One-electron singular spectral features of the 1D Hubbard model at finite magnetic field

Carmelo, J. M. P.; Čadež, Tilen

doi:10.1016/j.nuclphysb.2016.11.009

Cited by 12 publications

(113 citation statements)

References 86 publications

Supporting

Mentioning

111

Contrasting

Order By: Relevance

“…Another type of spectral-function singularity is located on the c − s boundary lines shown in Fig 1. The spectralfunction expressions near them are forδ c = 0 provided by the PDT 30 . They involve an exponent −1/2 that remains invariant under the ξ c →ξ c transformation.…”

Section: B the One-electron Spectral Function Near The C − S Boundarmentioning

confidence: 99%

“…It is uniquely defined in Ref. 30 in terms of the 4 L × 4 L matrix elements between all theδ c = 0 bare model energy eigenstates. An important property is that rotated-electron single and double occupancy are good quantum numbers for the whole u > 0 range.…”

Section: The General Rotated-electron Representationmentioning

confidence: 99%

“…The rotated-electron operators, Eq. (B1), naturally factorize as follows upon acting onto the full Hilbert space 30…”

Section: General Fractionalized Particles Representation From Rotatedmentioning

confidence: 99%

“…Here ε c (q) and ε s (q ) are defined in Ref. 6 and f † q ,s and f q ,s are s particle creation and annihilation operators 17,30 . For u → 0 and u → ∞, δε c (q) reads,…”

Section: Appendix A: Useful Mqim-ho Quantitiesmentioning

confidence: 99%

See 3 more Smart Citations

Effects of finite-range interactions on the one-electron spectral properties of TTF-TCNQ

et al. 2019

View full text Add to dashboard Cite

The electronic dispersions of the quasi-one-dimensional organic conductor TTF-TCNQ are studied by angle-resolved photoelectron spectroscopy (ARPES) with higher angular resolution and accordingly smaller step width than in previous studies. Our experimental results suggest that a refinement of the single-band 1D Hubbard model that includes finite-range interactions is needed to explain these photoemission data. To account for the effects of these finite-range interactions we employ a mobile quantum impurity scheme that describes the scattering of fractionalized particles at energies above the standard Tomonaga-Luttinger liquid limit. Our theoretical predictions agree quantitatively with the location in the (k, ω) plane of the experimentally observed ARPES structures at these higher energies. The non-perturbative microscopic mechanisms that control the spectral properties are found to simplify in terms of the exotic scattering of the charge fractionalized particles. We find that the scattering occurs in the unitary limit of (minus) infinite scattering length, which limit occurs within neutron-neutron interactions in shells of neutron stars and in the scattering of ultra-cold atoms but not in perturbative electronic condensed-matter systems. Our results provide important physical information on the exotic processes involved in the finite-range electron interactions that control the high-energy spectral properties of TTF-TCNQ. Our results also apply to a wider class of 1D and quasi-1D materials and systems that are of theoretical and potential technological interest.

show abstract

Section: B the One-electron Spectral Function Near The C − S Boundarmentioning

confidence: 99%

Section: The General Rotated-electron Representationmentioning

confidence: 99%

“…The rotated-electron operators, Eq. (B1), naturally factorize as follows upon acting onto the full Hilbert space 30…”

Section: General Fractionalized Particles Representation From Rotatedmentioning

confidence: 99%

“…Here ε c (q) and ε s (q ) are defined in Ref. 6 and f † q ,s and f q ,s are s particle creation and annihilation operators 17,30 . For u → 0 and u → ∞, δε c (q) reads,…”

Section: Appendix A: Useful Mqim-ho Quantitiesmentioning

confidence: 99%

See 2 more Smart Citations

Effects of finite-range interactions on the one-electron spectral properties of TTF-TCNQ

et al. 2019

View full text Add to dashboard Cite

show abstract

“…The spectrum of general form, Eq. (44), that defines the (k, ω)-plane shape of the up-spin and down-spin one-fermion removal and addition c + branch line reads,…”

Section: Specific One-fermion Removal and Addition Spectral Singumentioning

confidence: 99%

One-particle spectral function singularities in a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction

2019

Self Cite

View full text Add to dashboard Cite

The momentum, fermionic density, spin density, and interaction dependencies of the exponents that control the (k, ω)-plane singular features of the one-fermion spectral functions of a onedimensional gas of spin-1/2 fermions with repulsive delta-function interaction both at zero and finite magnetic field are studied in detail. Our results refer to energy scales beyond the reach of the low-energy Tomonaga-Luttinger liquid and rely on the pseudofermion dynamical theory for integrable models. The one-fermion spectral weight distributions associated with the spectral functions studied in this paper may be observed in systems of spin-1/2 ultra-cold fermionic atoms in optical lattices.PACS numbers: I. INTRODUCTIONThe one-dimensional (1D) continuous fermionic gas with repulsive delta-function interaction, which in this paper we call 1D repulsive fermion model, was one of the first quantum problems solved by the Bethe ansatz (BA) [1]. This was achieved by Yang [2] and by Gaudin [3]. Yang's solution of the 1D repulsive fermion model was actually the precursor of the BA solution of the lattice 1D Hubbard model by . That the latter is the simplest condensed-matter toy model for the description of the role of correlations in the exotic properties of 1D and quasi-1D lattice condensed matter systems [8,9] justifies why for several decades it had attracted more attention than its continuous cousin, the fermionic gas with repulsive delta-function interaction. This refers both to its metallic and Mott-Hubbard insulator phases [10], the latter not existing in the case of the continuous 1D repulsive fermion model.However, in the last years the interest in that Yang-Baxter integrable model has been renewed by its new found impact on experiments in both condensed matter physics and ultra-cold atomic gases [11]. The latter have provided new opportunities for studying 1D systems of spin-1/2 fermions with repulsive interaction [12,13]. The present model can indeed be implemented with ultra-cold atoms [11][12][13][14][15][16][17]. Ultra-cold Fermi gases trapped inside a tight atomic waveguide offer for instance the opportunity to measure the spin-drag relaxation rate that controls the broadening of a spin packet. It has been found that while the propagation of long-wavelength charge excitations is essentially ballistic, spin propagation is intrinsically damped and diffusive [18,19]. A related interesting problem is the force applied to a spin-flipped fermion in a gas, which may lead to Bloch oscillations of the fermion's position and velocity. The existence of such oscillations has been found crucially to depend on the viscous friction force exerted by the rest of the gas on the spin excitation [20].The ground-state energy of the relative motion of a system of two fermions with spin up and spin down interacting via a delta-function potential in a 1D harmonic trap has been calculated by combining the BA with the variational principle [21]. Recently, related ground-state properties of a 1D repulsive Fermi gas subjected to a commensurate per...

show abstract

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

2018

Self Cite

View full text Add to dashboard Cite

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...

show abstract

One-electron singular spectral features of the 1D Hubbard model at finite magnetic field

Cited by 12 publications

References 86 publications

Effects of finite-range interactions on the one-electron spectral properties of TTF-TCNQ

Effects of finite-range interactions on the one-electron spectral properties of TTF-TCNQ

One-particle spectral function singularities in a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction

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

Contact Info

Product

Resources

About