Two-leg Ladder Research Articles

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landau's Fermi-liquid theory is of central importance to many outstanding problems in condensed matter physics. One such problem is that, above the transition temperature and near optimal doping, high-transition-temperature copper-oxide superconductors exhibit 'strange metal' behaviour that is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of a strange-metal quantum phase could shed new light on the interesting low-temperature behaviour in the pseudogap regime and on the d-wave superconductor itself. Here we present a theory for a specific example of a strange metal--the 'd-wave metal'. Using variational wavefunctions, gauge theoretic arguments, and ultimately large-scale density matrix renormalization group calculations, we show that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian--the usual t-J model with electron kinetic energy t and two-spin exchange J supplemented with a frustrated electron 'ring-exchange' term, which we here examine extensively on the square lattice two-leg ladder. These findings constitute an explicit theoretical example of a genuine non-Fermi-liquid metal existing as the ground state of a realistic model.

Low temperature Raman study of the spin ladder compound BiCu2PO6

We have investigated the temperature (40–295K) dependence of the Raman active phonons of BiCu2PO6 single crystals oriented along a- and b- axis. The comparison between the two orientations did not show any remarkable effect along the b-axis (two-leg zigzag spin ladder direction). At low temperatures the modes appear shifted and narrowed. The spectral characteristics of the modes below ∼60 K show constant values, indicating strong coupling between the formation of spin-ladder and the crystal lattice.

Spin-lattice relaxation time in pressure-induced two-leg ladder cuprate superconductors

Spin-lattice relaxation time in pressure-induced two-leg ladder cuprate superconductors is investigated based on the kinetic energy driven superconducting mechanism. It is shown that the spin-lattice relaxation time exhibits a temperature linear dependence at low temperature followed by a peak developed below the superconducting transition temperature, in qualitative agreement with experiments.

Magnetic Field-Induced Phase Transitions in theS=1/2 Two-Leg Spin-Ladder Material Cu(DEP)Br2

From heat capacity ( C p ) measurements on a single crystal sample of the spin ( S ) 1/2 two-leg spin-ladder material Cu(DEP)Br 2 above a critical magnetic field ( H c0 ) where the energy gap between the singlet ground state and the excited magnetic state closes, we have observed a peak anomaly, which is indicative of a magnetic long-range ordering. We have examined how the position of the anomaly in C p changes with temperature ( T ) and magnetic field ( H ) to obtain the experimental H – T phase diagram of this S =1/2 two-leg spin ladder material. From the low-temperature specific heat below H c0 , we have evaluated the field-dependent energy gap that vanishes at about 7.6 T.

Symmetry-protected topological phases in spin ladders with two-body interactions

Spin-1/2 two-legged ladders respecting interleg exchange symmetry $\ensuremath{\sigma}$ and spin rotation symmetry ${D}_{2}$ have new symmetry-protected topological (SPT) phases which are different from the Haldane phase. Three of the new SPT phases are ${t}_{x},{t}_{y},{t}_{z}$, which all have symmetry-protected twofold degenerate edge states on each end of an open chain. However, the edge states in different phases have different responses to magnetic field. For example, the edge states in the ${t}_{z}$ phase will be split by the magnetic field along the $z$ direction, but not by the fields in the $x$ and $y$ directions. We give the Hamiltonian that realizes each SPT phase and demonstrate a proof-of-principle quantum simulation scheme for Hamiltonians of the ${t}_{0}$ and ${t}_{z}$ phases based on the coupled-QED-cavity ladder.

Inverse magnetocaloric effects in two-leg spin ladder system

Magnetocaloric properties of the two-leg frustrated spin ladder system are investigated by the use of transfer-matrix method. Exact results for the magnetization, entropy, entropy change and magnetocaloric cooling rate versus temperature and field are presented and discussed in detail. Large inverse magnetocaloric effects induced by the field arise at low temperature, and exhibit strong dependency relationship on the exchange couplings. In the vicinity of the critical field, the enhanced inverse magnetocaloric effects and normal magnetocaloric effects are both observed. Besides, the influences of the single-ion anisotropy on the entropy change are discussed as well.

