Phenomenology of one-dimensional quantum liquids beyond the low-energy limit

Navier-Stokes Equations for Low-Temperature One-Dimensional Quantum Fluids

We consider one-dimensional interacting quantum fluids, such as the Lieb-Liniger gas. By computing the low-temperature limit of its (generalized) hydrodynamics we show how in this limit the gas is well described by a conventional viscous (Navier-Stokes) hydrodynamics for density, fluid velocity, and the local temperature, and the other generalized temperatures in the case of integrable gases. The dynamic viscosity is proportional to temperature and can be expressed in a universal form only in terms of the emergent Luttinger liquid parameter K and its density. We show that the heating factor is finite even in the zero temperature limit, which implies that viscous contribution remains relevant also at zero temperatures. Moreover, we find that in the semiclassical limit of small couplings, kinematic viscosity diverges, reconciling with previous observations of Kardar-Parisi-Zhang fluctuations in mean-field quantum fluids.

Experimental realization of one dimensional helium

As the spatial dimension is lowered, locally stabilizing interactions are reduced, leading to the emergence of strongly fluctuating phases of matter without classical analogues. Here we report on the experimental observation of a one dimensional quantum liquid of 4He using nanoengineering by confining it within a porous material preplated with a noble gas to enhance dimensional reduction. The resulting excitations of the confined 4He are qualitatively different than bulk superfluid helium, and can be analyzed in terms of a mobile impurity allowing for the characterization of the emergent quantum liquid beyond the Luttinger liquid paradigm. The low dimensional helium system offers the possibility of tuning via pressure—from weakly interacting, all the way to the super Tonks-Girardeau gas of strongly interacting hard-core particles.

Spectral Function of the Chiral One-Dimensional Fermi Liquid in the Regime of Strong Interactions

We study momentum-resolved tunneling into a system of spinless chiral one-dimensional fermions, such as electrons at the edge of an integer quantum Hall system. Interactions between particles give rise to broadening of the spectral function of the system. We develop an approach that enables one to obtain the shape of the peak in the spectral function in the regime of strong interaction. We apply our technique to the special cases of short-range and Coulomb interactions.

Anomalous Hydrodynamics in a One-Dimensional Electronic Fluid

We construct multimode viscous hydrodynamics for one-dimensional spinless electrons. Depending on the scale, the fluid has six (shortest lengths), four (intermediate, exponentially broad regime), or three (asymptotically long scales) hydrodynamic modes. Interaction between hydrodynamic modes leads to anomalous scaling of physical observables and waves propagating in the fluid. In the four-mode regime, all modes are ballistic and acquire Kardar-Parisi-Zhang (KPZ)-like broadening with asymmetric power-law tails. "Heads" and "tails" of the waves contribute equally to thermal conductivity, leading to ω^{-1/3} scaling of its real part. In the three-mode regime, the system is in the universality class of a classical viscous fluid [O. Narayan and S. Ramaswamy, Anomalous Heat Conduction in One-Dimensional Momentum-Conserving Systems, Phys. Rev. Lett. 89, 200601 (2002).PRLTAO0031-900710.1103/PhysRevLett.89.200601, H. Spohn, Nonlinear fluctuating hydrodynamics for anharmonic chains, J. Stat. Phys. 154, 1191 (2014).JSTPBS0022-471510.1007/s10955-014-0933-y]. Self-interaction of the sound modes results in a KPZ-like shape, while the interaction with the heat mode results in asymmetric tails. The heat mode is governed by Levy flight distribution, whose power-law tails give rise to ω^{-1/3} scaling of heat conductivity.

Exact Spectral Function of a Tonks-Girardeau Gas in a Lattice

The single-particle spectral function of a strongly correlated system is an essential ingredient to describe its dynamics and transport properties. We develop a method to evaluate exactly the spectral function for a gas of one-dimensional bosons with infinitely strong repulsions valid for any type of external confinement. Focusing on the case of a lattice confinement, we find that the spectral function displays three main singularity lines. One of them is due uniquely to lattice effects, while the two others correspond to the Lieb-I and Lieb-II modes occurring in a uniform fluid. Differently from the dynamical structure factor, in the spectral function the Lieb-II mode shows a divergence, thus providing a route to probe such mode in experiments with ultracold atoms.

