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The Hall effect has a paramount role in a wide range of disciplines, from applied sciences to the fundamental exploration of novel topological phases of matter. In the solid state, this effect describes the emergence of a voltage drop perpendicular to the current flow in the presence of a magnetic field, leading to a transverse Hall resistance. Despite its fundamental nature, a full understanding and control of the Hall effect in interacting quantum systems is still lacking. This has led to the development of quantum simulators based on neutral atoms, where strongly correlated and universal manifestations of the Hall effect were recently unveiled. However, a direct measurement of the Hall voltage and of the Hall resistance in those systems was not achieved so far. Here, we demonstrate a technique for the measurement of the Hall voltage in a neutral-atom-based quantum simulator. From that we provide the first direct measurement of the Hall resistance in a non-electron-based system and study its dependence on the carrier density, along with theoretical analyses. Our work closes a major gap between analog quantum simulations and measurements performed in real solid-state systems, providing a key tool for the exploration of the Hall effect in highly tunable and strongly correlated systems.

Supersymmetry is an algebraic property of a class of quantum Hamiltonians, a guiding principle used in the development of nuclear theory and a concept that may underpin physics beyond the Standard Model. In condensed matter, any symmetry between bosonic and fermionic entities is usually strongly broken, as for the spin and charge sectors of the $t$-$J$ model describing the dynamics of fractionalized electrons in one-dimensional materials. While the triplet excitations of a quantum spin ladder in an applied magnetic field provide a close analogue of the $t$-$J$ chain, the supersymmetric nature of this system has not been explored. Here we perform neutron spectroscopy on the spin-ladder compounds (C$_5$D$_{12}$N)$_2$CuBr$_4$ and (C$_5$D$_{12}$N)$_2$CuCl$_4$ over a range of applied fields and temperatures, and apply matrix-product-state (MPS) methods to the ladder and equivalent chain models, to analyse the full, momentum-resolved dynamics of a single charge excitation in a bath of fractionalized spins. We find a dramatic difference in the effects of thermal fluctuations, where strong and coherent shifts of spectral weight at the zone edge contrast with a strict pole at the zone centre, whose persistence at all temperatures constitutes an observable consequence of supersymmetry in a quantum spin ladder.

We use bosonization, retaining band curvature terms, to analyze the Hall response of interacting bosonic and fermionic two-leg ladders threaded by a flux. We derive an explicit expression of the Hall imbalance in a perturbative expansion in the band curvature, retaining fully the interactions. We show that the flux dependence of the Hall imbalance allows to distinguish the two phases (Meissner and Vortex) that are present for a bosonic ladder. For small magnetic field we relate the Hall resistance, both for bosonic and fermionic ladders, to the density dependence of the charge sitffness of the system in absence of flux. Our expression unveil a universal interaction-independent behavior in the Galilean invariant case., Comment: 7 pages, 1 figure, supplemental material

We characterize the particle transport, particle loss, and nonequilibrium steady states in a dissipative one-dimensional lattice connected to reservoirs at both ends. The free-fermion reservoirs are fixed at different chemical potentials, giving rise to particle transport. The dissipation is due to a local particle loss acting on the center site. We compute the conserved current and loss current as functions of voltage in the nonlinear regime using a Keldysh description. The currents show step-like features which are affected differently by the local loss: The steps are either smoothened, nearly unaffected, or even enhanced, depending on the spatial symmetry of the single-particle eigenstate giving rise to the step. Additionally, we compute the particle density and momentum distributions in the chain. At a finite voltage, two Fermi momenta can occur, connected to different wavelengths of Friedel oscillations on either side of the lossy site. We find that the wavelengths are determined by the chemical potentials in the reservoirs rather than the average density in the lattice., Comment: 19 pages, 19 figures

The Hall effect, which originates from the motion of charged particles in magnetic fields, has deep consequences for the description of materials, extending far beyond condensed matter. Understanding such an effect in interacting systems represents a fundamental challenge, even for small magnetic fields. In this work, we used an atomic quantum simulator in which we tracked the motion of ultracold fermions in two-leg ribbons threaded by artificial magnetic fields. Through controllable quench dynamics, we measured the Hall response for a range of synthetic tunneling and atomic interaction strengths. We unveil a universal interaction-independent behavior above an interaction threshold, in agreement with theoretical analyses. The ability to reach hard-to-compute regimes demonstrates the power of quantum simulation to describe strongly correlated topological states of matter., Comment: Main Text: 6 pages, 4 figures; Supplementary Material: 9 pages, 10 figures