Dynamics of doublon-holon pairs in Hubbard two-leg ladders

The dynamics of holon-doublon pairs is studied in Hubbard two-leg ladders using the time-dependent density matrix renormalization group method. We find that the geometry of the two-leg ladder, which is qualitatively different from a one-dimensional chain due to the presence of a spin gap, strongly affects the propagation of a doublon-holon pair. Two distinct regimes are identified. For weak interleg coupling, the results are qualitatively similar to the case of the propagation previously reported in Hubbard chains, with only a renormalization of parameters. More interesting is the case of strong interleg coupling where substantial differences arise, particularly regarding the double occupancy and properties of the excitations such as the doublon speed. Our results suggest a connection between the presence of a spin gap and qualitative changes in the doublon speed, indicating a weak coupling between the doublon and the magnetic excitations.

Weak localization and magnetoresistance in a two-leg ladder model

We analyze the weak localization correction to the conductivity of a spinless two-leg ladder model in the limit of strong dephasing \tau_\phi << \tau_tr, paying particular attention to the presence of a magnetic field, which leads to an unconventional magnetoresistance behavior. We find that the magnetic field leads to three different effects: (i) negative magnetoresistance due to the regular weak localization correction (ii) effective decoupling of the two chains, leading to positive magnetoresistance and (iii) oscillations in the magnetoresistance originating from the nature of the low-energy collective excitations. All three effects can be observed depending on the parameter range, but it turns out that large magnetic fields always decouple the chains and thus lead to the curious effect of magnetic field enhanced localization.

Nonequilibrium Propagation and Decay of a Bound Pair in Drivent−JModels

We perform an accurate time-dependent numerical study of an out-of-equilibrium response of a bound state within t-J systems on a two-leg ladder and a square lattice. We show that the bound hole pair decays with the onset of finite steady current if both mechanisms for binding and the dissipation share matching degrees of freedom. Moreover, by investigating the mechanism of decay on the square lattice we find that the dynamics is governed by the decay in the direction perpendicular to the electric field, leading to much shorter decay times in comparison to the ladder where such dynamics is topologically restricted.

Enhanced perturbative continuous unitary transformations

Unitary transformations are an essential tool for the theoretical understanding of many systems by mapping them to simpler effective models. A systematically controlled variant to perform such a mapping is a perturbative continuous unitary transformation (pCUT) among others. So far, this approach required an equidistant unperturbed spectrum. Here, we pursue two goals: First, we extend its applicability to non-equidistant spectra with the particular focus on an efficient derivation of the differential flow equations, which define the enhanced perturbative continuous unitary transformation (epCUT). Second, we show that the numerical integration of the flow equations yields a robust scheme to extract data from the epCUT. The method is illustrated by the perturbation of the harmonic oscillator with a quartic term and of the two-leg spin ladders in the strong-rung-coupling limit for uniform and alternating rung couplings. The latter case provides an example of perturbation around a non-equidistant spectrum.

Entanglement entropy of the low-lying excited states and critical properties of an exactly solvable two-leg spin ladder with three-spin interactions

In this work, we investigate an exactly solvable two-leg spin ladder with three-spin interactions. We obtain analytically the finite-size corrections of the low-lying energies and determine the central charge as well as the scaling dimensions. The model considered in this work is in the same universality class of critical behavior of the $XX$ chain with central charge $c=1$. By using the correlation matrix method, we also study the finite-size corrections of the R\'enyi entropy of the ground state and of the excited states. Our results are in agreement with the predictions of the conformal field theory.

Tensor network states and ground-state fidelity for quantum spin ladders

We have developed an efficient tensor network algorithm for spin ladders, which generates ground-state wave functions for infinite-size quantum spin ladders. The algorithm is able to efficiently compute the ground-state fidelity per lattice site, a universal phase transition marker, thus offering a powerful tool to unveil quantum many-body physics underlying spin ladders. To illustrate our scheme, we consider the two-leg and three-leg Heisenberg spin ladders with staggering dimerization, the two-leg Heisenberg spin ladder with cyclic four-spin exchange, and the ferromagnetic frustrated two-leg ladder. The ground-state phase diagrams thus yielded are reliable, compared with the previous studies based on the the exact diagonalization and the density matrix renormalization group. Our results indicate that the ground-state fidelity per lattice site successfully captures quantum criticalities in spin ladders.

