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Physical review. B, Condensed matter

Electron destruction in a fractionized system

T. McMullen

Published Oct 1, 1990• 0 citations
Publisher

Abstract

Several experimental techniques, such as photoemission, Compton scattering, and positron annihilation, use the excitation or destruction of an electron to measure the momentum distribution of the electrons. The structure in these momentum distributions that results from the Fermi surface of a Fermi liquid is well known, but structure can also arise from the electron correlations in a strongly correlated system. The momentum distribution of a highly correlated two-dimensional electron system in which the spin and charge degrees of freedom are decoupled is examined using, as a model system, a noninteracting spinon-holon description of the excitations of the two-dimensional Hubbard model.

DOI
10.1103/physrevb.42.6791

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Several experimental techniques, such as photoemission, Compton scattering, and positron annihilation, use the excitation or destruction of an electron to measure the momentum distribution of the electrons. The structure in these momentum distributions that results from the Fermi surface of a Fermi liquid is well known, but structure can also arise from the electron correlations in a strongly correlated system. The momentum distribution of a highly correlated two-dimensional electron system in which the spin and charge degrees of freedom are decoupled is examined using, as a model system, a noninteracting spinon-holon description of the excitations of the two-dimensional Hubbard model.
Elementary particles carry several quantum numbers, such as charge and spin. However, in an ensemble of strongly interacting particles, the emerging degrees of freedom can fundamentally differ from those of the individual constituents. For example, one-dimensional systems are described by independent quasiparticles carrying either spin (spinon) or charge (holon). Here, we report on the dynamical deconfinement of spin and charge excitations in real space after the removal of a particle in Fermi-Hubbard chains of ultracold atoms. Using space- and time-resolved quantum gas microscopy, we tracked the evolution of the excitations through their signatures in spin and charge correlations. By evaluating multipoint correlators, we quantified the spatial separation of the excitations in the context of fractionalization into single spinons and holons at finite temperatures.
The momentum distribution function n(k) and spin-correlation function S(k) are determined for the one-dimensional large-U Hubbard model with various electron densities. The present work is featured with an application of the Bethe-ansatz wave function, which has a simple form in the large-U limit for any electron density. Namely, its charge degrees of freedom are expressed as a Slater determinant of spinless fermions, while its spin degrees of freedom are equivalent to the one-dimensional S=(1/2 Heisenberg model. The singularity of n(k) at k=kF{k}_{F}kF​ is analyzed from the system size dependence. In addition to the kF{k}_{F}kF​ singularity, n(k) has a weak singularity at k=3kF{k}_{F}kF​; however, no detectable singularity is present at 2kF{k}_{F}kF​, which one might expect from the spinless fermion wave function. The singularity of S(k) at 2kF{k}_{F}kF​ is also examined in detail. It is concluded from the size dependence that, when the system is away from half-filling, the nature of the singularity at 2kF{k}_{F}kF​ is different from that in the Heisenberg model. The results are compared with the behavior in the weak-correlation regime examined with the perturbation calculation, the prediction of g-ology, and recent Monte Carlo calculations.
Strong antiferromagnetic correlations can radically change the behavior of an otherwise paramagnetic system, inducing anomalous effects in the single particle properties and driving the behavior of spin-spin response functions. In order to investigate such physics, we have studied the momentum distribution function of the two-dimensional Hubbard model at low doping, low temperatures and high values of the on-site Coulomb repulsion. The interpretation of the results has greatly benefited from the parallel analysis of the filling, temperature and interaction dependences of the spin-spin correlation function, the antiferromagnetic correlation length and the pole of the spin-spin propagator. On reducing doping or temperature and on increasing the interaction strength, the correlations become stronger and stronger and the Fermi surface develops hole and electron pockets and shows a dual nature (small-large).
The authors consider the electronic momentum distribution in systems displaying spin-charge separation. In particular, then consider the t-J model in the large-N limit. Assuming that there is no Bose condensation of holons at low temperatures in one and two dimensions, the authors find that the momentum distribution of the electron shows no Migdal discontinuity in one and two dimensions. In three dimensions, the Migdal discontinuity prevails as a signature of a Fermi-liquid state due to the presence of a holon condensate.