We study particle transport through a chain of coupled sites connected to free-fermion reservoirs at both ends, subjected to a local particle loss. The transport is characterized by calculating the conductance and particle density in the steady state using the Keldysh formalism for open quantum systems. Besides a reduction of conductance, we find that transport can remain (almost) unaffected by the loss for certain values of the chemical potential in the lattice. We show that this "protected" transport results from the spatial symmetry of single-particle eigenstates. At a finite voltage, the density profile develops a drop at the lossy site, connected to the onset of non-ballistic transport., Comment: 6 pages, 3 figures

We analyze the spin transport through a finite-size one-dimensional interacting wire connected to noninteracting leads. By combining renormalization-group arguments with other analytic considerations such as the memory function technique and instanton tunneling, we find the temperature dependence of the spin conductance in different parameter regimes in terms of interactions and the wire length. The temperature dependence is found to be nonmonotonic. In particular, the system approaches perfect spin conductance at zero temperature for both attractive and repulsive interactions, in contrast with the static spin conductivity. We discuss the connection of our results to recent experiments with ultracold atoms and compare the theoretical prediction to experimental data in the parameter regime where temperature is the largest energy scale., Comment: 16 pages, 10 figures

We study the correlation functions of quantum spin $1/2$ ladders at finite temperature, under a magnetic field, in the gapless phase at various relevant temperatures $T\neq 0$, momentum $q$ and frequencies $\omega$. We compute those quantities using the time dependent density matrix renormalization group (T-DMRG) in some optimal numerical scheme. We compare these correlations with the ones of dimerized quantum spin chains and simple spin chains, that we compute by a similar technique. We analyze the intermediate energy modes and show that the effect of temperature lead to the formation of an essentially dispersive mode corresponding to the propagation of a triplet mode in an incoherent background, with a dispersion quite different from the one occurring at very low temperatures. We compare the low energy part of the spectrum with the predictions of the Tomonaga-Luttinger liquid field theory at finite temperature. We shows that the field theory describes in a remarkably robust way the low energy correlations for frequencies or temperatures up to the natural cutoff (the effective dispersion) of the system. We discuss how our results could be tested in e.g. neutron scattering experiments., Comment: 17 pages, 14 figures

We study the time-dependent occupation of an impurity state hybridized with a continuum of extended or localized states. Of particular interest is the return probability, which gives the long-time limit of the average impurity occupation. In the extended case, the return probability is zero unless there are bound states of the impurity and continuum. We present exact expressions for the return probability of an impurity state coupled to a lattice, and show that the existence of bound states depends on the dimension of the lattice. In a disordered lattice with localized eigenstates, the finite extent of the eigenstates results in a non-zero return probability. We investigate different parameter regimes numerically by exact diagonalization, and show that the return probability can serve as a measure of the localization length in the regime of weak hybridization and disorder. Possible experimental realizations with ultracold atoms are discussed., Comment: 19 pages, 17 figures

We study a dynamic boundary, e.g. a mobile impurity, coupled to N independent Tomonaga-Luttinger liquids (TLLs) each with interaction parameter K. We demonstrate that for N>2 there is a quantum phase transition at K>1/2, where the TLL phases lock together at the particle position, resulting in a non-zero transconductance equal to e^2/Nh. The transition line terminates for strong coupling at K=1- 1/N, consistent with results at large N. Another type of a dynamic boundary is a superconducting (or Bose-Einstein condensate) grain coupled to N>2 TLLs, here the transition signals also the onset of a relevant Josephson coupling., Comment: 21 pages, 1 figure

We present measurements of the dynamical structure factor $S(q,\omega)$ of an interacting one-dimensional (1D) Fermi gas for small excitation energies. We use the two lowest hyperfine levels of the $^6$Li atom to form a pseudo-spin-1/2 system whose s-wave interactions are tunable via a Feshbach resonance. The atoms are confined to 1D by a two-dimensional optical lattice. Bragg spectroscopy is used to measure a response of the gas to density ("charge") mode excitations at a momentum $q$ and frequency $\omega$. The spectrum is obtained by varying $\omega$, while the angle between two laser beams determines $q$, which is fixed to be less than the Fermi momentum $k_\textrm{F}$. The measurements agree well with Tomonaga-Luttinger theory.

