Delocalized carriers in the t−J model with strong charge disorder

Abstract

We study the influence of the electron-magnon interaction on the particle transport in strongly disordered systems. The analysis is based on results obtained for a single hole in the one-dimensional t-J model. Unless there exists a mechanism that localizes spin excitations, the charge carrier remains delocalized even for a very strong disorder and shows subdiffusive motion up to the longest accessible times. However, upon inspection of the propagation times between neighboring sites as well as a careful finite-size scaling we conjecture that the anomalous subdiffusive transport may be transient and should eventually evolve into a normal diffusive motion. 71.27.+a, 71.30.+h, 71.10.Fd Introduction.-The many-body localization (MBL) represents a promising concept of macroscopic devices which do not thermalize [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and may store the quantum information [19,20]. Most of the inherent properties of MBL systems have been investigated using the generic one-dimensional (1D) disordered models of interacting spinless fermions [21][22][23][24][25][26][27][28][29][30][31]. Emerging characteristic features of MBL systems are: the existence of localized many-body states in the whole energy spectrum that leads to vanishing of d.c. transport at any temperature [32][33][34][35][36][37][38][39], Poisson-like level statistics [40], and the logarithmic growth of the entanglement entropy [5,7,[41][42][43][44][45]. Numerical calculations of dynamical conductivity [34,37,38] and other dynamic properties based on the renormalizationgroup approach [7,35,46,47] indicate that in the vicinity of the transition to MBL state the optical conductivity shows a characteristic linear ω-dependence. In the presence of strong disorder but still below the MBL transition, several studies predict a subdiffusive transport [34,35,48,49].The presence of MBL has been rigorously shown so far only for the transverse-field Ising model [50], whereas the indisputable numerical evidence is available mostly for interacting spinless fermions or equivalent spin Hamiltonians. However, in real systems, the particles are coupled to other degrees of freedom and this coupling may be important not only for solids but also for the cold-atom experiments. In particular, the recent experiments [4, 51, 52] address the problem of MBL in the spin-1/2 Hubbard model, where charge carriers are coupled to spin excitation. On the other hand, well established results [53,54] indicate that phonons destroy the Anderson localization, hence they should destroy the MBL phase as well. Nevertheless, in contrast to phonons, the energy spectrum of many other excitations in the tight-binding models (e.g., the spin excitations) is bounded from above. It remains unclear whether strict MBL survives in the presence of the latter excitations. Solving this problem is important for answering the fundamental question whether MBL exists also in more realistic models including the Hubbard model [55,56]. The preliminary numerical results suggest ...

Dynamics of the one-dimensional Anderson insulator coupled to various bosonic baths

“…[24][25][26][27][28][29] The many-body interaction is responsible for several distinctive features of the MBL systems, in particular for the unusually slow dynamics. [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] The particle localization is not immune against arbitrary many-body interaction and mechanisms which are known to destroy the Anderson insulator may destroy the MBL as well. In particular, the Anderson insulator may be destroyed by the electron-phonon interaction via the so called phonon-assisted hopping.…”

“…magnons) or the boson-boson interaction remains unexplored. In particular, it is an open problem whether coupling between charge carriers and magnetic excitations 47,[53][54][55][56][57][58] may play the same role as the electron-phonon coupling. The essential difference between both types of bosons is that the energy density of the magnetic excitations is bounded from above, whereas phonons can in principle absorb arbitrary energy.…”

Transient and persistent particle subdiffusion in a disordered chain coupled to bosons

“…Due to reduced Hilbert space, the model with HCB offers the advantage for full many-body simulations. 44,47 Moreover, the connection of HCB to spin systems in 1D allows closer relation with the disordered Hubbard model 53,54,67 and the disordered Heisenberg model. 4,56,63 Using the standard relation of HCB with S = 1/2 local spin operators, we can follow previous procedure and eliminate the diagonal l = l term via local transformation U l = i U li ,…”

Einstein Relation for a Driven Disordered Quantum Chain in the Subdiffusive Regime

“…Among several characteristic features of strongly disordered systems is unusually slow time evolution of characteristic physical properties [27,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]] that typically emerges as subdiffusive dynamics as a precursor to MBL transition [18,39,[49][50][51][52][53][54].In this Letter we consider the effect of driving (via the constant electric field) on a quantum particle in a random chain coupled to itinerant hard-core bosons (HCB). We note that such a system simulates the propagation of a (single) charge coupled to spin degrees in strongly correlated systems, as e.g., the disordered Hubbard typemodels [44,55,56], being realized in cold-atom experiments [23][24][25][26][27][28]. It has long been assumed that the AL phenomenon is destroyed by the electron-phonon coupling via the mechanism of phonon-assisted hopping [57,58].…”

“…Moreover, the existence of MBL has been found in a few experimental studies [23][24][25][26][27][28]. Among several characteristic features of strongly disordered systems is unusually slow time evolution of characteristic physical properties [27,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] that typically emerges as subdiffusive dynamics as a precursor to MBL transition [18,39,[49][50][51][52][53][54].…”