Correlation length of the 1D Hubbard model at half-filling: Equal-time one-particle Green's function

Umeno, Yukiko; Shiroishi, Masahiro; Klümper, Andreas

doi:10.1209/epl/i2003-00408-4

Cited by 9 publications

(11 citation statements)

References 51 publications

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“…A consequence of such properties is that the following inequality involving the average values of the square of the charge current in Eqs. (96) and (102) holds,…”

Section: Stiffness Upper Bounds Within the Grand-canonical Ensembmentioning

confidence: 99%

“…[91,92] allowed the quantum transfer matrix approach to the thermodynamics of the 1D Hubbard model [94]. Within it, the thermodynamic quantities and correlation lengths can be calculated numerically for finite temperatures [95,96]. The 1D Hubbard model Hamiltonian was found in the TL to be invariant under the direct sum of two Y (sl(2)) Yangians [97].…”

Section: Introductionmentioning

confidence: 99%

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

2018

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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...

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“…A consequence of such properties is that the following inequality involving the average values of the square of the charge current in Eqs. (96) and (102) holds,…”

Section: Stiffness Upper Bounds Within the Grand-canonical Ensembmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2018

View full text Add to dashboard Cite

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“…[127,128] allowed the quantum transfer matrix approach to the thermodynamics of the 1D Hubbard model [246]. Within it, the thermodynamic quantities and correlation lengths can be calculated numerically for finite temperatures [247,248]. The 1D Hubbard model Hamiltonian was found in the TL to be invariant under the direct sum of two Y (sl(2)) Yangians [249].…”

Section: The 1d Hubbard Model: a Short Summary Of Its Developmentmentioning

confidence: 99%

Pseudoparticle approach to 1D integrable quantum models

Carmelo

Sacramento

2018

Physics Reports

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Over the last three decades a large number of experimental studies on several quasi onedimensional (1D) metals and quasi 1D Mott-Hubbard insulators have produced evidence for distinct spectral features identified with charge-only and spin-only fractionalized particles. They can be also observed in ultra-cold atomic 1D optical lattices and quantum wires. 1D exactly solvable models provide nontrivial tests of the approaches for these systems relying on field theories. Different schemes such as the pseudofermion dynamical theory (PDT) and the mobile quantum impurity model (MQIM) have revealed that the 1D correlated models high-energy physics is qualitatively different from that of a lowenergy Tomonaga-Luttinger liquid (TLL). This includes the momentum dependence of the exponents that control the one-and two-particle dynamical correlation functions near their spectra edges and in the vicinity of one-particle singular spectral features.On the one hand, the low-energy charge-only and spin-only fractionalized particles are usually identified with holons and spinons, respectively. On the other hand, ''particlelike'' representations in terms of pseudoparticles, related PDT pseudofermions, and MQIM particles are suitable for the description of both the low-energy TLL physics and highenergy spectral and dynamical properties of 1D correlated systems.The main goal of this review is to revisit the usefulness of pseudoparticle and PDT pseudofermion representations for the study of both static and high-energy spectral and dynamical properties of the 1D Lieb-Liniger Bose gas, spin-1/2 isotropic Heisenberg chain, and 1D Hubbard model. Moreover, the relation between the PDT and the MQIM is clarified. The fractionalized particles and related composite pseudoparticles/pseudofermions emerging within such non-perturbative 1D correlated systems are qualitatively different from the Fermi-liquid quasiparticles. In contrast to the holons and spinons, the relation to the electron creation and annihilation operators of the operators associated with the 1D Hubbard model three fractionalized particles is uniquely defined. The occupancy configurations of such fractionalized particles generate all energy and momentum eigenstates of that model. Both the static and dynamical properties of the three models under review are shown to be controlled at all energy scales by pseudofermion phase shifts associated with only zero-momentum forward scattering. The corresponding microscopic processes are much simpler than those of the underlying particles non-perturbative interactions.

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“…point and in its vicinity a critical correlation may be characterized by a diverging length. 23 In this case, the correlation at finite temperature 24 would be cut off at some finite temperature-dependent thermal coherence length.…”

Section: Electron-electron Interactionmentioning

confidence: 99%

Theory of local electronic properties and finite-size effects in nanoscale open chains

Souza

Herrmann

2008

Phys. Rev. B

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The local electronic structure of nanoscale chains is investigated theoretically. We propose a mechanism to explain the even-odd oscillation observed in the length distribution of atom chains. We study the spatial peak structure as obtained by scanning-tunneling-microscopy constant-current topography as a function of the electron-electron interaction, band filling, and temperature. The site-dependent magnetic moment is also examined.

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Correlation length of the 1D Hubbard model at half-filling: Equal-time one-particle Green's function

Cited by 9 publications

References 51 publications

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

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

Pseudoparticle approach to 1D integrable quantum models

Theory of local electronic properties and finite-size effects in nanoscale open chains

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