Conservation laws in the one-dimensional Hubbard model

Carmelo, J. M. P.; Prosen, Tomaž; Campbell, D. K.

doi:10.1103/physrevb.63.205114

Cited by 9 publications

(16 citation statements)

References 22 publications

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“…That for 1D all such operators commute both with the Hamiltonian and momentum operator is behind the integrability of the 1D Hubbard model in that limit. Indeed, such an infinite set of translation generators is equivalent to the infinite set of conservation laws, which are known to be behind that model integrability 16,46 . Such laws are also equivalent to the conservation of the set of αν fermion numbers {N αν } where α = η, s, ν = 1, ..., C α and the maximum C α magnitude is N D a /2 and thus N a /2 for 1D 46 .…”

Section: Composite αν Fermions αν Bond Particles and Corresponding αν...mentioning

confidence: 99%

“…Indeed, such an infinite set of translation generators is equivalent to the infinite set of conservation laws, which are known to be behind that model integrability 16,46 . Such laws are also equivalent to the conservation of the set of αν fermion numbers {N αν } where α = η, s, ν = 1, ..., C α and the maximum C α magnitude is N D a /2 and thus N a /2 for 1D 46 . In turn, the Hubbard model on the square lattice is not integrable and consistently the set of αν translation generators ˆ q αν of Eq.…”

Section: Composite αν Fermions αν Bond Particles and Corresponding αν...mentioning

confidence: 99%

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A description of the Hubbard model on a square lattice consistent with its global $SO(3)\times SO(3)\times U(1)$ symmetry

Carmelo,

Sampaio

2008

Preprint

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In this paper a description of the Hubbard model on the square lattice with nearest-neighbor transfer integral t, on-site repulsion U , and N 2 a ≫ 1 sites consistent with its exact global SO(3) × SO(3) × U (1) symmetry is constructed. Our studies profit from the interplay of that recently found global symmetry of the model on any bipartite lattice with the transformation laws under a suitable electron -rotated-electron unitary transformation of a well-defined set of operators and quantum objects. For U/4t > 0 the occupancy configurations of these objects generate the energy eigenstates that span the one-and two-electron subspace. Such a subspace as defined in this paper contains nearly the whole spectral weight of the excitations generated by application onto the zero-spindensity ground state of one-and two-electron operators. Our description involves three basic objects: charge c fermions, spin-1/2 spinons, and η-spin-1/2 η-spinons. Independent spinons and independent η-spinons are invariant under the above unitary transformation. Alike in chromodynamics the quarks have color but all quark-composite physical particles are color-neutral, the η-spinon (and spinons) that are not invariant under that transformation have η spin 1/2 (and spin 1/2) but are part of η-spinneutral (and spin-neutral) 2ν-η-spinon (and 2ν-spinon) composite ην fermions (and sν fermions) where ν = 1, 2, ... is the number of η-spinon (and spinon) pairs. The occupancy configurations of the c fermions, independent spinons and 2ν-spinon composite sν fermions, and independent η-spinons and 2ν-η-spinon composite ην fermions correspond to the state representations of the U (1), spin SU (2), and η-spin SU (2) symmetries, respectively, associated with the model2 global symmetry. The components of the αν fermion discrete momentum values qj = [qj x1 , qj x2 ] are eigenvalues of the corresponding set of αν translation generators in the presence of fictitious magnetic fields Bαν. Our operator description has been constructed to inherently the αν translation generators ˆ q αν in the presence of the fictitious magnetic field Bαν commuting with the momentum operator, consistently with their component operators qαν x 1 and qαν x 1 commuting with each other. In turn, unlike for the 1D model such generators not commute in general with the Hamiltonian, except for the Hubbard model on the square lattice in the oneand two-electron subspace. Concerning one-and two-electron excitations, the picture that emerges is that of a two-component quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions. The description introduced here is consistent with a Mott-Hubbard insulating ground state with antiferromagnetic long-range order for half filling at x = 0 hole concentration and a ground state with short-range spin order for a well-defined range of finite hole concentrations x > 0. For 0 < x ≪ 1 the latter short-range spin order has an incomensurate-spiral character. Our results are of interest for studies of ultra-cold fermionic atoms on optical lattices ...

