Charge and spin fractionalization beyond the Luttinger-liquid paradigm

Moreno, Alexander; Muramatsu, A.; Carmelo, J. M. P.

doi:10.1103/physrevb.87.075101

Cited by 20 publications

(17 citation statements)

References 32 publications

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“…The exponents characterizing the dynamical correlation functions singularities have been found by both such schemes to be functions of momenta. They differ significantly from the predictions of the linear TLL theory [13,[51][52][53][54][55][56][57][58][59][60][61][62][63][64].…”

Section: Introductioncontrasting

confidence: 76%

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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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Section: Introductioncontrasting

confidence: 76%

“…This follows from the boundary conditions, Eqs. ( 55) and (60). In contrast to the pseudoparticles of that Bose gas, for the spin-chain all n-pseudoparticles have internal degrees of freedom.…”

Section: Outlook Of the Relation Between The Model Physical Spins-1/2 And The N Pseudoparticles/n Pseudofermions And Corresponding N-bandmentioning

confidence: 99%

Pseudoparticle approach to 1D integrable quantum models

Carmelo

Sacramento

2018

Physics Reports

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Section: Introductioncontrasting

confidence: 56%

Pseudoparticle approach to 1D integrable quantum models

Carmelo,

Sacramento

2018

Preprint

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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 low-energy 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, "particle-like" representations in terms of pseudoparticles, related PDT pseudofermions, and MQIM particles are suitable for the description of both the low-energy TLL physics and high-energy 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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“…Upon doping a hole, another fractional elementary excitation called a holon appears. Unlike spinons which carry spin 1/2 but no charge, holons carry spin 0 and charge e. The spinon and holon are decoupled and propagate at different velocities, showing the separation of spin and charge quantum numbers carried respectively by two different fractionalized quasiparticles [9][10][11][12][13] .…”

Section: A a Reference System: Spin Chainmentioning

confidence: 99%

Fractionalization, entanglement, and separation: Understanding the collective excitations in a spin-orbital chain

et al. 2015

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Using a combined analytical and numerical approach, we study the collective spin and orbital excitations in a spin-orbital chain under a crystal field. Irrespective of the crystal field strength, these excitations can be universally described by fractionalized fermions. The fractionalization phenomenon persists and contrasts strikingly with the case of a spin chain, where fractionalized spinons cannot be individually observed but confined to form magnons in a strong magnetic field. In the spin-orbital chain, each of the fractional quasiparticles carries both spin and orbital quantum numbers, and the two variables are always entangled in the collective excitations. Our result further shows that the recently reported separation phenomenon occurs when crystal fields fully polarize the orbital degrees of freedom. In this case, however, the spinon and orbiton dynamics are decoupled solely because of a redefinition of the spin and orbital quantum numbers.

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Charge and spin fractionalization beyond the Luttinger-liquid paradigm

Cited by 20 publications

References 32 publications

Pseudoparticle approach to 1D integrable quantum models

Pseudoparticle approach to 1D integrable quantum models

Pseudoparticle approach to 1D integrable quantum models

Fractionalization, entanglement, and separation: Understanding the collective excitations in a spin-orbital chain

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