Since the seminal ideas of Berezinskii, Kosterlitz and Thouless, topological excitations are at the heart of our understanding of a whole novel class of phase transitions. In most of the cases, those transitions are controlled by a single type of topological objects. There are however some situations, still poorly understood, where two dual topological excitations fight to control the phase diagram and the transition. Finding experimental realization of such cases is thus of considerable interest. We show here that this situation occurs in BaCo$_2$V$_2$O$_8$, a spin-1/2 Ising-like quasi-one dimensional antiferromagnet when subjected to a uniform magnetic field transverse to the Ising axis. Using neutron scattering experiments, we measure a drastic modification of the quantum excitations beyond a critical value of the magnetic field. This quantum phase transition is identified, through a comparison with theoretical calculations, to be a transition between two different types of solitonic topological objects, which are captured by different components of the dynamical structure factor., Comment: 9 pages, 4 figures; 10 additional pages of supplemental information containing 6 figures

We study spinless fermions with repulsive nearest-neighbor interactions perturbed by an impurity particle or a local potential quench. Using the numerical time-evolving block decimation method and a simplified analytic model, we show that the pertubations create a soliton-antisoliton pair. If solitons are already present in the bath, the two excitations have a drastically different dynamics: The antisoliton does not annihilate with the solitons and is therefore confined close to its origin while the soliton excitation propagates. We discuss the consequences for experiments with ultracold gases., Comment: 12 pages, 16 figures

Materials where the electron filling is close to commensurate filling provide one of the great challenges in materials science. Several proposals of unconventional orderings, where the electronic liquid self-organizes into components with distinct properties, were recently put forward, in particular in cuprates and pnictides where electronic nematic orders have been observed. The electrons self-organization is expected to yield complex intra and inter unit cell patterns, and a reduction of dimensionality. Nevertheless, an unambiguous experimental proof of such complex orders, namely the direct observation of distinct dispersions, is still missing. Here we report a Nano Angle Resolved Photo-emission Spectroscopy (Nano-ARPES) study of NbSe$_3$, a material that has been considered a paradigm of charge order. The new data (Fig.1) invalidate the canonical picture of imperfect nesting and reveals the emergence of a novel order. The electrons self-organization uncovers the one-dimensional (1D) physics hidden in a material which naively should be the most 3D of all columnar chalcogenides., Comment: 15 pages, 4 figures; Supplementary Material (14 pages) available upon request

The challenge of one-dimensional systems is to understand their physics beyond the level of known elementary excitations. By high-resolution neutron spectroscopy in a quantum spin ladder material, we probe the leading multiparticle excitation by characterizing the two-magnon bound state at zero field. By applying high magnetic fields, we create and select the singlet (longitudinal) and triplet (transverse) excitations of the fully spin-polarized ladder, which have not been observed previously and are close analogs of the modes anticipated in a polarized Haldane chain. Theoretical modelling of the dynamical response demonstrates our complete quantitative understanding of these states., Comment: 6 pages, 3 figures plus supplementary material 7 pages 5 figures

We use recent developments in the framework of time dependent matrix product state method (t-MPS) to compute the NMR relaxation rate $1/T_1$ for spin-1/2 chains under magnetic field and for different Hamiltonians (XXX, XXZ, isotropically dimerized). We compute numerically the temperature dependence of the $1/T_1$. We consider both gapped and gapless phases, and also the proximity of quantum critical points. At temperatures much lower than the typical exchange energy scale our results are in excellent agreement with analytical results, such as the ones derived from the Tomonaga-Luttinger liquid (TLL) theory and bosonization which are valid in this regime. We also cover the regime for which the temperature $T$ is comparable to the exchange coupling. In this case analytical theories are not appropriate but this regime is relevant for various new compounds with exchange couplings in the range of tens of Kelvin. For the gapped phases, either the fully polarized phase for spins chains or the low magnetic field phase for the dimerized systems, we find an exponential decrease in $\Delta/(k_BT)$ of the relaxation time and can compute the gap $\Delta$. Close to the quantum critical point our results are in good agreement with the a scaling behavior based on the existence of free excitations.

We study analytically and with the numerical time-evolving block decimation method the dynamics of an impurity in a bath of spinless fermions with nearest-neighbor interactions in a one-dimensional lattice. The bath is in a Mott insulator state with alternating sites occupied and the impurity interacts with the bath by repulsive on-site interactions. We find that when the magnitudes of the on-site and nearest-neighbor interactions are close to each other, the system shows excitations of two qualitatively distinct types. For the first type, a domain wall and an anti-domain wall of density propagate in opposite directions, while the impurity stays at the initial position. For the second one, the impurity is bound to the anti-domain wall while the domain wall propagates, an excitation where the impurity and bath are closely coupled., Comment: 10 pages, 12 figures

We investigate the superfluid-insulator transition of one-dimensional interacting Bosons in both deep and shallow periodic potentials. We compare a theoretical analysis based on Monte-Carlo simulations in continuum space and Luttinger liquid approach with experiments on ultracold atoms with tunable interactions and optical lattice depth. Experiments and theory are in excellent agreement. It provides a quantitative determination of the critical parameter for the Mott transition and defines the regime of validity of widely used approximate models, namely the Bose-Hubbard and sine-Gordon models, Comment: Technical problem in references fixed. Text and figures identical to version 1

Magnetic excitations in the strong-leg quantum spin ladder compound (C$_7$H$_{10}$N)$_2$CuBr$_4$ (known as DIMPY) in the field-induced Tomonaga-Luttinger spin liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual non-linear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a fingerprint of the spin dynamics in a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder and owe its ESR observability to the uniform Dzyaloshinskii-Moriya interaction.