Semiclassical approach to competing orders in a two-leg spin ladder with ring exchange

We investigate the competition between different orders in the two-leg spin ladder with a ring-exchange interaction by means of a bosonic approach. The latter is defined in terms of spin-1 hardcore bosons which treat the N\'eel and vector chirality order parameters on an equal footing. A semiclassical approach of the resulting model describes the phases of the two-leg spin ladder with a ring-exchange. In particular, we derive the low-energy effective actions which govern the physical properties of the rung-singlet and dominant vector chirality phases. As a by-product of our approach, we reveal the mutual induction phenomenon between spin and chirality with, for instance, the emergence of a vector-chirality phase from the application of a magnetic field in bilayer systems coupled by four-spin exchange interactions.

Anderson localization of one-dimensional hybrid particles

We solve the Anderson localization problem on a two-leg ladder by the Fokker-Planck equation approach. The solution is exact in the weak disorder limit at a fixed interchain coupling. The study is motivated by progress in investigating the hybrid particles such as cavity polaritons. This application corresponds to parametrically different intrachain hopping integrals (a ``fast'' chain coupled to a ``slow'' chain). We show that the canonical Dorokhov-Mello-Pereyra-Kumar (DMPK) equation is insufficient for this problem. Indeed, the angular variables describing the eigenvectors of the transmission matrix enter into an extended DMPK equation in a nontrivial way, being entangled with the two transmission eigenvalues. This extended DMPK equation is solved analytically and the two Lyapunov exponents are obtained as functions of the parameters of the disordered ladder. The main result of the paper is that near the resonance energy, where the dispersion curves of the two decoupled and disorder-free chains intersect, the localization properties of the ladder are dominated by those of the slow chain. Away from the resonance they are dominated by the fast chain: a local excitation on the slow chain may travel a distance of the order of the localization length of the fast chain.

Quantum phase transitions in the exactly solved spin-1/2 Heisenberg–Ising ladder

The ground-state behaviour of the frustrated quantum spin-1/2 two-leg ladder with the Heisenberg intra-rung and Ising inter-rung interactions is examined in detail. The investigated model is transformed into the quantum Ising chain with composite spins in an effective transverse and longitudinal field by employing either the bond-state representation or the unitary transformation. It is shown that the ground state of the Heisenberg–Ising ladder can be descended from three exactly solvable models: the quantum Ising chain in a transverse field, the ‘classical’ Ising chain in a longitudinal field or the spin-chain model in a staggered longitudinal–transverse field. The last model serves in evidence of the staggered bond phase with alternating singlet and triplet bonds on the rungs of a two-leg ladder, which appears at moderate values of the external magnetic field and consequently leads to a fractional plateau at a half of the saturation magnetization. The ground-state phase diagram totally consists of five ordered and one quantum paramagnetic phase, which are separated from each other either by the lines of discontinuous or continuous quantum phase transitions. The order parameters are exactly calculated for all five ordered phases and the quantum paramagnetic phase is characterized through different short-range spin–spin correlations.

Theory ofL-edge resonant inelastic x-ray scattering for magnetic excitations in two-leg spin ladders

We study the magnetic excitation spectra of Cu ${L}_{2,3}$-edge resonant inelastic x-ray scattering (RIXS) from the spin-liquid ground state in two-leg spin ladder cuprates. By applying the projection method developed by the present authors, we have derived the formulas of the magnetic RIXS spectra, which are expressed by one- and two-spin correlation functions in the polarization changing and preserving channels, respectively. The one-spin correlation function includes both one- and two-triplon excitations and they are picked up separately by choosing rung wave vectors $\ensuremath{-}{q}_{a}=\ensuremath{\pi}$ and 0, respectively. An application to Sr${}_{14}$Cu${}_{24}$O${}_{41}$ reveals that the calculated RIXS spectrum captures well the dispersive behavior shown by the lower boundary of two-triplon continuum. An exception is absence of the intensity at zero-momentum transfer where weak but finite intensity was observed in the experiment. By adjusting the geometrical configuration of the measurement, one-triplon dispersion around the zone center could be detectable in the RIXS experiment. The observed weak intensity in the higher-energy region might be attributed to the two-spin correlation function, which could be detected more clearly at the ${M}_{3}$-edge RIXS spectra.

