boundary and at a junction with a uniform d-wave one-dimensional superconductor. Similarly to a conventional finite-momentum paired state, the order parameter of the PDW state is a charge-2e field with finite momentum. However, the order parameter here is a quartic electron operator and conventional mean-field theory cannot be applied to study this state. We use bosonization to show that the 1D PDW state has a MZM at a boundary. This superconducting state is an exotic topological phase supporting Majorana fermions with finite-momentum pairing fields and charge-4e superconductivity.

The effect of FM inter-ladder coupling in spin-1/2 AFM two-leg ladders in the presence of a magnetic field: Quantum Monte Carlo study

We study the effect of inter-ladder ferromagnetic (FM) coupling in spin-1/2 two-leg ladders with antiferromagnetic (AFM) legs and rungs interactions using the stochastic series expansion quantum Monte Carlo. We have compared the results with the experimental measurement on Sr14−xCaxCu24O41 cuprate which is the candidate for spin-1/2 AFM two-leg ladders with FM inter-ladder interaction. A remarkable asymptotic behavior of susceptibility is observed at very low temperature. In the absence of the magnetic field, thermodynamic behavior of an individual spin-1/2 two-leg ladder is similar to coupled one up to −0.5Jleg interaction. But, the gaped phase is not clear in the Jin=−0.2Jleg of FM coupled two-leg ladder even at low magnetic fields, which shows that the inter-ladder FM interaction can induce a new quantum ordered gapless phase at zero temperature.

Plaquette order in a dimerized frustrated spin ladder

We study the effect of spin-Peierls instability on the phase-diagram of a frustrated antiferromagnetic spin-1/2 ladder, with weak transverse and diagonal rung coupling. Our analysis focuses on a one-dimensional version of the model (i.e. a single two-leg ladder) where we consider two forms of spin-Peierls (SP) instabilities on the legs: columnar dimers (CD) and staggered dimers (SD). We particularly examine the regime of parameters (corresponding to an intermediate XXZ anisotropy) where the SP and rung coupling terms are equally relevant. In both the CD and SD cases we find that the effective field theory describing the system is a self-dual sine-Gordon model, which favors ordering and the opening of a gap to excitations. The order parameter, which reflects the interplay between the SP and rung interactions, represents a crystal of 4-spin plaquettes on which longitudinal and transverse dimers are in a superposition. Depending on the SP instability mode these plaquettes are closed or open, however both types spontaneously break reflection symmetry across the ladder. The closed plaquettes are stable, while the open plaquette-order is relatively fragile and the corresponding gap may be tuned to zero under extreme conditions. We further find that a first order transition occurs from the Plaquette order to a valence bond crystal (VBC) of dimers on the legs. It is suggestive that in a higher dimensional version of this system, this variety of distinct VBC states with comparable energies leads to the formation of domains. Effectively one-dimensional gapless spinon modes on domain boundaries can possibly account for the experimental observation of a spin-liquid behavior in a physical realization of the model.

Resonant extended states in driven quasiperiodic lattices: Aubry-Andre localization by design

We consider a quasiperiodic Aubry-Andre (AA) model and add a weak time-space-periodic perturbation. The undriven AA model is chosen to be well in the localized regime. The driving term controls the effective number of propagation channels. For a spatial resonance which reduces the reciprocal space dynamics to an effective one-dimensional two-leg ladder, the ac perturbation resonantly couples certain groups of localized eigenstates of the undriven AA model and turns them into extended ones. Slight detuning of the spatial and temporal frequencies off resonance returns these states into localized ones. We analyze the details of the resonant extended eigenstates using Floquet representations. In particular, we find that their size grows linearly with the system size. Initial wave packets overlap with resonant extended eigenstates and lead to ballistic spreading.

Thermodynamics of the Spin-1/2 Two-Leg Ladder Compound (C $$_5$$ 5 H $$_{12}$$ 12 N) $$_2$$ 2 CuBr $$_4$$ 4

The thermodynamic behavior of the spin $S=1/2$ antiferromagnetic two-leg ladder compound $(C_{5}H_{12}N)_{2} CuBr_{4}$ in a uniform magnetic field is studied using numerical and analytical approaches. The entropy $S(H,T)$ and specific heat $C(H,T)$ are calculated. The specific heat shows various behaviors in different regions of the magnetic field. The field-dependence of the specific heat is almost symmetric about the average of quantum critical fields in complete agreement with experimental results. In addition, it is found that during an adiabatic demagnetization process, temperature drops in the vicinity of the field induced zero-temperature quantum phase transitions.

Strange correlations in spin-1 Heisenberg antiferromagnets

We study the behavior of the recently proposed "strange correlator" [Phys. Rev. Lett. {\bf 112}, 247202 (2014)] in spin-1 Heisenberg antiferromagnetic chains with uniaxial single-ion anisotropy. Using projective quantum Monte Carlo, we are able to directly access the strange correlator in a variety of phases, as well as to examine its critical behavior at the quantum phase transition between trivial and non-trivial symmetry protected topological phases. After finding the expected long-range behavior in these two symmetry conserving phases, we go on to verify the topological nature of two-leg and three-leg spin-1 Heisenberg antiferromagnetic ladders. This demonstrates the power of the strange correlator in distinguishing between trivial and non-trivial symmetry protected topological phases.

