Absence of ballistic charge transport in the half-filled 1D Hubbard model

Abstract

Whether in the thermodynamic limit of lattice length L → ∞, hole concentration m z η = −2S z η /L = 1 − ne → 0, nonzero temperature T > 0, and U/t > 0 the charge stiffness of the 1D Hubbard model with first neighbor transfer integral t and on-site repulsion U is finite or vanishes and thus whether there is or there is no ballistic charge transport, respectively, remains an unsolved and controversial issue, as different approaches yield contradictory results. (Here S z η = −(L − Ne)/2 is the η-spin projection and ne = Ne/L the electronic density.) In this paper we provide an upper bound on the charge stiffness and show that (similarly as at zero temperature), for T > 0 and U/t > 0 it vanishes for m z η → 0 within the canonical ensemble in the thermodynamic limit L → ∞. Moreover, we show that at high temperature T → ∞ the charge stiffness vanishes as well within the grandcanonical ensemble for L → ∞ and chemical potential µ → µu where (µ − µu) ≥ 0 and 2µu is the Mott-Hubbard gap. The lack of charge ballistic transport indicates that charge transport at finite temperatures is dominated by a diffusive contribution. Our scheme uses a suitable exact representation of the electrons in terms of rotated electrons for which the numbers of singly occupied and doubly occupied lattice sites are good quantum numbers for U/t > 0. In contrast to often less controllable numerical studies, the use of such a representation reveals the carriers that couple to the charge probes and provides useful physical information on the microscopic processes behind the exotic charge transport properties of the 1D electronic correlated system under study. PACS numbers:agree with some preliminary conjectures by Zotos and Prelovšek according to which lim u→∞ D(T ) should be zero for the 1D Hubbard model at m z η = 0 and T > 0. Recently, a general formalism of hydrodynamics for the 1D Hubbard model and other integrable models was introduced in Refs. [17,18]. By linearizing hydrodynamic equations, the closed-form expressions for the stiffnesses that were conjectured to be valid on the hydrodynamic scale have been accessed. The stiffness is then calculated from the stationary currents generated in an inhomogeneous quench from bipartitioned initial states [17]. Within such an hydrodynamic ansatz for the stiffnesses, the studies of Refs. [17,18] clearly established vanishing at finite temperature of charge or spin Drude weights when the corresponding chemical potentials vanish, irrespective of the interaction strength. In our work we, however, take a different perspective. We start from the standard linear-response expressions for the charge and spin Drude weights and reach conclusions that are consistent with the results of Ref. [18]. Although there is no reasonable doubt that the hydrodynamics ansatz used in Refs. [17,18] is correct, it has, nevertheless, not yet been rigorously justified. Hence we believe that adding our independent and complementary result is a valuable contribution to the solution of this important problem. Actually, both methods r...

Spin crossovers and superdiffusion in the one-dimensional Hubbard model

“…We thus give a comprehensive picture of temperature-dependent transport and response in the one-dimensional Hubbard model. The present discussion thus complements existing studies that have addressed transport in the one-dimensional Hubbard model using rigorous bounds on transport coefficients, [100][101][102][103][104] and via numerical simulations [100,[105][106][107][108][109][110][111][112][113]. It also substantially extends previous GHD results [55,81] by studying superdiffusion, crossovers in spin dynamics, and the associated experimental signatures.…”

Finite-temperature transport in one-dimensional quantum lattice models

“…Nevertheless, some rigorous results have been obtained at half filling. It has been shown in (Carmelo et al, 2018) that for any U > 0 and any positive temperature T > 0 and within the canonical ensemble where N = N ↑ + N ↓ − L is held fixed (while L → ∞), one has a strict upper bound on the charge Drude weight…”

“…Several early studies reported evidence for a finite Drude weight (Fujimoto and Kawakami, 1998;Kirchner et al, 1999). This result was later challenged by Bethe-ansatz studies that emphasized symmetry constraints on the diagonal matrix elements of the charge-current operator (Carmelo et al, 2013(Carmelo et al, , 2018. Numerically, charge transport was studied using exact diagonalization and MCLM (Prelovšek et al, 2004), finite-T tDMRG (Karrasch et al, 2016(Karrasch et al, , 2014a, dynamical typicality (Jin et al, 2015) and tDMRG simulations of open quantum systems (Prosen andŽnidarič, 2012).…”

Pseudoparticle approach to 1D integrable quantum models

“…[263] remains solvable by the BA. Its coupling to the charge/η-spin and spin degrees of freedom the flux Φ reads Φ = Φ ↑ = Φ ↓ and Φ = Φ ↑ = −Φ ↓ , respectively [263,264]. The LWSs momentum eigenvalues, P(Φ ↑ , Φ ↓ ), have the general form [264],…”