arXiv subjects

J. Sirker

Publications and source records attributed to J. Sirker.

At least 55 records · Page 3Linked to original sources

arXiv2013

Theory of the conductance of interacting quantum wires with good contacts and applications to carbon nanotubes

Using bosonization we derive the dc conductance G(L,T) of an interacting quantum wire with good contacts including current relaxing backscattering and Umklapp processes. Our result yields the dependence of the conductance on length L and temperature T in the energy range where the Luttinger model is applicable. For a system where only a part of the current is protected by a conservation law we surprisingly find an unreduced ideal quantum conductance as for a fully ballistic wire. As a second application, we calculate the conductance of metallic single-wall carbon nanotubes in an energy range where backscattering due to phonons dominates. In contrast to previous studies we treat the electrons as interacting by using the Luttinger liquid formulation. The obtained results for the scaling of the dc conductance with temperature and length are compared with experimental data and yield a better description than the previously used non-interacting theory. Possible reasons for the remaining discrepancies in the temperature dependence between theory and experiment are discussed.

cond-mat.str-el↗

arXiv2012

Transport and scattering in inhomogeneous quantum wires

We consider scattering and transport in interacting quantum wires that are connected to leads. Such a setup can be represented by a minimal model of interacting fermions with inhomogeneities in the form of sudden changes in interaction strength and/or velocity. The inhomogeneities generally cause relevant backscattering, so it is a priori unclear if a perfectly ballistic quantum wire can exist in the low temperature limit. We are able to identify such a perfectly conducting fixed point even for large abrupt changes, which in the considered model corresponds to a velocity matching condition. The general position dependent Green's function is calculated in the presence of a sudden change, which is confirmed numerically with high accuracy. The exact form of the interference pattern in the form of density oscillations around inhomogeneities can be used to estimate the effective strength of local backscattering sources.

cond-mat.str-el↗

arXiv2012

The Luttinger liquid and integrable models

Many fundamental one-dimensional lattice models such as the Heisenberg or the Hubbard model are integrable. For these microscopic models, parameters in the Luttinger liquid theory can often be fixed and parameter-free results at low energies for many physical quantities such as dynamical correlation functions obtained where exact results are still out of reach. Quantum integrable models thus provide an important testing ground for low-energy Luttinger liquid physics. They are, furthermore, also very interesting in their own right and show, for example, peculiar transport and thermalization properties. The consequences of the conservation laws leading to integrability for the structure of the low-energy effective theory have, however, not fully been explored yet. I will discuss the connection between integrability and Luttinger liquid theory here, using the anisotropic Heisenberg model as an example. In particular, I will review the methods which allow to fix free parameters in the Luttinger model with the help of the Bethe ansatz solution. As applications, parameter-free results for the susceptibility in the presence of non-magnetic impurities, for spin transport, and for the spin-lattice relaxation rate are discussed.

cond-mat.str-el↗

arXiv2012

Entanglement measures and the quantum to classical mapping

A quantum model can be mapped to a classical model in one higher dimension. Here we introduce a finite-temperature correlation measure based on a reduced density matrix rho_A obtained by cutting the classical system along the imaginary time (inverse temperature) axis. We show that the von-Neumann entropy S_ent of rho_A shares many properties with the mutual information, yet is based on a simpler geometry and is thus easier to calculate. For one-dimensional quantum systems in the thermodynamic limit we proof that S_ent is non-extensive for all temperatures T. For the integrable transverse Ising and XXZ models we demonstrate that the entanglement spectra of rho_A in the limit T-> 0 are described by free-fermion Hamiltonians and reduce to those of the regular reduced density matrix---obtained by a spatial instead of an imaginary-time cut---up to degeneracies.