Criticality and Mott glass phase in a disordered two-dimensional quantum spin system

We use quantum Monte Carlo simulations to study a disordered $S=1/2$ Heisenberg quantum spin model with three different nearest-neighbor interactions, ${J}_{1}\ensuremath{\le}{J}_{2}\ensuremath{\le}{J}_{3}$, on the square lattice. We consider the regime in which ${J}_{1}$ represents weak bonds, and ${J}_{2}$ and ${J}_{3}$ correspond to two kinds of stronger bonds (dimers) which are randomly distributed on columns forming coupled two-leg ladders. When increasing the average intradimer coupling $({J}_{2}+{J}_{3})/2$, the system undergoes a N\'eel to quantum glass transition of the ground state and later a second transition into a quantum paramagnet. The quantum glass phase is of the gapless Mott glass type (i.e., in boson language it is incompressible at temperature $T=0$), and we find that the temperature dependence of the uniform magnetic susceptibility follows the stretched exponential form $\ensuremath{\chi}\ensuremath{\sim}exp(\ensuremath{-}b/{T}^{\ensuremath{\alpha}})$, with $0<\ensuremath{\alpha}<1$. At the N\'eel-glass transition, we observe the standard O(3) critical exponents, which implies that the Harris criterion for the relevance of the disorder is violated in this system.

Superfluid/Bose-glass transition in one dimension

We consider a one-dimensional system of interacting bosons in a random potential. At zero temperature, it can be either in the superfluid or in the insulating phase. We study the transition at weak disorder and moderate interaction. Using a systematic approach, we derive the renormalization group equations at two-loop order and discuss the phase diagram. We find the universal form of the correlation functions at the transitions and compute the logarithmic corrections to the main universal power-law behavior. In order to mimic large density fluctuations on a single site, we study a simplified model of disordered two-leg bosonic ladders with correlated disorder across the rung. Contrarily to the single-chain case, the latter system exhibits a transition between a superfluid and a localized phase where the exponents of the correlation functions at the transition do not take universal values.

Entropy of the quantum soliton lattice and multiple magnetization steps inBiCu2PO6

${\mathrm{BiCu}}_{2}{\mathrm{PO}}_{6}$, a spin-gapped material in a frustrated two-leg ladder lattice, exhibits a complex $(H,T)$ phase diagram in external magnetic fields. We have characterized the field-induced phases through specific heat, magnetocaloric effect, Faraday rotation, and magnetization measurements in fields up to 120 T. In addition to observing a magnetic phase above 60 T which we attribute to the crystallization of triplet excitations, our measurements reveal the emergence and the subsequent disappearance of a high-entropy (short-range-ordered) phase at first and second critical magnetic fields, respectively. This is in good agreement with the theoretical prediction of a quantum soliton lattice at intermediate fields.

Magnetism and its interplay with lattice in the iron-based ladder compounds

Since the discovery, research on iron-based superconductivity (SC) has become one of the main streams in condensed matter physics [1]. The interplay between structure, magnetism and SC is one of most intriguing subjects of this field. The common structural feature is the presence of square planar sheets of Fe atoms coordinated tetrahedrally by pnictogens or chalcogens. They have been, at the early stage, realized in the ZrCuSiAs (1111), ThCr2Si2 (122), anti-PbO (11) and Cu2Sb (111) structures. To gain further insight into the mechanism of the SC and variation of magnetic orders, investigation of Fe-based compounds with a separate spatial dimension is important. This is because the dimensionality should influence magnetism and can control itinerancy of electrons by changing Fermi surface topology. As spin ladders in copper oxides shed a new light on the mechanism of SC, a study on an analogue with ladder geometry among Fe-based compounds is highly desired. Here we report our recent studies of iron-based ladder compounds AFe2X3 (A = K, Rb, Cs, Ba; X = S, Se, Te) [2,3]. Crystal structure is novel, comprising of FeX4 tetrahedra with channels which host A atoms, and four-fold coordinated Fe2+ ions form two-leg ladder geometry. Unlike most of parent compounds of the Fe-based SCs, the ladder compounds are insulating down to the lowest measured temperature. Through bulk properties and neutron diffraction measurements, a variety of magnetic structures and low dimensional characteristics were elucidated. These would provide a clue of the SC realized in a separate dimension systems. The description of theory that accounts for the observed magnetic structures will be also presented.

Electronic screening-enhanced hole pairing in two-leg spin ladders studied by high-resolution resonant inelastic x-ray scattering at Cu M edges.

We study the electronic screening mechanisms of the effective Coulomb on-site repulsion in hole-doped Sr(14)Cu(24)O(41) compared to undoped La(6)Ca(8)Cu(24)O(41) using polarization dependent high-resolution resonant inelastic x-ray scattering at Cu M edges. By measuring the energy of the effective Coulomb on-site repulsion and the spin excitations, we estimate superexchange and hopping matrix element energies along rungs and legs, respectively. Interestingly, hole doping locally screens the Coulomb on-site repulsion reducing it by as much as 25%. We suggest that the increased ratio of the electronic kinetic to the electronic correlation energy contributes to the local superexchange mediated pairing between holes.