Magnetic skyrmions are promising candidates as information carriers in logic or storage devices thanks to their robustness, guaranteed by the topological protection, and their nanometric size. Currently, little is known about the influence of parameters such as disorder, defects or external stimuli, on the long-range spatial distribution and temporal evolution of the skyrmion lattice. Here, using a large (7.3x7.3{\mu}m$^{2}$) single crystal nano-slice of Cu$_{2}$OSeO$_{3}$, we image up to 70,000 skyrmions, by means of cryo-Lorentz Transmission Electron Microscopy as a function of the applied magnetic field. The emergence of the skyrmion lattice from the helimagnetic phase is monitored, revealing the existence of a glassy skyrmion phase at the phase transition field, where patches of an octagonally distorted skyrmion lattice are also discovered. In the skyrmion phase, dislocations are shown to cause the emergence and switching between domains with different lattice orientations and the temporal fluctuations of these domains is filmed. These results demonstrate the importance of direct-space and real-time imaging of skyrmion domains for addressing both their long-range topology and stability., Comment: 31 pages (16 + 15 supplementary material),17 figures (4 + 13 supplementary material)

We present a theoretical description of the radio-frequency (rf) spectroscopy of fermionic atomic gases, based on the second-order response theory at finite temperature. This approach takes into account the energy resolution due to the envelope of the rf pulse. For a noninteracting final state, the momentum- and energy-resolved rf intensity depends on the fermion spectral function and pulse envelope. The contributions due to interactions in the final state can be classified by means of diagrams. Using this formalism, as well as the local density approximation in two and three dimensions, we study the interplay of inhomogeneities and Hartree energy in forming the line shape of the rf signal. We show that the effects of inhomogeneities can be minimized by taking advantage of interactions in the final state, and we discuss the most relevant final-state effects at low temperature and density, in particular the effect of a finite lifetime., Comment: Published version

Magnetic field-driven domain wall motion in an ultrathin Pt/Co(0.45nm)/Pt ferromagnetic film with perpendicular anisotropy is studied over a wide temperature range. Three different pinning dependent dynamical regimes are clearly identified: the creep, the thermally assisted flux flow and the depinning, as well as their corresponding crossovers. The wall elastic energy and microscopic parameters characterizing the pinning are determined. Both the extracted thermal rounding exponent at the depinning transition, $\psi=$0.15, and the Larkin length crossover exponent, $\phi=$0.24, fit well with the numerical predictions., Comment: 5 pages, 4 figures

Using the model system of ferroelectric domain walls, we explore the effects of long-range dipolar interactions and periodic ordering on the behavior of pinned elastic interfaces. In piezoresponse force microscopy studies of the characteristic roughening of intrinsic 71{\deg} stripe domains in BiFeO$_3$ thin films, we find unexpectedly high values of the roughness exponent {\zeta} = 0.74 $\pm$ 0.10, significantly different from those obtained for artificially written domain walls in this and other ferroelectric materials. The large value of the exponent suggests that a random field-dominated pinning, combined with stronger disorder and strain effects due to the step-bunching morphology of the samples, could be the dominant source of pinning in the system., Comment: 5 pages, 4 figures

Magnetic insulators have proven to be usable as quantum simulators for itinerant interacting quantum systems. In particular the compound (C$_{5}$H$_{12}$N)$_{2}$CuBr$_{4}$ (short (Hpip)$_{2}$CuBr$_{4}$) was shown to be a remarkable realization of a Tomonaga-Luttinger liquid (TLL) and allowed to quantitatively test the TLL theory. Substitution weakly disorders this class of compounds and allows thus to use them to tackle questions pertaining to the effect of disorder in TLL as well, such as the formation of the Bose glass. As a first step in this direction we present in this paper a study of the properties of the related (Hpip)$_{2}$CuCl$_{4}$ compound. We determine the exchange couplings and compute the temperature and magnetic field dependence of the specific heat, using a finite temperature Density Matrix Renormalization group (DMRG) procedure. Comparison with the measured specific heat at zero magnetic field confirms the exchange parameters and Hamiltonian for the (Hpip)$_{2}$CuCl$_{4}$ compound, giving the basis needed to start studying the disorder effects., Comment: Part of the special issue "Physics in one dimension", A van Houselt, J Sch\"afer, H J W Zandvliet and R Claessen ed