quant-ph↗

arXiv2012

Spinons and helimagnons in the frustrated Heisenberg chain

We investigate the dynamical spin structure factor S(q,w) for the Heisenberg chain with ferromagnetic nearest (J1<0) and antiferromagnetic next-nearest (J2>0) neighbor exchange using bosonization and a time-dependent density-matrix renormalization group algorithm. For |J1|<< J2 and low energies we analytically find and numerically confirm two spinon branches with different velocities and different spectral weights. Following the evolution of S(q,w) with decreasing J1/J2 we find that helimagnons develop at high energies just before entering the ferromagnetic phase. Furthermore, we show that a recent interpretation of neutron scattering data for LiCuVO4 in terms of two weakly coupled antiferromagnetic chains (|J_1|<< J2) is not viable. We demonstrate that the data are instead fully consistent with a dominant ferromagnetic coupling, J1/J2 ~ -2.

cond-mat.str-el↗

arXiv2011

Particle injection into a chain: decoherence versus relaxation for Hermitian and non-Hermitian dynamics

We investigate a model system for the injection of fermionic particles from filled source sites into an empty chain. We study the ensuing dynamics for Hermitian as well as for non-Hermitian time evolution where the particles cannot return to the bath sites (quantum ratchet). A non-homogeneous hybridization between bath and chain sites permits transient currents in the chain. Non-interacting particles show decoherence in the thermodynamic limit: the average particle number and the average current density in the chain become stationary for long times, whereas the single-particle density matrix displays large fluctuations around its mean value. Using the numerical time-dependent density-matrix renormalization group ($t$-DMRG) method we demonstrate, on the other hand, that sizable density-density interactions between the particles introduce relaxation which is by orders of magnitudes faster than the decoherence processes.

cond-mat.str-el↗

arXiv2011

The J1-J2 Heisenberg model at and close to its z=4 quantum critical point

We study the frustrated J1-J2 Heisenberg model with ferromagnetic nearest neighbor coupling J1<0 and antiferromagnetic next-nearest neighbor coupling J2>0 at and close to the z=4 quantum critical point (QCP) at J1/J2=-4. The J1-J2 model plays an important role for recently synthesized chain cuprates as well as in supersymmetric Yang Mills theories. We study the thermodynamic properties using field theory, a modified spin-wave theory as well as numerical density-matrix renormalization group calculations. Furthermore, we compare with results for the classical model obtained by analytical methods and Monte-Carlo simulations. As one of our main results we present numerical evidence that the susceptibility at the QCP seems to diverge with temperature T as chi ~ T^{-1.2} in the quantum case in contrast to the classical model where chi ~ T^{-4/3}.

cond-mat.str-el↗

arXiv2011

The dimerized ferromagnetic Heisenberg chain

Ferromagnetic, in contrast to antiferromagnetic, Heisenberg chains can undergo a Spin-Peierls dimerization only at finite temperatures. They show reentrant behavior as a function of temperature, which might play a role for systems with small effective elastic constants as, for example, monatomic chains on surfaces. We investigate the physical properties of the dimerized ferromagnetic Heisenberg chain using a modified spin-wave theory. We calculate the exponentially decaying spin and dimer correlation functions, analyze the temperature dependence of the corresponding coherence lengths, the susceptibility, as well as the static and dynamic spin structure factor. By comparing with numerical data obtained by the density-matrix renormalization group applied to transfer matrices, we find that the modified spin wave theory yields excellent results for all these quantities for a wide range of dimerizations and temperatures.

cond-mat.str-el↗

arXiv2011

Electron scattering from domain walls in ferromagnetic Luttinger liquids

We study the properties of interacting electrons in a one-dimensional conduction band coupled to bulk non-collinear ferromagnetic order. The specific form of non-collinearity we consider is that of an extended domain wall. The presence of ferromagnetic order breaks spin-charge separation and the domain wall introduces a spin-dependent scatterer active over the length of the wall l. Both forward and backward scattering off the domain wall can be relevant perturbations of the Luttinger liquid and we discuss the possible low temperature phases. Our main finding is that backward scattering, while determining the ultimate low temperature physics, only becomes important at temperatures T/J < exp(-l/l_+) with J being the magnetic exchange and l_+ the backward scattering length scale. In physical realizations, l >> l_+ and the physics will be dominated by forward scattering which can lead to a charge conducting but spin insulating phase. In a perturbative regime at higher temperatures we furthermore calculate the spin and charge densities around the domain wall and quantitatively discuss the interaction induced changes.

