Pseudoparticle approach to 1D integrable quantum models

Abstract

Over the last three decades a large number of experimental studies on several quasi one-dimensional (1D) metals and quasi1D 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 a nd 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 {\it pseudoparticles}, related PDT {\it 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.

100 pages, 28 figures

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Cited by in corpus (14)

• One-particle spectral functions of the one-dimensional Fermionic Hubbard model with one fermion per site at zero and finite magnetic fields
• Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain
• Zigzag materials: selective interchain couplings control the coexistence of one-dimensional physics and deviations from it
• The role of q-spin singlet pairs of physical spins in the dynamical properties of the spin-1/2 Heisenberg-Ising XXZ chain
• Robust one-dimensionality at twin-grain-boundaries in MoSe${}_2$
• Effects of finite-range interactions on the one-electron spectral properties of one-dimensional metals: Application to Bi/InSb(001)
• Exact ground state and elementary excitations of a competing spin chain with twisted boundary condition
• Exact results for the entanglement in 1D Hubbard models with spatial constraints
• Effects of finite-range interactions on the one-electron spectral properties of TTF-TCNQ
• Bethe strings in the spin dynamical structure factor of the Mott-Hubbard phase in one-dimensional fermionic Hubbard model
• Elementary excitations in an integrable twisted J1-J2 spin chain in the thermodynamic limit
• Ising spin-1/2 XXZ chain's quantum problems beyond the spinon paradigm
• Exact results for the Hubbard model on bipartite lattices in spatial dimensions $d>1$: Seven theorems from the full [SU(2)$\times$SU(2)$\times$U(1)]/${\mathbb{Z}}_2^2$ symmetry
• One-particle spectral function singularities in a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction