Complete Many-Body Localization in the t−J Model Caused by a Random Magnetic Field

Abstract

The many body localization (MBL) of spin-1/2 fermions poses a challenging problem. It is known that the disorder in the charge sector may be insufficient to cause full MBL. Here, we study dynamics of a single hole in one dimensional t-J model subject to a random magnetic field. We show that strong disorder that couples only to the spin sector localizes both spin and charge degrees of freedom. Charge localization is confirmed also for a finite concentration of holes. While we cannot precisely pinpoint the threshold disorder, we conjecture that there are two distinct transitions. Weaker disorder first causes localization in the spin sector. Carriers become localized for somewhat stronger disorder, when the spin localization length is of the order of a single lattice spacing. 71.27.+a, 71.30.+h, 71.10.Fd Introduction.-The many-body localization (MBL) has been demonstrated by various numerical [1][2][3][4][5][6][7][8][9][10][11] and analytical studies [12,13] carried out mostly for one-dimensional (1D) systems of spinless particles or equivalent spin-models. Among unusual properties of MBL we only emphasize the logarithmic growth of the entanglement entropy [14][15][16][17][18][19][20], and the subdiffusive transport in the regime of strong disorder but still below the MBL transition [21][22][23][24].

Many-body localization of 1D disordered impenetrable two-component fermions

“…For instance, the Hubbard model for two-component fermions possesses two local degrees of freedom, charge and spin, both of which can be coupled to disorder. Recent numerical studies deal with the disordered 1D Hubbard model in the regime of a finite interaction strength [27][28][29][30][31][32]. The results suggest that a sufficiently strong random potential localizes the charge degree of freedom, whereas spin excitations apperently exhibit a subdiffusive transport, i.e.…”

Spin Subdiffusion in the Disordered Hubbard Chain

“…Recent numerical studies of such a model [47,[51][52][53] reveal that even at strong disorder, localization and nonergodicity occurs only in the charge subsystem, implying a partial MBL. Unless one introduces also an additional random magnetic field [47,54], the spin remain delocalized, [52,[55][56][57][58][59], although the spin transport is anomalously slow and subdiffusive [52].…”

Many-body localization with synthetic gauge fields in disordered Hubbard chains

“…The absence of fully localized phase is due to the SU(2) symmetry of the model. The choice of a different random potential for up and down polarized fermions, a random magnetic field or a weak spin asymmetry which breaks the SU(2) spin symmetry recovers the full MBL phase [34,58,59]. Moreover, the subdiffusive transport of spins is due to a singular random distribution of effective spin exchange interactions [33] and at long time evolution the transport is strongly suppressed [35].…”