Inelastic neutron scattering is used to measure the spin excitation spectrum of the Heisenberg $S=1/2$ ladder material (C$_7$H$_10$N)$_2$CuBr$_4$ in its entirety, both in the gapped spin-liquid and the magnetic field induced Tomonaga-Luttinger spin liquid regimes. A fundamental change of the spin dynamics is observed between these two regimes. DMRG calculations quantitatively reproduce and help understand the observed commensurate and incommensurate excitations. The results validate long-standing quantum field theoretical predictions, but also test the limits of that approach.

The zero-field excitation spectrum of the strong-leg spin ladder (C$_7$H$_10$N)$_2$CuBr$_4$ (DIMPY) is studied with a neutron time-of-flight technique. The spectrum is decomposed into its symmetric and asymmetric parts with respect to the rung momentum and compared with theoretical results obtained by the density matrix renormalization group method. Additionally, the calculated dynamical correlations are shown for a wide range of rung and leg coupling ratios in order to point out the evolution of arising excitations, as e.g. of the two-magnon bound state from the strong to the weak coupling limit.

We study various realizations of collective coordinates, e.g. the position of a particle, the charge of a Coulomb box or the phase of a Bose or a superconducting condensate, coupled to Luttinger liquids (LL) with N flavors. We find that for Luttinger parameter 1/2

We realize and study an attractively interacting two-dimensional Fermi liquid. Using momentum resolved photoemission spectroscopy, we measure the self-energy, determine the contact parameter of the short-range interaction potential, and find their dependence on the interaction strength. We successfully compare the measurements to a theoretical analysis, properly taking into account the finite temperature, harmonic trap, and the averaging over several two-dimensional gases with different peak densities.

Using multiscaling analysis, we compare the characteristic roughening of ferroelectric domain walls in PZT thin films with numerical simulations of weakly pinned one-dimensional interfaces. Although at length scales up to a length scale greater or equal to 5 microns the ferroelectric domain walls behave similarly to the numerical interfaces, showing a simple mono-affine scaling (with a well-defined roughness exponent), we demonstrate more complex scaling at higher length scales, making the walls globally multi-affine (varying roughness exponent at different observation length scales). The dominant contributions to this multi-affine scaling appear to be very localized variations in the disorder potential, possibly related to dislocation defects present in the substrate., Comment: 5 pages, 4 figures

Molybdenum purple bronze Li$_{0.9}$Mo$_{6}$O$_{17}$ is an exceptional material known to exhibit one dimensional (1D) properties for energies down to a few meV. This fact seems to be well established both in experiments and in band structure theory. We use the unusual, very 1-dimensional band dispersion obtained in \emph{ab-initio} DFT-LMTO band calculations as our starting point to study the physics emerging below 300meV. A dispersion perpendicular to the main dispersive direction is obtained and investigated in detail. Based on this, we derive an effective low energy theory within the Tomonaga Luttinger liquid (TLL) framework. We estimate the strength of the possible interactions and from this deduce the values of the TLL parameters for charge modes. Finally we investigate possible instabilities of TLL by deriving renormalization group (RG) equations which allow us to predict the size of potential gaps in the spectrum. While $2k_F$ instabilities strongly suppress each other, the $4k_F$ instabilities cooperate, which paves the way for a possible CDW at the lowest energies. The aim of this work is to understand the experimental findings, in particular the ones which are certainly lying within the 1D regime. We discuss the validity of our 1D approach and further perspectives for the lower energy phases., Comment: We wish to acknowledge financial support of MaNEP, SectionII

We perform a scaling analysis of the mean velocity of extended magnetic domain walls driven in ultrathin Pt/Co/Pt ferromagnetic films with perpendicular anisotropy, as a function of the applied external field for different film-thicknesses. We find that the scaling of the experimental data around the thermally rounded depinning transition is consistent with the universal depinning exponents theoretically expected for elastic interfaces described by the one-dimensional quenched Edwards-Wilkinson equation. In particular, values for the depinning exponent $\beta$ and thermal rounding exponent $\psi$ are tested and the present analysis of the experimental data is compatible with $\beta=0.33$ and $\psi=0.2$, in agreement with numerical simulations., Comment: 8 pages, 8 figures

We study numerically thermal effects at the depinning transition of an elastic string driven in a two-dimensional uncorrelated disorder potential. The velocity of the string exactly at the sample critical force is shown to behave as $V \sim T^\psi$, with $\psi$ the thermal rounding exponent. We show that the computed value of the thermal rounding exponent, $\psi = 0.15$, is robust and accounts for the different scaling properties of several observables both in the steady-state and in the transient relaxation to the steady-state. In particular, we show the compatibility of the thermal rounding exponent with the scaling properties of the steady-state structure factor, the universal short-time dynamics of the transient velocity at the sample critical force, and the velocity scaling function describing the joint dependence of the steady-state velocity on the external drive and temperature.

