Numerical study of many-body localization and the associated quantum phase transitions employing the finite-temperature density-matrix-renormalization group

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Due to the phenomenon of Anderson-localization there cannot be a metallic wire at zero temperature; strictly speaking, all (generic one-dimensional) wires are insulators, and the associated conductance vanishes. The effect is due to an interplay of disorder and quantum-interference that ultimately localizes all propagating modes even if the disorder strength is very weak. Until recently there was a widely held belief that the wire would turn metallic at any finite temperature due to the effect of interactions. However, about a decade ago two teams presented theoretical arguments indicating that a generalized version of Anderson localization persists in Fock-space, that inhibits delocalization unless the temperature exceeds a critical value Tc. The results of subsequent work, computational and analytical, have lent full support to these claims. The existence of many-body-localization (MBL) is nowadays considered to be confirmed; experimental tests of (MBL) have been proposed and first measurements are being discussed. MBL implies the existence of classes of many-body states that represent insulators and other classes that represent metals. Each one of these classes fills a spectral window that is separated from a neighboring window by a quantum phase transition. The goal of the present proposal is to advance our knowledge and understanding of these transitions and the neighboring phases. Specifically, we propose a computational transport study of a disordered quantum wire of spin-half and spin-less fermions with short-range interactions. Main observables will be the charge, spin and energy densities and their relaxation behavior, together with the associated dynamical conductances. Our computational tool will be the density-matrix-renormalization group (DMRG) in a finite-temperature implementation. The first part of our study focuses on the relaxation dynamics of wavepackets near the phase transition. The goal is to extract from the time-dependent moments of the wave-packet distribution the relaxation time scales near and at the quantum phase transitions. When approaching the critical temperature from above, these time scales should exhibit a singular behavior (presumably with critical exponents) that we would like to study. At present, very little is known about the critical dynamics and its temperature dependency. The topic is important not only for fundamental reasons, but also because it will likely be relevant for the analysis of future experiments. Another part of the research addresses critical exponents that describe the frequency dependency of the conductance near and at the critical point. We begin by confirming very recent results about the charge-conductivity exponents. We proceed by calculating spin- and heat-exponents, which are still unknown. A comparison of exponents will provide information about the microscopic mechanism of spin- and heat flows, such as enthalpy and entropy per particle.