cond-mat.str-el↗

arXiv2011

Spin exchange dominated by charge fluctuations of the Wigner lattice in the newly synthesized chain cuprate Na5Cu3O6

Na5Cu3O6, a new member of one dimensional charge ordered chain cuprates, was synthesized via the azide/nitrate route by reacting NaN3, NaNO3 and CuO. According to single crystal X-ray analysis, one dimensional CuO2 chains built up from planar, edge-sharing CuO4 squares are a dominant feature of the crystal structure. From the analysis of the Cu-O bond lengths we find that the system forms a Wigner lattice. The commensurate charge order allows to explicitly assign the valence states of either +2 or +3 to each copper atom resulting in a repetition according to Cu(2+)-Cu(3+)-Cu(2+)-Cu(2+)-Cu(3+)-Cu(2+). Following the theoretical analysis of the previously synthesized compounds Na3Cu2O4 and Na8Cu5O10, the magnetic susceptibility was expected to show a large dimer gap. Surprisingly, this is not the case. To resolve this puzzle, we show that the magnetic couplings in this compound are strongly affected by excitations across the Wigner charge gap. By including these contributions, which are distinct from conventional superexchange in Mott-insulators, we obtain a quantitative satisfying theoretical description of the magnetic susceptibility data.

cond-mat.str-el↗

arXiv2011

Magnetic excitations in one-dimensional spin-orbital models

We study the dynamics and thermodynamics of one-dimensional spin-orbital models relevant for transition metal oxides. We show that collective spin, orbital, and combined spin-orbital excitations with infinite lifetime can exist, if the ground state of both sectors is ferromagnetic. Our main focus is the case of effectively ferromagnetic (antiferromagnetic) exchange for the spin (orbital) sector, respectively, and we investigate the renormalization of spin excitations via spin-orbital fluctuations using a boson-fermion representation. We contrast a mean-field decoupling approach with results obtained by treating the spin-orbital coupling perturbatively. Within the latter self-consistent approach we find a significant increase of the linewidth and additional structures in the dynamical spin structure factor as well as Kohn anomalies in the spin-wave dispersion caused by the scattering of spin excitations from orbital fluctuations. Finally, we analyze the specific heat c(T) by comparing a numerical solution of the model obtained by the density-matrix renormalization group with perturbative results. At low temperatures T we find numerically c(T) T pointing to a low-energy effective theory with dynamical critical exponent z=1.

cond-mat.str-el↗

arXiv2010

Diffusion and ballistic transport in one-dimensional quantum systems

It has been conjectured that transport in integrable one-dimensional (1D) systems is necessarily ballistic. The large diffusive response seen experimentally in nearly ideal realizations of the S=1/2 1D Heisenberg model is therefore puzzling and has not been explained so far. Here, we show that, contrary to common belief, diffusion is universally present in interacting 1D systems subject to a periodic lattice potential. We present a parameter-free formula for the spin-lattice relaxation rate which is in excellent agreement with experiment. Furthermore, we calculate the current decay directly in the thermodynamic limit using a time-dependent density matrix renormalization group algorithm and show that an anomalously large time scale exists even at high temperatures.

cond-mat.str-el↗

arXiv2010

Conservation laws, integrability and transport in one-dimensional quantum systems

In integrable one-dimensional quantum systems an infinite set of local conserved quantities exists which can prevent a current from decaying completely. For cases like the spin current in the XXZ model at zero magnetic field or the charge current in the attractive Hubbard model at half filling, however, the current operator does not have overlap with any of the local conserved quantities. We show that in these situations transport at finite temperatures is dominated by a diffusive contribution with the Drude weight being either small or even zero. For the XXZ model we discuss in detail the relation between our results, the phenomenological theory of spin diffusion, and measurements of the spin-lattice relaxation rate in spin chain compounds. Furthermore, we study the Haldane-Shastry model where the current operator is also orthogonal to the set of conserved quantities associated with integrability but becomes itself conserved in the thermodynamic limit.