The band structures of ordered and thermally disordered Li$_2$Mo$_{12}$O$_{34}$ are calculated by use of ab-initio DFT-LMTO method. The unusual, very 1-dimensional band dispersion obtained in previous band calculations is confirmed for the ordered structure, and the overall band structure agrees reasonably with existing photoemission data. Dispersion and bandstructure perpendicular to the main dispersive direction is obtained. A temperature dependent band broadening is calculated from configurations with thermal disorder of the atomic positions within the unit cell. This leads a band broadening of the two bands at the Fermi energy which can become comparable to their energy separation. The bands are particularly sensitive to in-plane movements of Mo sites far from the Li-sites, where the density-of-states is highest. The latter fact makes the effect of Li vacancies on the two bands relatively small. Spin-polarized band results for the ordered structure show a surprisingly large exchange enhancement on the high DOS Mo sites. Consequences for spin fluctuations associated with a cell doubling along the conducting direction are discussed.

One of the most relevant manifestations of the Beresinskii-Kosterlitz-Thouless transition occurs in quasi-two-dimensional superconducting systems. The experimental advances made in the last decade in the investigation of superconducting phenomena in low-dimensional correlated electronic systems raised new questions on the nature of the BKT transitions in real materials. A general issue concerns the possible limitations of theoretical predictions based on the XY model, that was studied as a paradigmatic example in the original formulation. Here we review the work we have done in revisiting the nature of the BKT transition within the general framework provided by the mapping into the sine-Gordon model. While this mapping was already known since long, we recently emphasized the advantages on such an approach to account for new variables in the BKT physics. One such variable is the energy needed to create the core of the vortex, that is fixed within the XY model, while it attains substantially different values in real materials. This has interesting observable consequences, especially in the case when additional relevant perturbations are present, as a coupling between stacked two-dimensional superconducting layers or a finite magnetic field., Comment: Chapter contribution for the forthcoming book,"Berezinskii-Kosterlitz-Thouless Transition", Edited by Jorge V. Jos\'e, and to be published by World Scientific (2012)

The strong-leg S=1/2 Heisenberg spin ladder system (C7H10N)2CuBr4 is investigated using Density Matrix Renormalization Group (DMRG) calculations, inelastic neutron scattering, and bulk magneto-thermodynamic measurements. Measurements showed qualitative differences compared to the strong-rung case. A long-lived two-triplon bound state is confirmed to persist across most of the Brillouin zone in zero field. In applied fields, in the Tomonaga-Luttinger spin liquid phase, elementary excitations are attractive, rather than repulsive. In the presence of weak inter-ladder interactions, the strong-leg system is considerably more prone to 3-dimensional ordering., Comment: 4 pages 4 figures

Using a species-selective dipole potential, we create initially localized impurities and investigate their interactions with a majority species of bosonic atoms in a one-dimensional configuration during expansion. We find an interaction-dependent amplitude reduction of the oscillation of the impurities' size with no measurable frequency shift, and study it as a function of the interaction strength. We discuss possible theoretical interpretations of the data. We compare, in particular, with a polaronic mass shift model derived following Feynman variational approach., Comment: 7 pages, 6 figures

We examine the influence of collective excitations on the transport properties (resistivity, magneto- optical conductivity) for semimetals, focusing on the case of bismuth. We show, using an RPA approximation, that the properties of the system are drastically affected by the presence of an acoustic plasmon mode, consequence of the presence of two types of carriers (electrons and holes) in this system. We found a crossover temperature T* separating two different regimes of transport. At high temperatures T > T* we show that Baber scattering explains quantitatively the DC resistivity experiments, while at low temperatures T < T* interactions of the carriers with this collective mode lead to a T^5 behavior of the resistivity. We examine other consequences of the presence of this mode, and in particular predict a two plasmon edge feature in the magneto-optical conductivity. We compare our results with the experimental findings on bismuth. We discuss the limitations and extensions of our results beyond the RPA approximation, and examine the case of other semimetals such as graphite or 1T-TiSe_2.

