Two-leg Ladder Research Articles

Pressure-induced non-superconducting phase of β-Na0.33V2O5 and the mechanism of high-pressure phase transitions in β-Na0.33V2O5 and β-Li0.33V2O5 at room temperature

The crystal structure of β-Na0.33V2O5 (C2/m, Z = 6) has been studied on compression to 19 GPa at room temperature using synchrotron single-crystal diffraction in a diamond anvil cell. The vanadate bronze undergoes a phase transition to a non-superconducting phase at about 12 GPa due to changes of polyhedral connectivities in the vanadate framework and due to ordering of the Na+ cations. This novel structure (Cm, Z = 6) is interpreted as an intermediate stage in the sequence of pressure-induced transformations in the β-A0.33V2O5 bronzes (A: Li, Na) at room temperature. This study reveals the close relation between the loss of the two-leg ladder V–V system and non-superconducting state of the β-A0.33V2O5 materials.

Sudden expansion and domain-wall melting of strongly interacting bosons in two-dimensional optical lattices and on multileg ladders

We numerically investigate the expansion of clouds of hard-core bosons in the two-dimensional square lattice using a matrix-product-state based method. This nonequilibrium set-up is induced by quenching the trapping potential to zero and our work is specifically motivated by a recent experiment with interacting bosons in an optical lattice [Ronzheimer et al., Phys. Rev. Lett. 110, 205301 (2013)]. As the anisotropy of the amplitudes $J_x$ and $J_y$ for hopping in different spatial directions is varied from the one- to the two-dimensional case, we observe a crossover from a fast ballistic expansion in the one-dimensional limit $J_x \gg J_y$ to much slower dynamics in the isotropic two-dimensional limit $J_x=J_y$. We further study the dynamics on multi-leg ladders and long cylinders. For these geometries we compare the expansion of a cloud to the melting of a domain wall, which helps us to identify several different regimes of the expansion as a function of time. By studying the dependence of expansion velocities on both the anisotropy $J_y/J_x$ and the number of legs, we observe that the expansion on two-leg ladders, while similar to the two-dimensional case, is slower than on wider ladders. We provide a qualitative explanation for this observation based on an analysis of the rung spectrum.

Bosons with long-range interactions on two-leg ladders in artificial magnetic fields

Motivated by experiments exploring the physics of neutral atoms in artificial magnetic fields, we study the ground state of bosons interacting with long range dipolar interactions on a two-leg ladder. Using two complimentary variational approaches, valid for weak interactions, we find rich physics driven by the long range forces. Generically, long range interactions tend to destroy the Meissner phase in favor of modulated density wave phases. Nearest neighbor interactions produce a novel interleg charge density wave phase, where the total density remains uniform, but the density on each leg of the ladder is modulating in space, out-of-phase with one another. At weak magnetic fields, next nearest neighbor interactions lead to a fully modulated biased ladder phase, where all the particles are on one leg of the ladder, and the density is modulating in space. This state simultaneously breaks $Z_{2}$ reflection symmetry and $U(1)$ symmetry associated with translation in real space. For values of the flux near $\phi = \pi$, we find that a switching effect occurs for arbitrarily weak interactions, where the density modulates in space, but the chiral current changes sign on every plaquette. Arbitrarily weak attractive interactions along the rungs destroy the Meissner phase completely, in favor of a modulated density wave phase. Varying magnetic field produces a cascade of first order transitions between modulated density wave states with different wave-vectors, which manifests itself as discrete jumps in the chiral current. Polarizing the dipoles along the ladder direction yields a region of phase space where a stable biased ladder phase occurs even at arbitrarily weak magnetic fields. We discuss the experimental consequences of our work, in particular, how the interleg charge density wave can manifest itself in recent experiments on bosons in synthetic dimensions.

Ground-state phases of a rung-alternatedspin−12Heisenberg ladder

The ground-state phase diagram of Heisenberg spin-1/2 system on a two-leg ladder with rung alternation is studied by combining analytical approaches with numerical simulations. For the case of ferromagnetic leg exchanges a unique ferrimagnetic ground state emerges, whereas for the case of antiferromagnetic leg exchanges several different ground states are stabilized depending on the ratio between exchanges along legs and rungs. For the more general case of a honeycomb-ladder model for the case of ferromagnetic leg exchanges besides usual rung-singlet and saturated ferromagnetic states we obtain a ferrimagnetic Luttinger liquid phase with both linear and quadratic low energy dispersions and ground state magnetization continuously changing with system parameters. For the case of antiferromagnetic exchanges along legs, different dimerized states including states with additional topological order are suggested to be realized.