Nonlinear Luttinger liquid plasmons in semiconducting single-walled carbon nanotubes

Interacting electrons confined in one dimension are generally described by the Luttinger liquid formalism, where the low-energy electronic dispersion is assumed to be linear and the resulting plasmonic excitations are non-interacting. Instead, a Luttinger liquid in one-dimensional materials with nonlinear electronic bands is expected to show strong plasmon-plasmon interactions, but an experimental demonstration of this behaviour has been lacking. Here, we combine infrared nano-imaging and electronic transport to investigate the behaviour of plasmonic excitations in semiconducting single-walled carbon nanotubes with carrier density controlled by electrostatic gating. We show that both the propagation velocity and the dynamic damping of plasmons can be tuned continuously, which is well captured by the nonlinear Luttinger liquid theory. These results contrast with the gate-independent plasmons observed in metallic nanotubes, as expected for a linear Luttinger liquid. Our findings provide an experimental demonstration of one-dimensional electron dynamics beyond the conventional linear Luttinger liquid paradigm and are important for understanding excited-state properties in one dimension.

Momentum-dependent power law measured in an interacting quantum wire beyond the Luttinger limit

Power laws in physics have until now always been associated with a scale invariance originating from the absence of a length scale. Recently, an emergent invariance even in the presence of a length scale has been predicted by the newly-developed nonlinear-Luttinger-liquid theory for a one-dimensional (1D) quantum fluid at finite energy and momentum, at which the particle’s wavelength provides the length scale. We present experimental evidence for this new type of power law in the spectral function of interacting electrons in a quantum wire using a transport-spectroscopy technique. The observed momentum dependence of the power law in the high-energy region matches the theoretical predictions, supporting not only the 1D theory of interacting particles beyond the linear regime but also the existence of a new type of universality that emerges at finite energy and momentum.

Power laws are usually associated with a scale invariance due to the absence of a length scale. Here, Jin et al. report experimental evidence of a new type of power law in a GaAs/AlGaAs double quantum-well heterostructure, suggesting existence of a new type of universality that emerges at finite energy and momentum.

Thermal Transport in One-Dimensional Electronic Fluids

We study thermal conductivity for one-dimensional electronic fluids. The many-body Hilbert space is partitioned into bosonic and fermionic sectors that carry the thermal current in parallel. For times shorter than the bosonic umklapp time, the momenta of Bose and Fermi components are separately conserved, giving rise to the ballistic heat propagation and imaginary heat conductivity proportional to T/iω. The real part of thermal conductivity is controlled by decay processes of fermionic and bosonic excitations, leading to several regimes in frequency dependence. At lowest frequencies or longest length scales, the thermal transport is dominated by Lévy flights of low-momentum bosons that lead to a fractional scaling, ω^{-1/3} and L^{1/3}, of heat conductivity with the frequency ω and system size L, respectively.

Universal Broadening of the Light Cone in Low-Temperature Transport

We consider the low-temperature transport properties of critical one-dimensional systems that can be described, at equilibrium, by a Luttinger liquid. We focus on the prototypical setting where two semi-infinite chains are prepared in two thermal states at small but different temperatures and suddenly joined together. At large distances x and times t, conformal field theory characterizes the energy transport in terms of a single light cone spreading at the sound velocity v. Energy density and current take different constant values inside the light cone, on its left, and on its right, resulting in a three-step form of the corresponding profiles as a function of ζ=x/t. Here, using a nonlinear Luttinger liquid description, we show that for generic observables this picture is spoiled as soon as a nonlinearity in the spectrum is present. In correspondence of the transition points x/t=±v, a novel universal region emerges at infinite times, whose width is proportional to the temperatures on the two sides. In this region, expectation values have a different temperature dependence and show smooth peaks as a function of ζ. We explicitly compute the universal function describing such peaks. In the specific case of interacting integrable models, our predictions are analytically recovered by the generalized hydrodynamic approach.

