Microscopic origin of ideal conductivity in integrable quantum models

Non-ergodic dynamical systems display anomalous transport properties. A prominent example are integrable quantum systems, whose exceptional property are diverging DC conductivities. In this Letter, we explain the microscopic origin of ideal conductivity by resorting to the thermodynamic particle content of a system. Using group-theoretic arguments we rigorously resolve the long-standing controversy regarding the nature of spin and charge Drude weights in the absence of chemical potentials. In addition, by employing a hydrodynamic description, we devise an efficient computational method to calculate exact Drude weights from the stationary currents generated in an inhomogeneous quench from bi-partitioned initial states. We exemplify the method on the anisotropic Heisenberg model at finite temperatures for the entire range of anisotropies, accessing regimes which are out of reach with other approaches. Quite remarkably, spin Drude weight and asymptotic spin current rates reveal a completely discontinuous (fractal) dependence on the anisotropy parameter.Comment: 4 pages + Supplemental Materia

Particle-hole pairs and density-density correlations in the Lieb-Liniger model

We review the recently introduced thermodynamic form factors for pairs of particle-hole excitations on finite-entropy states in the Lieb-Liniger model. We focus on the density operator and we show how the form factors can be used for analytic computations of dynamical correlation functions. We derive a new representation for the form factors and we discuss some aspects of their structure. We rigorously show that in the small momentum limit (or equivalently, on hydrodynamic scales) a single particle-hole excitation fully saturates the spectral sum and we also discuss the contribution from two particle-hole pairs. Finally we show that thermodynamic form factors can be also used to study the ground state correlations and to derive the edge exponents.Comment: 46 pages, 2 figures, final version (corrected a typo in formula 115

Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach

We outline a general formalism of hydrodynamics for quantum systems with multiple particle species which undergo completely elastic scattering. In the thermodynamic limit, the complete kinematic data of the problem consists of the particle content, the dispersion relations, and a universal dressing transformation which accounts for interparticle interactions. We consider quantum integrable models and we focus on the one-dimensional fermionic Hubbard model. By linearizing hydrodynamic equations, we provide exact closed-form expressions for Drude weights, generalized static charge susceptibilities and charge-current correlators valid on hydrodynamic scale, represented as integral kernels operating diagonally in the space of mode numbers of thermodynamic excitations. We find that, on hydrodynamic scales, Drude weights manifestly display Onsager reciprocal relations even for generic (i.e. non-canonical) equilibrium states, and establish a generalized detailed balance condition for a general quantum integrable model. We present the first exact analytic expressions for the general Drude weights in the Hubbard model, and explain how to reconcile different approaches for computing Drude weights from the previous literature.Comment: 4 pages + supplemental materia

Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons

We apply the logic of the quench action to give an exact analytical expression for the time evolution of the one-body density matrix after an interaction quench in the Lieb-Liniger model from the ground state of the free theory (BEC state) to the infinitely repulsive regime. In this limit there exists a mapping between the bosonic wavefuntions and the free fermionic ones but this does not help the computation of the one-body density matrix which is sensitive to particle statistics. The final expression, given in terms of the difference of the square root of two Fredholm determinants, can be numerically evaluated and is valid in the thermodynamic limit and for all times after the quench.Comment: 24 pages, 2 figur

Hydrodynamic gauge fixing and higher order hydrodynamic expansion

Hydrodynamics is a powerful emergent theory for the large-scale behaviours in many-body systems, quantum or classical. It is a gradient series expansion, where different orders of spatial derivatives provide an effective description on different length scales. We here report the first general derivation of third-order, or "dispersive", terms in the hydrodynamic expansion. We obtain fully general Kubo-like expressions for the associated hydrodynamic coefficients, and we determine their expressions in quantum integrable models, introducing in this way purely quantum higher-order terms into generalised hydrodynamics. We emphasise the importance of hydrodynamic gauge fixing at diffusive order, where we claim that it is parity-time-reversal, and not time-reversal, invariance that is at the source of Einstein's relation, Onsager's reciprocal relations, the Kubo formula and entropy production. At higher hydrodynamic orders we introduce a more general, n-th order "symmetric" gauge, which we show implies the validity of the higher-order hydrodynamic description

Density form factors of the 1D Bose gas for finite entropy states

We consider the Lieb-Liniger model for a gas of bosonic $\delta-$interacting particles. Using Algebraic Bethe Ansatz results we compute the thermodynamic limit of the form factors of the density operator between finite entropy eigenstates such as finite temperature states or generic non-equilibrium highly excited states. These form factors are crucial building blocks to obtain the thermodynamic exact dynamic correlation functions of such physically relevant states. As a proof of principle we compute an approximated dynamic structure factor by including only the simplest types of particle-hole excitations and show the agreement with known results.Comment: Corrected a typo in the final formula 3.41, figures 2 and 3 updated accordingl

Super-diffusion in one-dimensional quantum lattice models

We identify a class of one-dimensional spin and fermionic lattice models which display diverging spin and charge diffusion constants, including several paradigmatic models of exactly solvable strongly correlated many-body dynamics such as the isotropic Heisenberg spin chains, the Fermi-Hubbard model, and the t-J model at the integrable point. Using the hydrodynamic transport theory, we derive an analytic lower bound on the spin and charge diffusion constants by calculating the curvature of the corresponding Drude weights at half filling, and demonstrate that for certain lattice models with isotropic interactions some of the Noether charges exhibit super-diffusive transport at finite temperature and half filling.Comment: 4 pages + appendices, v2 as publishe