Current drag in two leg quantum ladders

A two-leg ladder of either interacting bosons or tightly bound cooper pairs is investigated when a supercurrent is forced in one of the legs of the ladder. The two legs of the ladder are connected by a tunneling term. Using a bosonization representation of such an interacting ladder we show that up to a certain critical current the current in the first wire induces an identical supercurrent in the second wire. When this threshold is exceeded vortices are formed in the system and the current in the second wire reduces even if the driving current increases. Potential applications to condensed matter or cold atomic systems are discussed.

Spontaneous Increase of Magnetic Flux and Chiral-Current Reversal in Bosonic Ladders: Swimming against the Tide.

The interplay between spontaneous symmetry breaking in many-body systems, the wavelike nature of quantum particles and lattice effects produces an extraordinary behavior of the chiral current of bosonic particles in the presence of a uniform magnetic flux defined on a two-leg ladder. While noninteracting as well as strongly interacting particles, stirred by the magnetic field, circulate along the system's boundary in the counterclockwise direction in the ground state, interactions stabilize vortex lattices. These states break translational symmetry, which can lead to a reversal of the circulation direction. Our predictions could readily be accessed in quantum gas experiments with existing setups or in arrays of Josephson junctions.

Ultrafast electronic state conversion at room temperature utilizing hidden state in cuprate ladder system.

Photo-control of material properties on femto- (10−15) and pico- (10−12) second timescales at room temperature has been a long-sought goal of materials science. Here we demonstrate a unique ultrafast conversion between the metallic and insulating state and the emergence of a hidden insulating state by tuning the carrier coherence in a wide temperature range in the two-leg ladder superconductor Sr14-xCaxCu24O41 through femtosecond time-resolved reflection spectroscopy. We also propose a theoretical scenario that can explain the experimental results. The calculations indicate that the holes injected by the ultrashort light reduce the coherence among the inherent hole pairs and result in suppression of conductivity, which is opposite to the conventional photocarrier-doping mechanism. By using trains of ultrashort laser pulses, we successively tune the carrier coherence to within 1 picosecond. Control of hole-pair coherence is shown to be a realistic strategy for tuning the electronic state on ultrafast timescales at room temperature.

Chiral currents in one-dimensional fractional quantum Hall states

We study bosonic and fermionic quantum two-leg ladders with orbital magnetic flux. In such systems, the ratio, $\nu$, of particle density to magnetic flux shapes the phase-space, as in quantum Hall effects. In fermionic (bosonic) ladders, when $\nu$ equals one over an odd (even) integer, Laughlin fractional quantum Hall (FQH) states are stabilized for sufficiently long ranged repulsive interactions. As a signature of these fractional states, we find a unique dependence of the chiral currents on particle density and on magnetic flux. This dependence is characterized by the fractional filling factor $\nu$, and forms a stringent test for the realization of FQH states in ladders, using either numerical simulations or future ultracold-atom experiments. The two-leg model is equivalent to a single spinful chain with spin-orbit interactions and a Zeeman magnetic field, and results can thus be directly borrowed from one model to the other.

Magnetization plateaus by reconstructed quasispinons in a frustrated two-leg spin ladder under a magnetic field

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-spinons, while the plateaux at 1/3 and 2/3 can be associated with the array of quasi-spinons such as soliton lattice. This is different from the usual Bose-Einstein-condensation picture of triplons. Our results will be useful to understand magnetization curves in BiCu$_2$PO$_6$.

Density-dependent synthetic magnetism for ultracold atoms in optical lattices

Raman-assisted hopping can allow for the creation of density-dependent synthetic magnetism for cold neutral gases in optical lattices. We show that the density-dependent fields lead to a nontrivial interplay between density modulations and chirality. This interplay results in a rich physics for atoms in two-leg ladders, characterized by a density-driven Meissner-superfluid to vortex-superfluid transition, and a nontrivial dependence of the density imbalance between the legs. Density-dependent fields also lead to intriguing physics in square lattices. In particular, it leads to a density-driven transition between a nonchiral and a chiral superfluid, both characterized by nontrivial charge density-wave amplitude. We finally show how the physics due to the density-dependent fields may be easily probed in experiments by monitoring the expansion of doublons and holes in a Mott insulator, which presents a remarkable dependence on quantum fluctuations.

