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

The Finite Basis Problem for Kiselman Monoids

In an earlier paper, the second-named author has described the identities holding in the so-called Catalan monoids. Here we extend this description to a certain family of Hecke--Kiselman monoids including the Kiselman monoids $\mathcal{K}_n$. As a consequence, we conclude that the identities of $\mathcal{K}_n$ are nonfinitely based for every $n\ge 4$ and exhibit a finite identity basis for the identities of each of the monoids $\mathcal{K}_2$ and $\mathcal{K}_3$. In the third version a question left open in the initial submission has beed answered.Comment: 16 pages, 1 table, 1 figur

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

Calculated NMR T_2 relaxation due to vortex vibrations in cuprate superconductors

We calculate the rate of transverse relaxation arising from vortex motion in the mixed state of YBa_2Cu_3O_7 with the static field applied along the c axis. The vortex dynamics are described by an overdamped Langevin equation with a harmonic elastic free energy. We find that the variation of the relaxation with temperature, average magnetic field, and local field is consistent with experiments; however, the calculated time dependence is different from what has been measured and the value of the rates calculated is roughly two orders of magnitude slower than what is observed. Combined with the strong experimental evidence pointing to vortex motion as the dominant mechanism for T_2 relaxation, these results call into question a prior conclusion that vortex motion is not significant in T_1 measurements in the vortex state.Comment: 6 pages, 5 figures, to be published in Phys. Rev.