Spin-charge separation: From one hole to finite doping

In the presence of nonlocal phase shift effects, a quasiparticle can remain topologically stable even in a spin-charge separation state due to the confinement effect introduced by the phase shifts at finite doping. True deconfinement only happens in the zero-doping limit where a bare hole can lose its integrity and decay into holon and spinon elementary excitations. The Fermi surface structure is completely different in these two cases, from a large band-structure-like one to four Fermi points in one-hole case, and we argue that the so-called underdoped regime actually corresponds to a situation in between.Comment: 4 pages, 2 figures, presented in M2S-HTSC-VI conference (2000

Phase String Effect in the t-J Model: General Theory

We reexamine the problem of a hole moving in an antiferromagnetic spin background and find that the injected hole will always pick up a sequence of nontrivial phases from the spin degrees of freedom. Previously unnoticed, such a string-like phase originates from the hidden Marshall signs which are scrambled by the hopping of the hole. We can rigorously show that this phase string is non-repairable at low energy and give a general proof that the spectral weight Z must vanish at the ground-state energy due to the phase string effect. Thus, the quasiparticle description fails here and the quantum interference effect of the phase string dramatically affects the long-distance behavior of the injected hole. We introduce a so-called phase-string formulation of the t-J model for a general number of holes in which the phase string effect can be explicitly tracked. As an example, by applying this new mathematical formulation in one dimension, we reproduce the well-known Luttinger-liquid behaviors of the asymptotic single-electron Green's function and the spin-spin correlation function. We can also use the present phase string theory to justify previously developed spin-charge separation theory in two dimensions, which offers a systematic explanation for the transport and magnetic anomalies in the high-T_c cuprates.Comment: Revtex, 36 pages, no figure, to appear in Phys. Rev. B

Representations of hom-Lie algebras

In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations, deformations, central extensions and derivation extensions of hom-Lie algebras are also studied as an application.Comment: 16 pages, multiplicative and regular hom-Lie algebras are used, Algebra and Representation Theory, 15 (6) (2012), 1081-109