Luttinger Liquid Properties Research Articles

Probing Luttinger liquid properties in a multichannel two-site charge Kondo simulator

Probing Luttinger liquid properties in a multichannel two-site charge Kondo simulator

Confinement and Mott Transitions of Dynamical Charges in One-Dimensional Lattice Gauge Theories.

Confinement is an ubiquitous phenomenon when matter couples to gauge fields, which manifests itself in a linear string potential between two static charges. Although gauge fields can be integrated out in one dimension, they can mediate nonlocal interactions which in turn influence the paradigmatic Luttinger liquid properties. However, when the charges become dynamical and their densities finite, understanding confinement becomes challenging. Here we show that confinement in 1D Z_{2} lattice gauge theories, with dynamical matter fields and arbitrary densities, is related to translational symmetry breaking in a nonlocal basis. The exact transformation to this string-length basis leads us to an exact mapping of Luttinger parameters reminiscent of a Luther-Emery rescaling. We include the effects of local, but beyond contact, interactions between the matter particles, and show that confined mesons can form a Mott-insulating state when the deconfined charges cannot. While the transition to the Mott state cannot be detected in the Green's function of the charges, we show that the metallic state is characterized by hidden off-diagonal quasi-long-range order. Our predictions provide new insights to the physics of confinement of dynamical charges, and can be experimentally addressed in Rydberg-dressed quantum gases in optical lattices.

Luttinger liquid properties from tensor network data

We study the XXZ Heisenberg model in a staggered magnetic field using the HOTRG tensor renormalization method. Built into the tensor representation of the XXZ model is the U(1) symmetry, which is systematically maintained at each renormalization step. We determine the phase diagram of the model from the low lying spectrum, and from the finite size dependence of the spectrum we extract scaling dimensions, which are compared to predictions of low energy field theory.

Luttinger liquid properties of the steady state after a quantum quench

We study the dynamics resulting out of an abrupt change of the two-particle interaction in two models of closed one-dimensional Fermi systems: (a) the field theoretical Tomonaga-Luttinger model and (b) a microscopic lattice model. Using a nonperturbative approach which is controlled for small two-particle interactions we are able to reach large times allowing us to access the properties of the steady state of the lattice model. Comparing those to the exact solution of the full dynamics in the Tomonaga-Luttinger model we provide evidence for universal Luttinger liquid behavior.

Local spectral properties of Luttinger liquids: scaling versus nonuniversal energy scales

Motivated by recent scanning tunneling and photoemission spectroscopy measurements on self-organized gold chains on a germanium surface, we reinvestigate the local single-particle spectral properties of Luttinger liquids. In the first part we use the bosonization approach to exactly compute the local spectral function of a simplified field theoretical low-energy model and take a closer look at scaling properties as a function of the ratio of energy and temperature. Translational-invariant Luttinger liquids as well as those with an open boundary (cut chain geometry) are considered. We explicitly show that the scaling functions of both set-ups have the same analytical form. The scaling behavior suggests a variety of consistency checks which can be performed on measured data to experimentally verify Luttinger liquid behavior. In the second part we approximately compute the local spectral function of a microscopic lattice model—the extended Hubbard model—close to an open boundary using the functional renormalization group. We show that it follows the field theoretical prediction in the low-energy regime as a function of energy and temperature, and point out the importance of nonuniversal energy scales inherent to any microscopic model. The spatial dependence of this spectral function is characterized by oscillatory behavior and an envelope function which follows a power law in accordance with the field theoretical continuum model. Interestingly, for the lattice model we find a phase shift which is proportional to the two-particle interaction and not accounted for in the standard bosonization approach to Luttinger liquids with an open boundary. We briefly comment on the effects of several one-dimensional branches cutting the Fermi energy and Rashba spin–orbit interaction.