Spectrum of Elementary Excitations in Galilean-Invariant Integrable Models

The spectrum of elementary excitations in one-dimensional quantum liquids is generically linear at low momenta. It is characterized by the sound velocity that can be related to the ground-state energy. Here we study the spectrum at higher momenta in Galilean-invariant integrable models. Somewhat surprisingly, we show that the spectrum at arbitrary momentum is fully determined by the properties of the ground state. We find general exact relations for the coefficients of several terms in the expansion of the excitation energy at low momenta and arbitrary interaction and express them in terms of the Luttinger liquid parameter. We apply the obtained formulas to the Lieb-Liniger model and obtain several new results.

Nonlinear spectra of spinons and holons in short GaAs quantum wires

One-dimensional electronic fluids are peculiar conducting systems, where the fundamental role of interactions leads to exotic, emergent phenomena, such as spin-charge (spinon-holon) separation. The distinct low-energy properties of these 1D metals are successfully described within the theory of linear Luttinger liquids, but the challenging task of describing their high-energy nonlinear properties has long remained elusive. Recently, novel theoretical approaches accounting for nonlinearity have been developed, yet the rich phenomenology that they predict remains barely explored experimentally. Here, we probe the nonlinear spectral characteristics of short GaAs quantum wires by tunnelling spectroscopy, using an advanced device consisting of 6000 wires. We find evidence for the existence of an inverted (spinon) shadow band in the main region of the particle sector, one of the central predictions of the new nonlinear theories. A (holon) band with reduced effective mass is clearly visible in the particle sector at high energies.

Recently, theories have emerged that describe the nonlinear high-energy excitations of one-dimensional electronic fluids. Here, the authors report experimental evidence of their existence and behaviour in tunnelling spectra of short GaAs quantum wires.

Dynamics of a Mobile Impurity in a One-Dimensional Bose Liquid

We develop a microscopic theory of a quantum impurity propagating in a one-dimensional Bose liquid. As a result of scattering off thermally excited quasiparticles, the impurity experiences the friction. We find that, at low temperatures, the resulting force scales either as the fourth or the eighth power of temperature, depending on the system parameters. For temperatures higher than the chemical potential of the Bose liquid, the friction force is a linear function of temperature. Our approach enables us to find the friction force in the crossover region between the two limiting cases. In the integrable case, corresponding to the Yang-Gaudin model, the impurity becomes transparent for quasiparticles and thus the friction force is absent. Our results could be further generalized to study other kinetic phenomena.

One-Dimensional Liquid ^{4}He: Dynamical Properties beyond Luttinger-Liquid Theory

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.

Singularities of the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field

We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the 'pseudofermion dynamical theory' (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents ζ(τ)(k) controlling the singularities for both the longitudinal (τ = l) and transverse (τ = t) dynamical structure factors for the whole momentum range k ∈ ]0,π[, in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.

Hierarchy of modes in an interacting one-dimensional system

Studying interacting fermions in one dimension at high energy, we find a hierarchy in the spectral weights of the excitations theoretically, and we observe evidence for second-level excitations experimentally. Diagonalizing a model of fermions (without spin), we show that levels of the hierarchy are separated by powers of R^{2}/L^{2}, where R is a length scale related to interactions and L is the system length. The first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalized single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power laws at the spectral edge. We measure momentum-resolved tunneling of electrons (fermions with spin) from or to a wire formed within a GaAs heterostructure, which shows parabolic dispersion of the first-level mode and well-resolved spin-charge separation at low energy with appreciable interaction strength. We find structure resembling the second-level excitations, which dies away quite rapidly at high momentum.