cond-mat.str-el↗

arXiv2010

Finite temperature fidelity susceptibility for one-dimensional quantum systems

We calculate the fidelity susceptibility chi_f for the Luttinger model and show that there is a universal contribution linear in temperature T (or inverse length 1/L). Furthermore, we develop an algorithm - based on a lattice path integral approach - to calculate the fidelity F(T) in the thermodynamic limit for one-dimensional quantum systems. We check the Luttinger model predictions by calculating chi_f(T) analytically for free spinless fermions and numerically for the XXZ chain. Finally, we study chi_f at the two phase transitions in this model.

cond-mat.str-el↗

arXiv2009

Thermodynamics of multiferroic spin chains

The minimal model to describe many spin chain materials with ferroelectric properties is the Heisenberg model with ferromagnetic nearest neighbor coupling J1 and antiferromagnetic next-nearest neighbor coupling J2. Here we study the thermodynamics of this model using a density-matrix algorithm applied to transfer matrices. We find that the incommensurate spin-spin correlations - crucial for the ferroelectric properties and the analogue of the classical spiral pitch angle - depend not only on the ratio J2/|J1| but also strongly on temperature. We study small easy-plane anisotropies which can stabilize a vector chiral order as well as the finite-temperature signatures of multipolar phases, stable at finite magnetic field. Furthermore, we fit the susceptibilities of LiCuVO4, LiCu2O2, and Li2ZrCuO4. Contrary to the literature, we find that for LiCuVO4 the best fit is obtained with J2 ~ 90 K and J2/|J1| ~ 0.5 and show that these values are consistent with the observed spin incommensurability. Finally, we discuss our findings concerning the incommensurate spin-spin correlations and multipolar orders in relation to future experiments on these compounds.

cond-mat.str-el↗

arXiv2009

NMR Response in quasi one-dimensional Spin-1/2 Antiferromagnets

Non-magnetic impurities break a quantum spin chain into finite segments and induce Friedel-like oscillations in the local susceptibility near the edges. The signature of these oscillations has been observed in Knight shift experiments on the high-temperature superconductor YBa$_2$Cu$_3$O$_{6.5}$ and on the spin-chain compound Sr$_2$CuO$_3$. Here we analytically calculate NMR spectra, compare with the available experimental data for Sr$_2$CuO$_3$, and show that the interchain coupling is responsible for the complicated and so far unexplained lineshape. Our results are based on a parameter-free formula for the local susceptibility of a finite spin chain obtained by bosonization which is checked by comparing with quantum Monte Carlo and density-matrix renormalization group calculations.

cond-mat.str-el↗

arXiv2009

Consequences of lattice imperfections and interchain couplings for the critical properties of spin-1/2 chain compounds

To allow for a comparison of theoretical predictions for spin chains with experimental data, it is often important to take impurity effects as well as interchain couplings into account. Here we present the field theory for finite spin chains at finite temperature and calculate experimentally measurable quantities like susceptibilities and nuclear magnetic resonance spectra. For the interchain couplings we concentrate on geometries relevant for cuprate spin chains like Sr$_2$CuO$_3$ and SrCuO$_2$. The field theoretical results are compared to experimental as well as numerical data obtained by the density matrix renormalization group.

cond-mat.str-el↗

arXiv2008

Doping a Mott insulator with orbital degrees of freedom

We study the effects of hole doping on one-dimensional Mott insulators with orbital degrees of freedom. We describe the system in terms of a generalized t-J model. At a specific point in parameter space the model becomes integrable in analogy to the one-band supersymmetric t-J model. We use the Bethe ansatz to derive a set of nonlinear integral equations which allow us to study the thermodynamics exactly. Moving away from this special point in parameter space we use the density-matrix renormalization group applied to transfer matrices to study the evolution of various phases of the undoped system with doping and temperature. Finally, we study a one-dimensional version of a realistic model for cubic titanates which includes the anisotropy of the orbital sector due to Hund's coupling. We find a transition from a phase with antiferromagnetically correlated spins to a phase where the spins are fully ferromagnetically polarized, a strong tendency towards phase separation at large Hund's coupling, as well as the possibility of an instability towards triplet superconductivity.

cond-mat.str-el↗