We study the relationship between the differential conductance and the local density of states in tight-binding tunnel junctions where the junction' geometry can be varied between the point-contact and the planar-contact limits. The conductances are found to differ significantly in these two limiting cases. We also examine how the matrix element influences the tunneling characteristics and produces contrast in a simple model of scanning tunneling microscope (STM). Some implications regarding the interpretation of STM spectroscopic data in the cuprates are discussed. The calculations are carried out within the real-space Keldysh formalism., Comment: Published version

We review the physics of one-dimensional interacting bosonic systems. Beginning with results from exactly solvable models and computational approaches, we introduce the concept of bosonic Tomonaga-Luttinger Liquids relevant for one-dimension, and compare it with Bose-Einstein condensates existing in dimensions higher than one. We discuss the effects of various perturbations on the Tomonaga-Luttinger liquid state as well as extensions to multicomponent and out of equilibrium situations. Finally, we review the experimental systems that can be described in terms of models of interacting bosons in one dimension., Comment: RevTeX 4, 68 pages, 22 EPS figures, submitted to Rev. Mod. Phys

We study numerically the depinning transition of driven elastic interfaces in a random-periodic medium with localized periodic-correlation peaks in the direction of motion. The analysis of the moving interface geometry reveals the existence of several characteristic lengths separating different length-scale regimes of roughness. We determine the scaling behavior of these lengths as a function of the velocity, temperature, driving force, and transverse periodicity. A dynamical roughness diagram is thus obtained which contains, at small length scales, the critical and fast-flow regimes typical of the random-manifold (or domain wall) depinning, and at large length-scales, the critical and fast-flow regimes typical of the random-periodic (or charge-density wave) depinning. From the study of the equilibrium geometry we are also able to infer the roughness diagram in the creep regime, extending the depinning roughness diagram below threshold. Our results are relevant for understanding the geometry at depinning of arrays of elastically coupled thin manifolds in a disordered medium such as driven particle chains or vortex-line planar arrays. They also allow to properly control the effect of transverse periodic boundary conditions in large-scale simulations of driven disordered interfaces., Comment: 19 pages, 10 figures

We investigate the physical consequences of orbital current patterns (OCP) in doped two-leg Cu-O Hubbard ladders. The internal symmetry of the pattern, in the case of the ladder structure, differs slightly from that suggested so far for cuprates. We focus on this OCP and look for measurable signatures of its existence. We compute the magnetic field produced by the OCP at each lattice site, and estimate its value in view of a possible experimental detection. Using a renormalization group (RG) analysis, we determine the changes that are caused by the SU(2) spin-rotational symmetry breaking which occurs when the OCP is present in the ground state phase diagram. The most signifcant one is an in-plane SDW gap opening in an otherwise critical phase, at intermediate dopings. We estimate the value of this gap, give an analytic expression for the correlation functions and examine some of the magnetic properties of this new phase which can be revealed in measurements. We compute the conductance in the presence of a single impurity, using an RG analysis. A discussion of the various sources of SU(2) symmetry breaking underscores the specificity of the OCP induced effects., Comment: 12 pages, 3 figures, submitted to PRB

We discuss the crucial role played by finite-size effects and inhomogeneity on the Beresinkii-Kosterlitz-Thouless (BKT) transition in two-dimensional superconductors. In particular, we focus on the temperature dependence of the resistivity, that is dominated by superconducting fluctuations above the BKT transition temperature $T_{BKT}$ and by inhomogeneity below it. By means of a renormalization-group approach we establish a direct correspondence between the parameter values used to describe the BKT fluctuation regime and the distance between $T_{BKT}$ and the mean-field Ginzburg-Landau transition temperature. Below $T_{BKT}$ a resistive tail arises due to finite-size effect and inhomogeneity, that reflects also on the temperature dependence of the superfluid density. We apply our results to recent experimental data in superconducting LaAlO$_3$/SrTiO$_3$ heterostructures, and we extract several informations on the microscopic properties of the system from our BKT fitting parameters. Finally, we compare our approach to recent data analysis presented in the literature, where the physical meaning of the parameter values in the BKT formulas has been often overlooked., Comment: 11 pages, 9 figures, final version

We compute the absorption spectrum of strongly repulsive one-dimensional bosons in a disordered or quasi-periodic optical lattice. At commensurate filling, the particle-hole resonances of the Mott insulator are broadened as the disorder strength is increased. In the non-commensurate case, mapping the problem to the Anderson model allows us to study the Bose-glass phase. Surprisingly we find that a perturbative treatment in both cases, weak and strong disorder, gives a good description at all frequencies. In particular we find that the infrared absorption rate in the thermodynamic limit is quadratic in frequency. This result is unexpected, since for other quantities like the conductivity in one dimensional systems, perturbation theory is only applicable at high frequencies. We discuss applications to recent experiments on optical lattice systems, and in particular the effect of the harmonic trap., Comment: 11 pages, 8 figures