Symmetry protected topological phases in spin-1 ladders and their phase transitions

We study two-legged spin-1 ladder systems with D2×σ symmetry group, where D2 is discrete spin rotational symmetry and σ means interchain reflection symmetry. The system has one trivial phase and seven nontrivial symmetry protected topological (SPT) phases. We construct Hamiltonians to realize all of these SPT phases and study the phase transitions between them. Our numerical results indicate that there is no direct continuous transition between any two SPT phases we studied. We interpret our results via topological nonlinear sigma model effective field theory, and further conjecture that generally there is no direct continuous transition between two SPT phases in one dimension if the symmetry group is discrete at all length scales.

Persisting Meissner state and incommensurate phases of hard-core boson ladders in a flux

The phase diagram of a half-filled hard-core boson two-leg ladder in a flux is investigated by means of numerical simulations based on the density matrix renormalization group (DMRG) algorithm and bosonization. We calculate experimentally accessible observables such as the momentum distribution, as well as rung current, density wave, and bond-order wave correlation functions, allowing us to identify the Mott Meissner and Mott vortex states. We follow the transition from commensurate Meissner to incommensurate vortex state at increasing interchain hopping until the critical value [Piraud et al. Phys. Rev. B 91, 140406 (2015)] above which the Meissner state is stable at any flux. For flux close to $\ensuremath{\pi}$, and below the critical hopping, we observe the formation of a second incommensuration in the Mott vortex state that could be detectable in current experiments.

Bose-Hubbard ladder subject to effective magnetic field: Quench dynamics in a harmonic trap

Motivated by a recent experiment with optical lattices that has realized a ladder geometry with an effective magnetic field (Atala et al., Nature Physics \textbf{10}, 588 (2014)), we study the dynamics of bosons on a tight-binding two-leg ladder with complex hopping amplitudes. This system displays a quantum phase transition even without interactions. We study the non-equilibrium dynamics without and with interactions, in the presence of a harmonic trapping potential. In particular we consider dynamics induced by quenches of the trapping potential and of the magnitude of the rung hopping. We present a striking "slowing down" effect in the collective mode dynamics near the phase transition. This manifestation of a slowing down phenomenon near a quantum phase transition can be visualized unusually directly: the collective mode dynamics can be followed experimentally in real time and real space by imaging the atomic cloud.

Optimizing linked-cluster expansions by white graphs.

We introduce a white-graph expansion for the method of perturbative continuous unitary transformations when implemented as a linked-cluster expansion. The essential idea behind an expansion in white graphs is to perform an optimized bookkeeping during the calculation by exploiting the model-independent effective Hamiltonian in second quantization and the associated inherent cluster additivity. This approach is shown to be especially well suited for microscopic models with many coupling constants, since the total number of relevant graphs is drastically reduced. The white-graph expansion is exemplified for a two-dimensional quantum spin model of coupled two-leg XXZ ladders.

Block Magnetic Excitations in the Orbitally Selective Mott Insulator BaFe_{2}Se_{3}.

Iron pnictides and selenides display a variety of unusual magnetic phases originating from the interplay between electronic, orbital, and lattice degrees of freedom. Using powder inelastic neutron scattering on the two-leg ladder BaFe_{2}Se_{3}, we fully characterize the static and dynamic spin correlations associated with the Fe_{4} block state, an exotic magnetic ground state observed in this low-dimensional magnet and in Rb_{0.89}Fe_{1.58}Se_{2}. All the magnetic excitations of the Fe_{4} block state predicted by an effective Heisenberg model with localized spins are observed below 300 meV and quantitatively reproduced. However, the data only account for 16(3)μ_{B}^{2} per Fe^{2+}, approximatively 2/3 of the total spectral weight expected for localized S=2 moments. Our results highlight how orbital degrees of freedom in iron-based magnets can conspire to stabilize an exotic magnetic state.

