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arXiv:1808.03419 · Physical review. B./Physical review. B

Localization and delocalization of fermions in a background of correlated spins

Tetsuya Takaishi, Kazuhiko Sakakibara, Ikuo Ichinose, Tetsuo Matsui

Published Nov 19, 2018• 8 citations
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Abstract

We study the (de)localization phenomena of one-component lattice fermions in spin backgrounds. The O(3) classical spin variables on sites fluctuate thermally through the ordinary nearest-neighbor coupling. Their complex two-component ($\mathrm{CP}{}^{1}$-Schwinger boson) representation forms a composite U(1) gauge field on bond, which acts on fermions as a fluctuating hopping amplitude in a gauge invariant manner. For the case of antiferromagnetic (AF) spin coupling, the model has a close relationship with the $t\ensuremath{-}J$ model of strongly correlated electron systems. We measure the unfolded level spacing distribution of fermion energy eigenvalues and the participation ratio of energy eigenstates. The results for AF spin couplings suggest a possibility that, in two dimensions, all the energy eigenstates are localized. In three dimensions, we find that there exists a mobility edge, and we estimate the critical temperature ${T}_{\mathrm{L}\mathrm{D}}(\ensuremath{\delta})$ of the localization-delocalization transition at the fermion concentration $\ensuremath{\delta}$.

DOI
10.1103/physrevb.98.184204

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We study the (de)localization phenomena of one-component lattice fermions in spin backgrounds. The O(3) classical spin variables on sites fluctuate thermally through the ordinary nearest-neighbor coupling. Their complex two-component (CP1\mathrm{CP}{}^{1}CP1-Schwinger boson) representation forms a composite U(1) gauge field on bond, which acts on fermions as a fluctuating hopping amplitude in a gauge invariant manner. For the case of antiferromagnetic (AF) spin coupling, the model has a close relationship with the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model of strongly correlated electron systems. We measure the unfolded level spacing distribution of fermion energy eigenvalues and the participation ratio of energy eigenstates. The results for AF spin couplings suggest a possibility that, in two dimensions, all the energy eigenstates are localized. In three dimensions, we find that there exists a mobility edge, and we estimate the critical temperature TLD(\ensuremathδ){T}_{\mathrm{L}\mathrm{D}}(\ensuremath{\delta})TLD​(\ensuremathδ) of the localization-delocalization transition at the fermion concentration \ensuremathδ\ensuremath{\delta}\ensuremathδ.
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We suggest that if a localized phase at nonzero temperature T>0T>0T>0 exists for strongly disordered and weakly interacting electrons, as recently argued, it will also occur when both disorder and interactions are strong and TTT is very high. We show that in this high-TTT regime, the localization transition may be studied numerically through exact diagonalization of small systems. We obtain spectra for one-dimensional lattice models of interacting spinless fermions in a random potential. As expected, the spectral statistics of finite-size samples cross over from those of orthogonal random matrices in the diffusive regime at weak random potential to Poisson statistics in the localized regime at strong randomness. However, these data show deviations from simple one-parameter finite-size scaling: the apparent mobility edge ``drifts'' as the system's size is increased. Based on spectral statistics alone, we have thus been unable to make a strong numerical case for the presence of a many-body localized phase at nonzero TTT.
We study a system of doped antiferromagnet in three dimensions at finite temperatures using the ttt-JJJ model, a canonical model of strongly correlated electrons. We employ the slave-fermion representation of electrons, in which an electron is described as a composite of a charged spinless holon and a chargeless spinon. We introduce two kinds of U(1) gauge fields on links as auxiliary fields, one describing resonating valence bonds of antiferromagnetic nearest-neighbor spin pairs and the other for nearest-neighbor hopping amplitudes of holons and spinons in the ferromagnetic channel. To perform a numerical study of the system, we integrate out the fermionic holon field by using the hopping expansion in powers of the hopping amplitude, which is legitimate for the region in and near the insulating phase. The resultant effective model is described in terms of bosonic spinons, two U(1) gauge fields, and a collective field for hole pairs. We study this model by means of Monte Carlo simulations, calculating the specific heat, spin correlation functions, and instanton densities. We obtain a phase diagram in the hole concentration-temperature plane, which is in good agreement with that observed recently for clean and homogeneous underdoped samples.
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