Spectral properties of Luttinger liquids: A comparative analysis of regular, helical, and spiral Luttinger liquids

We provide analytic expressions for the Green's functions in position-frequency space as well as for the tunneling density of states of various Luttinger liquids at zero temperature: the standard spinless and spinful Luttinger liquids, the helical Luttinger liquid at the edge of a topological insulator, and the Luttinger liquid that appears either together with an ordering transition of nuclear spins in a one-dimensional conductor, or in spin-orbit split quantum wires in an external magnetic field. The latter system is often used to mimic a helical Luttinger liquid, yet we show here that it exhibits significantly different response functions and, to discriminate, we call it the spiral Luttinger liquid. We give fully analytic results for the tunneling density of state of all the Luttinger liquids as well as for most of the Green's functions. The remaining Green's functions are expressed by simple convolution integrals between analytic results.

Critical exponents for the spin Coulomb drag in the Hubbard chain

The spin Coulomb drag is the decay of the spin current in a metal as a consequence of the Coulomb interaction between up- and down-spin carriers. We calculate the critical exponents of the resistivity for up- and down-spin electrons and the transresistivity for the spin-polarized Hubbard chain with nonmagnetic impurities within the Kubo formalism using the Bethe Ansatz solution and conformal invariance. Due to the Luttinger liquid properties the temperature dependence of the transport correlation functions follows power laws of T with nonuniversal exponents.

Spin Coulomb drag in the Hubbard chain

The spin Coulomb drag is the decay of the spin current in a metal as a consequence of the Coulomb interaction between up- and down-spin carriers. This interaction reduces the spin current but does not change the spin-polarization. We calculate the critical exponents of the resistivity for up- and down-spin electrons and the transresistivity for the spin-polarized Hubbard chain with nonmagnetic impurities within the Kubo formalism using the Bethe ansatz solution and conformal invariance. Due to the Luttinger liquid properties the temperature dependence of the transport correlation functions follow power laws of $T$ with nonuniversal exponents.

Spin Coulomb Drag in a One-Dimensional Spin-Polarized Conductor

The spin Coulomb drag is a distinctive feature of spin-polarized transport. The current of majority spins can induce a current of minority spin carriers via the transconductivity. The friction is caused by the Coulomb interaction between up- and down-spin. This interaction reduces the current but does not change the spin-polarization. We calculate the conductivities and the transconductivity for a spin-polarized interacting 1-D electron gas for a lattice without inversion symmetry in the presence of nonmagnetic impurities. Due to the Luttinger liquid properties, the temperature dependence of the transport correlation functions follows power laws of with nonuniversal exponents.

Study of the charge correlation function in one-dimensional Hubbard heterostructures

We study inhomogeneous one-dimensional Hubbard systems using the density-matrix renormalization-group method (DMRG). Different heterostructures are investigated whose configuration is modeled varying parameters such as the on-site Coulomb potential and introducing local confining potentials. We investigate their Luttinger liquid properties through the parameter ${K}_{\ensuremath{\rho}}$, which characterizes the decay of the density-density correlation function at large distances. Our main goal is the investigation of possible realization of engineered materials and the ability to manipulate physical properties by choosing an appropriate spatial and/or chemical modulation.

Quantum condensation in electron–hole systems: excitonic BEC–BCS crossover andbiexciton crystallization

Quantum condensation of electron–hole (e–h) systems in photoexcited semiconductorsis reviewed from a theoretical viewpoint, stressing the exciton Bose–Einsteincondensation (BEC), the e–h BCS-type condensed state, the exciton Mott transition,and the biexciton crystallization. First, we discuss the crossover between theexciton BEC and the e–h BCS states at low temperature using the self-consistentt-matrix and local approximations, applied to the high-dimensional two-band Hubbardmodel with both repulsive and attractive on-site interactions. We also study themetal–insulator transition (called the ‘exciton Mott transition’) at zero and finitetemperatures, investigated with the dynamical mean-field theory. Away fromhalf-filling we find excitonic/biexcitonic insulating phases and the first-order transitionbetween metallic and insulating states. Second, in a one-dimensional e–h system,we employ the exciton bosonization and renormalization-group techniques toclarify quantum orders at zero temperature. The most probable ground stateexhibits the biexciton crystallization, which reflects the Tomonaga–Luttinger liquidproperties, the e–h backward scattering, and the long-range Coulomb interaction. Theone-dimensional e–h system is insulating even at the high-density limit, hencethe exciton Mott transition never occurs at zero temperature in one dimension.