Population-imbalance instability in a Bose-Hubbard ladder in the presence of a magnetic flux

We consider a two-leg Bose-Hubbard ladder in the presence of a magnetic flux. We make use of Gross-Pitaevskii, Bogoliubov, bosonization, and renormalization group approaches to reveal a structure of ground-state phase diagrams in a weak-coupling regime relevant to cold atom experiments. It is found that, except for a certain flux $\ensuremath{\phi}=\ensuremath{\pi}$, the system shows different properties as changing hoppings, which also leads to a quantum phase transition similar to the ferromagnetic $XXZ$ model. This implies that population-imbalance instability occurs for certain parameter regimes. On the other hand, for $\ensuremath{\phi}=\ensuremath{\pi}$, it is shown that an umklapp process caused by commensurability of a magnetic flux stabilizes a superfluid with chirality and the system does not experience such a phase transition.

First-order commensurate–incommensurate magnetic phase transition in the coupled FM spin-1/2 two-leg ladders

We consider the spin-1/2 two-leg ladders with ferromagnetic (FM) interactions along legs and rungs. Using the stochastic series expansion QMC method, we study the low-temperature magnetic behavior of the system. An isolated spin-1/2 FM two-leg ladder is in the gapped saturated FM phase at zero temperature. As soon as the spin-1/2 FM two-leg ladders are connected with antiferromagnetic (AFM) inter-ladder interaction, a first-order commensurate–incommensurate quantum phase transition occurs in the ground state magnetic phase diagram. In fact a jump in the magnetization curve is observed. We found that, coupled spin-1/2 FM two-leg ladders are in a nonmagnetic phase at zero temperature. Applying a magnetic field, the ground state of coupled spin-1/2 FM two-leg ladders remains in the nonmagnetic phase up to a quantum saturate critical field.

D-wave superconductivity in coupled ladders

We study the one-band Hubbard model on the trellis lattice, a two-dimensional frustrated lattice of coupled two-leg ladders, with hopping amplitude $t$ within ladders and ${t}^{\ensuremath{'}}$ between ladders. For large $U/t$ this is a model for the cuprate ${\mathrm{Sr}}_{14\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$. We investigate the phase diagram as a function of doping for $U=10t$ using two quantum cluster methods: The variational cluster approximation (VCA), with clusters of sizes 8 and 12, and cellular dynamical mean field theory (CDMFT), both at zero temperature. Both methods predict a superconducting dome, ending at roughly 20% doping in VCA and 15% in CDMFT. In VCA, the superconducting order parameter is complex in a range of doping centered around 10%, corresponding to bulk chiral, $T$-violating superconductivity. However, the CDMFT solution is not chiral. We find evidence for a migration of the Cooper pairs from the interladder region towards the plaquettes as doping is increased.

Two-legSU(2n)spin ladder: A low-energy effective field theory approach

We present a field theory analysis of a model of two SU(2n)-invariant magnetic chains coupled by a generic interaction preserving time reversal and inversion symmetry. Contrary to the SU(2)-invariant case the zero-temperature phase diagram of such two-leg spin ladder does not contain topological phases. Only generalized Valence Bond Solid phases are stabilized when n>1 with different wave vectors and ground-state degeneracies. In particular, we find a phase which is made of a cluster of 2n spins put in an SU(2n) singlet state. For n=3, this cluster phase is relevant to ytterbium ultracold atoms, with an emergent SU(6) symmetry, loaded in double well optical lattice.

Ground-state and spectral properties of an asymmetric Hubbard ladder

We investigate a ladder system with two inequivalent legs, namely a Hubbard chain and a one-dimensional electron gas. Analytical approximations, the density matrix renormalization group method, and continuous-time quantum Monte Carlo simulations are used to determine ground-state properties, gaps, and spectral functions of this system at half-filling. Evidence for the existence of four different phases as a function of the Hubbard interaction and the rung hopping is presented. First, a Luttinger liquid exists at very weak interchain hopping. Second, a Kondo-Mott insulator with spin and charge gaps induced by an effective rung exchange coupling is found at moderate interchain hopping or strong Hubbard interaction. Third, a spin-gapped paramagnetic Mott insulator with incommensurate excitations and pairing of doped charges is observed at intermediate values of the rung hopping and the interaction. Fourth, the usual correlated band insulator is recovered for large rung hopping. We show that the wavenumbers of the lowest single-particle excitations are different in each insulating phase. In particular, the three gapped phases exhibit markedly different spectral functions. We discuss the relevance of asymmetric two-leg ladder systems as models for atomic wires deposited on a substrate.