Low temperature dynamics of nonlinear Luttinger liquids

We develop a general nonlinear Luttinger liquid theory to describe the dynamics of one-dimensional quantum critical systems at low temperatures.To demonstrate the predictive power of our theory we compare results for the autocorrelation G(t) in the XXZ chain with numerical density-matrix renormalization group data and obtain excellent agreement.Our calculations provide, in particular, direct evidence that G(t) shows a diffusion-like decay, G t t 1 , ( ) in sharp contrast to the exponential decay in time predicted by conventional Luttinger liquid theory.We develop a general nonlinear Luttinger liquid theory to describe the dynamics of one-dimensional quantum critical systems at low temperatures.To demonstrate the predictive power of our theory we compare results for the autocorrelation G(t) in the XXZ chain with numerical density-matrix renormalization group data and obtain excellent agreement.Our calculations provide, in particular, direct evidence that G(t) shows a diffusion-like decay, G t t 1 , ( ) in sharp contrast to the exponential decay in time predicted by conventional Luttinger liquid theory.

arXiv:1410.2226New Journal of PhysicsSep 30, 201522 citations

One-Dimensional Liquid He4 : Dynamical Properties beyond Luttinger-Liquid Theory

Gianluca Bertaina, Mário Motta, M. Rossi +2 more

We compute the zero-temperature dynamical structure factor of one-dimensional liquid ^{4}He by means of state-of-the-art quantum Monte Carlo and analytic continuation techniques. By increasing the density, the dynamical structure factor reveals a transition from a highly compressible critical liquid to a quasisolid regime. In the low-energy limit, the dynamical structure factor can be described by the quantum hydrodynamic Luttinger-liquid theory, with a Luttinger parameter spanning all possible values by increasing the density. At higher energies, our approach provides quantitative results beyond the Luttinger-liquid theory. In particular, as the density increases, the interplay between dimensionality and interaction makes the dynamical structure factor manifest a pseudo-particle-hole continuum typical of fermionic systems. At the low-energy boundary of such a region and moderate densities, we find consistency, within statistical uncertainties, with predictions of a power-law structure by the recently developed nonlinear Luttinger-liquid theory. In the quasisolid regime, we observe a novel behavior at intermediate momenta, which can be described by new analytical relations that we derive for the hard-rods model.We compute the zero-temperature dynamical structure factor of one-dimensional liquid ^{4}He by means of state-of-the-art quantum Monte Carlo and analytic continuation techniques. By increasing the density, the dynamical structure factor reveals a transition from a highly compressible critical liquid to a quasisolid regime. In the low-energy limit, the dynamical structure factor can be described by the quantum hydrodynamic Luttinger-liquid theory, with a Luttinger parameter spanning all possible values by increasing the density. At higher energies, our approach provides quantitative results beyond the Luttinger-liquid theory. In particular, as the density increases, the interplay between dimensionality and interaction makes the dynamical structure factor manifest a pseudo-particle-hole continuum typical of fermionic systems. At the low-energy boundary of such a region and moderate densities, we find consistency, within statistical uncertainties, with predictions of a power-law structure by the recently developed nonlinear Luttinger-liquid theory. In the quasisolid regime, we observe a novel behavior at intermediate momenta, which can be described by new analytical relations that we derive for the hard-rods model.

arXiv:1412.7179Physical Review LettersApr 1, 201654 citations

LONG TIME CORRELATIONS OF NONLINEAR LUTTINGER LIQUIDS

Rodrigo G. Pereira

An overview is given of the limitations of Luttinger liquid theory in describing the real time equilibrium dynamics of critical one-dimensional systems with nonlinear dispersion relation. After exposing the singularities of perturbation theory in band curvature effects that break the Lorentz invariance of the Tomonaga–Luttinger model, the origin of high frequency oscillations in the long time behaviour of correlation functions is discussed. The notion that correlations decay exponentially at finite temperature is challenged by the effects of diffusion in the density–density correlation due to umklapp scattering in lattice models.An overview is given of the limitations of Luttinger liquid theory in describing the real time equilibrium dynamics of critical one-dimensional systems with nonlinear dispersion relation. After exposing the singularities of perturbation theory in band curvature effects that break the Lorentz invariance of the Tomonaga–Luttinger model, the origin of high frequency oscillations in the long time behaviour of correlation functions is discussed. The notion that correlations decay exponentially at finite temperature is challenged by the effects of diffusion in the density–density correlation due to umklapp scattering in lattice models.