The dynamic spin structure factor $\mathcal{S}(k,\omega)$ of a system of spin-1/2 bosons is investigated at arbitrary strength of interparticle repulsion. As a function of $\omega$ it is shown to exhibit a power-law singularity at the threshold frequency defined by the energy of a magnon at given $k.$ The power-law exponent is found exactly using a combination of the Bethe Ansatz solution and an effective field theory approach., Comment: 4 pages, 2 figures

We study the influence of non magnetic impurities on the phase diagram of doped two-leg Hubbard Cu-O ladders. In the absence of impurities this system posseses d-wave superconducting states and orbital current states depending on the doping. A single, strong, scatterer modifies its environment locally and this effect is assessed using a renormalization group analysis. At high doping, disorder causes intraband instabilities and at low doping it promotes interband instabilities. In the former case, we extend the boundary conformal field theory method, developed in the context of single chains, to handle the ladder problem, and we find exact closed-form analytical expressions for the correlation functions. This allows us to compute experimentally measurable local quantities such as the nuclear magnetic resonance line broadenings and scanning tunnelling microscope profiles. We also discuss the low doping regime where Kondo physics is at play, making qualitative predictions about its nature. Insight into collective effects is also given in the many weak impurities case, based on an RG approach. In this regime, one sees the interplay between interactions and disorder. We emphasize the influence of the O atoms on disorder effects both for the single- and for the many-defect situations., Comment: accepted to be published in NJP special edition

We study the conditions under which, using a canonical transformation, the phases sought after for the repulsive Hubbard model, namely a Mott insulator in the paramagnetic and anti-ferromagnetic phases, and a putative d-wave superfluid can be deduced from observations in an optical lattice loaded with a spin-imbalanced ultra-cold Fermi gas with attractive interactions, thus realizing the attractive Hubbard model. We show that the Mott insulator and antiferromagnetic phase of the repulsive Hubbard model are in fact more easy to observe as a paired, and superfluid phase respectively, in the attractive Hubbard model. The putative d-wave superfluid phase of the repulsive Hubbard model doped away from half-filling is related to a d-wave antiferromagnetic phase for the attractive Hubbard model. We discuss the advantages of this approach to 'quantum simulate' the Hubbard model in an optical lattice over the approach that attempts to directly simulate the doped Hubbard model in the repulsive regime. We also point out a number of technical difficulties of the proposed approach and, in some cases, suggest possible solutions., Comment: 11 pages, 5 figs. New version as accepted in PRA. We have clarified the models we are discussing in various places, and expanded on the critical number estimate to include both K40 and Li6 in section V. Also added references

We calculate a correlation function of the Jordan-Wigner operator in a class of free-fermion models formulated on an infinite one-dimensional lattice. We represent this function in terms of the determinant of an integrable Fredholm operator, convenient for analytic and numerical investigations. By using Wick's theorem, we avoid the form-factor summation customarily used in literature for treating similar problems., Comment: references added, introduction and conclusion modified, version accepted for publication in J. Stat. Mech

We investigate the dynamics of the one-dimensional strongly repulsive spin-1/2 Bose-Hubbard model for filling $\nu\le1.$ While at $\nu=1$ the system is a Hubbard-Mott insulator exhibiting dynamical properties of the Heisenberg ferromagnet, at $\nu<1$ it is a ferromagnetic liquid with complex spin dynamics. We find that close to the insulator-liquid transition the system admits for a complete separation of spin and density degrees of freedom valid at {\it all} energy and momentum scales within the $t-J$ approximation. This allows us to derive the propagator of transverse spin waves and the shape of the magnon peak in the dynamic spin structure factor., Comment: 4 pages, 2 figures, version accepted for publication in Phys. Rev. Lett

Many seemingly different macroscopic systems (magnets, ferroelectrics, CDW, vortices,..) can be described as generic disordered elastic systems. Understanding their static and dynamics thus poses challenging problems both from the point of view of fundamental physics and of practical applications. Despite important progress many questions remain open. In particular the temperature has drastic effects on the way these systems respond to an external force. We address here the important question of the thermal effect close to depinning, and whether these effects can be understood in the analogy with standard critical phenomena, analogy so useful to understand the zero temperature case. We show that close to the depinning force temperature leads to a rounding of the depinning transition and compute the corresponding exponent. In addition, using a novel algorithm it is possible to study precisely the behavior close to depinning, and to show that the commonly accepted analogy of the depinning with a critical phenomenon does not fully hold, since no divergent lengthscale exists in the steady state properties of the line below the depinning threshold., Comment: Proceedings of the International Workshop on Electronic Crystals, Cargese(2008)