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Section: Composite αν Fermions αν Bond Particles and Corresponding αν...mentioning

confidence: 99%

Section: Composite αν Fermions αν Bond Particles and Corresponding αν...mentioning

confidence: 99%

A description of the Hubbard model on a square lattice consistent with its global $SO(3)\times SO(3)\times U(1)$ symmetry

Carmelo,

Sampaio

2008

Preprint

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“…64 , our method relies in part on the integrability of the 1D Hubbard model, whereas the phenomenology developed in that reference does not require any special property of the underlying microscopic interaction. The solvability of the 1D Hubbard model is in the N a ≫ 1 limit the c and s1 fermion theory refers to associated with the occurrence of an infinite set of conservation laws 36,42 . As discussed in Ref.…”

Section: Charge and Spin Excitationsmentioning

confidence: 99%

“…According to the results of Ref. 42 such laws are equivalent to the independent conservation of the set of numbers {N αν } of αν fermions, which for that model are good quantum numbers.…”

Section: Introductionmentioning

confidence: 99%

The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

Carmelo

2010

Nuclear Physics B

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The momentum bands, energy dispersions, and velocities of the charge c fermions and spin-neutral two-spinon s1 fermions of a square-lattice quantum liquid referring to the Hubbard model on such a lattice of edge length L in the one-and two-electron subspace are studied. The model involves the effective nearest-neighbor integral t and on-site repulsion U and can be experimentally realized in systems of correlated ultra-cold fermionic atoms on an optical lattice and thus our results are of interest for such systems. Our investigations profit from a general rotated-electron description, which is consistent with the model global SO(3)×SO(3)×U (1) symmetry. For the model in the oneand two-electron subspace the discrete momentum values of the c and s1 fermions are good quantum numbers so that in contrast to the original strongly-correlated electronic problem their interactions are residual. The use of our description renders an involved many-electron problem into a quantum liquid with some similarities with a Fermi liquid. For the Hubbard model on a square lattice in the one-and two-electron subspace a composite s1 fermion consists of a spin-singlet spinon pair plus an infinitely thin flux tube attached to it. In the U/4t → ∞ limit of infinite on-site interaction the c fermions become non-interacting spinless fermions and the s1 fermion occupancy configurations that generate the spin degrees of freedom of spin-density m = 0 ground states become within a suitable mean-field approximation for the fictitious magnetic field Bs1 ex 3 brought about by the correlations of the original N electron problem those of a full lowest Landau level with N/2 degenerate one-s1 fermion states of the two-dimensional quantum Hall effect. In turn, for U/4t finite the degeneracy of the N/2 one-s1-fermion states is removed by the emergence of a finite-energy-bandwidth s1 fermion dispersion yet the number of s1 band discrete momentum values remains being given by Bs1 L 2 /Φ0 and the s1 effective lattice spacing by as1 = ls1/ √ 2π where ls1 is the fictitious-magnetic-field length and in our units the fictitious-magnetic-field flux quantum reads Φ0 = 1. Elsewhere it is found that the use of the square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions investigated here contributes to the further understanding of the role of electronic correlations in the unusual properties of the hole-doped cuprate superconductors. This indicates that quantum-Hall-type behavior with or without magnetic field may be ubiquitous in nature.

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“…This is a property specific to the pseudofermions of integrable 1D models. It results from the occurrence of an infinite number of conservation laws [250,251,274], which is associated with their integrability. The Hubbard model on the square lattice is not integrable.…”

Section: General Outlook and Future Developmentsmentioning

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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Conservation laws in the one-dimensional Hubbard model

Cited by 9 publications

References 22 publications

A description of the Hubbard model on a square lattice consistent with its global $SO(3)\times SO(3)\times U(1)$ symmetry

A description of the Hubbard model on a square lattice consistent with its global $SO(3)\times SO(3)\times U(1)$ symmetry

The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

Pseudoparticle approach to 1D integrable quantum models

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