Magnetic structure of quasi-one-dimensional antiferromagnetic TaFe1+yTe3

We report the magnetic structure of TaFe${}_{1+y}$Te${}_{3}$ single crystals by means of neutron diffraction measurements. TaFe${}_{1+y}$Te${}_{3}$ possesses a layered structure with a formation of two-leg zigzag ladders along the $b$ axis. We find that TaFe${}_{1+y}$Te${}_{3}$ undergoes an antiferromagnetic transition at 178 K with Fe1 spins of the intraladders ferromagnetically aligned and with Fe1 spins of the interladders antiferromagnetically coupled. Furthermore, spins of the neighboring interstitial Fe2 ($y$) ions align parallel to the Fe1 spins of each ladder. These findings are distinct from the magnetic structure of the recently discovered spin-ladder compound BaFe${}_{2}$Se${}_{3}$. TaFe${}_{1+y}$Te${}_{3}$ may serve as a model system for investigating the interesting physics of quasi-one-dimensional ferromagnetic systems.

Synthesis, Structure, Magnetic Behavior, and Theoretical Analysis of Diazine-Bridged Magnetic Ladders: Cu(quinoxoline)X2 and Cu(2,3-dimethylpyrazine)X2 (X = Cl, Br)

The synthesis, structure, and magnetic behavior of the complexes Cu(qnx)Br(2) (1), Cu(2,3-dmpz)Br(2) (2), Cu(qnx)Cl(2) (3), and Cu(2,3-dmpz)Cl(2) (4) (qnx = quinoxaline, dmpz = dimethylpyrazine) are described. Both X-ray structural data and fitting of the magnetic data suggest that the compounds are well-described as strong-rung, two-leg magnetic ladders with J(rung) ranging from -30 K to -37 K, and J(rail) ranging from -14 K to -24 K. An unexpected decrease in the exchange constant for J(rail) (through the diazine ligand) is observed when the halide ion is changed from bromide to chloride, along with a small decrease in the magnetic exchange through the halide ion. Theoretical calculations on 2 and 4 via a first-principles bottom-up approach confirmed the description of the complexes as two-leg magnetic ladders. Furthermore, the calculations provide an explanation for the experimentally observed change in the value of the magnetic exchange through the dmpz ligand when the halide ion is changed from bromide to chloride, and for the very small change observed in the exchange through the different halide ions themselves via a combination of changes in geometry, bond lengths, and anion volume.

Finite wave vector pairing in doped two-leg ladders

We consider the effects of umklapp processes in doped two-leg fermionic ladders. These may emerge either at special band fillings or as a result of the presence of external periodic potentials. We show that such umklapp processes can lead to profound changes of physical properties and in particular stabilize pair-density wave phases.

Bose-Hubbard model in a strong effective magnetic field: Emergence of a chiral Mott insulator ground state

Motivated by experiments on Josephson junction arrays, and cold atoms in an optical lattice in a synthetic magnetic field, we study the "fully frustrated" Bose-Hubbard (FFBH) model with half a magnetic flux quantum per plaquette. We obtain the phase diagram of this model on a two-leg ladder at integer filling via the density matrix renormalization group approach, complemented by Monte Carlo simulations on an effective classical XY model. The ground state at intermediate correlations is consistently shown to be a chiral Mott insulator (CMI) with a gap to all excitations and staggered loop currents which spontaneously break time reversal symmetry. We characterize the CMI state as a vortex supersolid or an indirect exciton condensate, and discuss various experimental implications.