Absence of dimer order and the Tomonaga–Luttinger liquid properties of the quarter-filled one-dimensional Kondo-lattice model

A novel spin dimer order is recently reported in the ground state of the one-dimensional Kondo lattice model at quarter-filling. Being dubious about such long-range order in the absence of a spin gap, we perform the density matrix renormalization group calculation at under several boundary conditions. It turns out that dimer spin structure is sensitive to the boundary conditions, and that the dimer correlation function decays in small power law at long distances, indicating the absence of dimer long-range order. This together with a possible absence of charge gap suggests that the true ground state remains to be a Tomonaga–Luttinger liquid with small K ρ .

Creation of nonlocal spin-entangled electrons via Andreev tunneling, Coulomb blockade, and resonant transport

We discuss several scenarios for the creation of nonlocal spin-entangled electrons which provide a source of electronic Einstein–Podolsky–Rosen (EPR) pairs. Such EPR pairs can be used to test nonlocality of electrons in solid state systems, and they form the basic resources for quantum information processing. The central idea is to exploit the spin correlations naturally present in superconductors in form of Cooper pairs possessing spin-singlet wavefunctions. We show that nonlocal spin-entanglement in form of an effective Heisenberg spin interaction is induced between electron spins residing on two quantum dots with no direct coupling between them, but each of them being tunnel-coupled to the same superconductor. We then discuss a nonequilibrium setup with an applied bias where mobile and nonlocal spin-entanglement can be created by coherent injection of two electrons, in a pair (Andreev) tunneling process, into two spatially separated quantum dots and subsequently into two Fermi liquid leads. The current for injecting two spin-entangled electrons into different leads shows a resonance and allows the injection of electrons at the same orbital energy, which is a crucial requirement for the detection of spin-entanglement via the current noise. On the other hand, tunneling via the same dot into the same lead is suppressed by the Coulomb blockade effect of the quantum dots. We discuss Aharonov–Bohm oscillations in the current and show that they contain h/e and h/2e periods, which provides an experimental means to test the nonlocality of the entangled pair. Finally, we discuss a structure consisting of a superconductor weakly coupled to two separate one-dimensional leads with Luttinger liquid properties. We show that strong correlations again suppress the coherent subsequent tunneling of two electrons into the same lead, thus generating again nonlocal spin-entangled electrons in the Luttinger liquid leads.

Correlated one-dimensional electron systems: Luttinger liquid properties and deviations at finite temperature

We present results of a novel treatment of finite temperature properties of the one-dimensional Hubbard model based on a Trotter–Suzuki mapping and a subsequent investigation of the quantum transfer matrix. Data are obtained for the specific heat, magnetic and charge susceptibilities for various particle densities and coupling strengths U. Special emphasis is placed on the study of the low-temperature behavior within our ab initio approach confirming the scaling predictions by Tomonaga–Luttinger liquid theory. The physical properties at finite temperature outside the universal Tomonaga–Luttinger liquid range are compared for the Hubbard and the supersymmetric tJ model. In particular the charge susceptibility shows interesting non-universal signatures.