Series on directions in condensed matter physicsOct 24, 20130 citations

LONG TIME CORRELATIONS OF NONLINEAR LUTTINGER LIQUIDS

RODRIGO G. PEREIRA

arXiv:1207.3548International Journal of Modern Physics BJul 26, 201223 citations

Luttinger liquid physics from the infinite-system density matrix renormalization group

Christoph Karrasch, Joel E. Moore

We study one-dimensional spinless fermions at zero and finite temperature $T$ using the density-matrix renormalization group. We consider nearest- as well as next-nearest-neighbor interactions; the latter render the system inaccessible by a Bethe ansatz treatment. Using an infinite-system algorithm we demonstrate the emergence of Luttinger liquid physics at low energies for a variety of static correlation functions as well as for thermodynamic properties. The characteristic power-law suppression of the momentum distribution $n(k)$ function at $T=0$ can be directly observed over several orders of magnitude. At finite temperature, we show that $n(k)$ obeys a scaling relation. The Luttinger liquid parameter and the renormalized Fermi velocity can be extracted from the density response function, the specific heat, or the susceptibility without the need to carry out any finite-size analysis. We illustrate that the energy scale below which Luttinger liquid power laws manifest vanishes as the half-filled system is driven into a gapped phase by large interactions.We study one-dimensional spinless fermions at zero and finite temperature $T$ using the density-matrix renormalization group. We consider nearest- as well as next-nearest-neighbor interactions; the latter render the system inaccessible by a Bethe ansatz treatment. Using an infinite-system algorithm we demonstrate the emergence of Luttinger liquid physics at low energies for a variety of static correlation functions as well as for thermodynamic properties. The characteristic power-law suppression of the momentum distribution $n(k)$ function at $T=0$ can be directly observed over several orders of magnitude. At finite temperature, we show that $n(k)$ obeys a scaling relation. The Luttinger liquid parameter and the renormalized Fermi velocity can be extracted from the density response function, the specific heat, or the susceptibility without the need to carry out any finite-size analysis. We illustrate that the energy scale below which Luttinger liquid power laws manifest vanishes as the half-filled system is driven into a gapped phase by large interactions.

arXiv:1207.0011Physical Review BOct 31, 201233 citations

Nonlinear Effects on Charge Fractionalization in Critical Chains

Flávia B. Ramos, Rodrigo G. Pereira, Sebastian Eggert +1 more

We investigate the generic transport in a one-dimensional strongly correlated fermionic chain beyond linear response. Starting from a Gaussian wave packet with positive momentum on top of the ground state, we find that the numerical time evolution splits the signal into at least three distinct fractional charges moving with different velocities. A fractional left-moving charge is expected from conventional Luttinger liquid theory, but for the prediction of the two separate right-moving packets the nonlinearity of the dispersion must also be taken into account. This out-of-equilibrium protocol therefore allows a direct measurement of nonlinear interaction parameters, which also govern threshold singularities of dynamic response functions. The nonlinear Luttinger liquid theory also predicts the correct dynamics at low energies, where it agrees with the conventional Luttinger liquid. Moreover, at high energies, the wave packet dynamics reveals signatures of composite excitations containing two-particle bound states. Our results uncover a simple strategy to probe the nonlinear regime in time-resolved experiments in quantum wires and ultracold-atom platforms.We investigate the generic transport in a one-dimensional strongly correlated fermionic chain beyond linear response. Starting from a Gaussian wave packet with positive momentum on top of the ground state, we find that the numerical time evolution splits the signal into at least three distinct fractional charges moving with different velocities. A fractional left-moving charge is expected from conventional Luttinger liquid theory, but for the prediction of the two separate right-moving packets the nonlinearity of the dispersion must also be taken into account. This out-of-equilibrium protocol therefore allows a direct measurement of nonlinear interaction parameters, which also govern threshold singularities of dynamic response functions. The nonlinear Luttinger liquid theory also predicts the correct dynamics at low energies, where it agrees with the conventional Luttinger liquid. Moreover, at high energies, the wave packet dynamics reveals signatures of composite excitations containing two-particle bound states. Our results uncover a simple strategy to probe the nonlinear regime in time-resolved experiments in quantum wires and ultracold-atom platforms.

arXiv:2406.05009Physical Review LettersAug 22, 20241 citation

G(t)\sim 1/\sqrt{t},

in sharp contrast to the exponential decay in time predicted by conventional Luttinger liquid theory.

We study one-dimensional spinless fermions at zero and finite temperature

T

using the density-matrix renormalization group. We consider nearest- as well as next-nearest-neighbor interactions; the latter render the system inaccessible by a Bethe ansatz treatment. Using an infinite-system algorithm we demonstrate the emergence of Luttinger liquid physics at low energies for a variety of static correlation functions as well as for thermodynamic properties. The characteristic power-law suppression of the momentum distribution

n(k)

function at

T=0

can be directly observed over several orders of magnitude. At finite temperature, we show that

n(k)

obeys a scaling relation. The Luttinger liquid parameter and the renormalized Fermi velocity can be extracted from the density response function, the specific heat, or the susceptibility without the need to carry out any finite-size analysis. We illustrate that the energy scale below which Luttinger liquid power laws manifest vanishes as the half-filled system is driven into a gapped phase by large interactions.