Phonon-mediated Casimir interaction between mobile impurities in one-dimensional quantum liquids

Virtual phonons of a quantum liquid scatter off impurities and mediate a long-range interaction, analogous to the Casimir effect. In one dimension the effect is universal and the induced interaction decays as 1/r3, much slower than the van der Waals interaction ∼1/r6, where r is the impurity separation. The sign of the effect is characterized by the product of impurity-phonon scattering amplitudes, which take a universal form and have been seen to vanish for several integrable impurity models. Thus, if the impurity parameters can be independently tuned to lie on opposite sides of such integrable points, one can observe an attractive interaction turned into a repulsive one.

One-dimensional fermions with neither Luttinger-liquid nor Fermi-liquid behavior

It is well known that, generically, one-dimensional interacting fermions cannot be described in terms of a Fermi liquid. Instead, they present a different phenomenology, that of a Tomonaga-Luttinger liquid: the Landau quasiparticles are ill defined, and the fermion occupation number is continuous at the Fermi energy. We demonstrate that suitable fine tuning of the interaction between fermions can stabilize a peculiar state of one-dimensional matter, which is dissimilar to both Tomonaga-Luttinger and Fermi liquids. We propose to call this state a quasi-Fermi liquid. Technically speaking, such a liquid exists only when the fermion interaction is irrelevant (in the renormalization group sense). The quasi-Fermi liquid exhibits the properties of both a Tomonaga-Luttinger liquid and a Fermi liquid. Similar to a Tomonaga-Luttinger liquid, no finite-momentum quasiparticles are supported by the quasi-Fermi liquid; on the other hand, its fermion occupation number demonstrates a finite discontinuity at the Fermi energy, which is a hallmark feature of a Fermi liquid. A possible realization of the quasi-Fermi liquid with the help of cold atoms in an optical trap is discussed.

Multispinon continua at zero and finite temperature in a near-ideal Heisenberg chain

The space-and time-dependent response of many-body quantum systems is the most informative aspect of their emergent behavior. The dynamical structure factor, experimentally measurable using neutron scattering, can map this response in wave vector and energy with great detail, allowing theories to be quantitatively tested to high accuracy. Here, we present a comparison between neutron scattering measurements on the one-dimensional spin-1/2 Heisenberg antiferromagnet KCuF3, and recent state-of-the-art theoretical methods based on integrability and density matrix renormalization group simulations. The unprecedented quantitative agreement shows that precise descriptions of strongly correlated states at all distance, time, and temperature scales are now possible, and highlights the need to apply these novel techniques to other problems in low-dimensional magnetism.

Fate of 1D spin-charge separation away from Fermi points

We consider the dynamic response functions of interacting one dimensional spin-1/2 fermions at arbitrary momenta. We build a nonperturbative zero-temperature theory of the threshold singularities using mobile impurity Hamiltonians. The interaction induced low-energy spin-charge separation and power-law threshold singularities survive away from Fermi points. We express the threshold exponents in terms of the spinon spectrum.

Universal relations for nonsolvable statistical models

We present the first rigorous derivation of a number of universal relations for a class of models with continuously varying indices (among which are interacting planar Ising models, quantum spin chains and 1D Fermi systems), for which an exact solution is not known, except in a few special cases. Most of these formulas were conjectured by Luther and Peschel, Kadanoff, and Haldane, but only checked in the special solvable models; one of them, related to the anisotropic Ashkin-Teller model, is novel.

Exact solution for 1D spin-polarized fermions with resonant interactions

Using the asymptotic Bethe ansatz, we obtain an exact solution of the many-body problem for 1D spin-polarized fermions with resonant p-wave interactions, taking into account the effects of both scattering volume and effective range. Under typical experimental conditions, accounting for the effective range, the properties of the system are significantly modified due to the existence of "shape" resonances. The excitation spectrum of the considered model has unexpected features, such as the inverted position of the particle- and holelike branches at small momenta, and rotonlike minima. We find that the frequency of the "breathing" mode in the harmonic trap provides an unambiguous signature of the effective range.