Exact thermodynamics and Luttinger liquid properties of the integrable t- J model

A Trotter-Suzuki mapping is used to calculate the finite-temperature properties of the one-dimensional supersymmetric t- J model. This approach allows for the exact calculation of various thermodynamical properties by means of the quantum transfer matrix (QTM). The free energy and other interesting quantities are obtained, such as the specific heat and compressibility. For the largest eigenvalue of the QTM leading to the free energy a set of just two non-linear integral equations is presented. These equations are studied analytically and numerically for different particle densities and temperatures. The structure of the specific heat is discussed in terms of the elementary charge as well as spin excitations. Special emphasis is placed on the study of the low-temperature behavior confirming scaling predictions by conformal field theory and Luttinger liquid theory. To our knowledge this is the first complete investigation of a strongly correlated electron system on a lattice at finite temperature.

Bosonization of one-dimensional exclusons and characterization of Luttinger liquids.

We achieve a bosonization of one-dimensional ideal gas of exclusion statistics $\lambda$ at low temperatures, resulting in a new variant of $c=1$ conformal field theory with compactified radius $R=\sqrt{1/\lambda}$. These ideal excluson gases exactly reproduce the low-$T$ critical properties of Luttinger liquids, so they can be used to characterize the fixed points of the latter. Generalized ideal gases with mutual statistics and non-ideal gases with Luttinger-type interactions have also similar behavior, controlled by an effective statistics varying in a fixed-point line.

Interacting one-dimensional electron gas with open boundaries

We discuss the properties of interacting electrons on a finite chain with open boundary conditions. We extend the Haldane Luttinger liquid description to these systems and study how the presence of the boundaries modifies various correlation functions. In view of possible experimental applications to quantum wires, we analyse how tunneling measurements can reveal the underlying Luttinger liquid properties. The two terminal conductance is calculated. We also point out possible applications to quasi one dimensional materials and study the effects of magnetic impurities.

Charge-spin separation and the spectral properties of Luttinger liquids

We compute the spectral function rho (q, omega ) of the one-dimensional Luttinger model. We discuss the distinct influences of charge-spin separation and of the anomalous dimensions of the fermion operators and their evolution with correlation strength. Charge-spin separation shows up in finite spectral weight at frequencies between vsigma q and vrho q, where vsigma and vrho are the velocities of spin and charge fluctuations, while spectral weight above vrho q and below -vrho q is generated by the hybridization of the Fermi surface at +or-kF by interactions. There are non-universal power-law singularities at these special frequencies. We discuss the consistency of recent photoemission experiments on low-dimensional conductors with a Luttinger-liquid picture, which then would suggest very strong long-range interactions. It is pointed out that many-particle correlation functions in principle exhibit similar singularities, but they probe different and complementary aspects of the Fermi-surface interactions.

Charge-spin separation and the spectral properties of Luttinger liquids.

We compute the spectral function p(q, ω) of the one-dimensional Luttinger model. We discuss the distinct influences of charge-spin separation and of the anomalous dimensions of the fermion operators and their evolution with correlation strength. Charge-spin separation shows up in finite spectral weight at frequencies between υσ q and υp q where υ p and υσ are the velocities of charge and spin fluctuations, while spectral weight above υp q and below -υp q is generated by the hybridization of the Fermi surface at ±k F by interactions. There are nonuniversal power-law singularities at these spectral frequencies. We discuss the consistency of recent photoemission experiments on low-dimensional conductors with a Luttinger liquid picture which then would suggest very strong long range interactions.

Luttinger liquid properties of highly correlated electron systems in one dimension

An exact description is given of the long-distance behaviour of the one-dimensional t-J model at t=J. The authors employ the Bathe ansatz method and the finite-size scaling technique in conformal field theory. The charge and spin degrees of freedom are separated, and described by two independent c=1 conformal theories. The critical exponents for the charge, spin, electron and superconducting correlation functions are obtained for arbitrary band filling. The authors then make detailed comparison of the t-J model with the repulsive Hubbard model with emphasis on the Luttinger liquid properties. Analysing the electron filling dependence they observe the enhancement of the superconducting correlations compared with the highly correlated Hubbard model. The effect of the external magnetic field at and near half-filling is also discussed.