As a potential window on transitions out of the ergodic, many-body-delocalized phase, we study the dephasing of weakly disordered, quasi-one-dimensional fermion systems due to a diffusive, non-Markovian noise bath. Such a bath is self-generated by the fermions, via inelastic scattering mediated by short-ranged interactions. We calculate the dephasing of weak localization perturbatively through second order in the bath coupling. However, the expansion breaks down at long times, and is not stabilized by including a mean-field decay rate, signaling a failure of the self-consistent Born approximation. We also consider a many-channel quantum wire where short-ranged, spin-exchange interactions coexist with screened Coulomb interactions. We calculate the dephasing rate, treating the short-ranged interactions perturbatively and the Coulomb interaction exactly. The latter provides a physical infrared regularization that stabilizes perturbation theory at long times, giving the first controlled calculation of quasi-1D dephasing due to diffusive noise. At first order in the diffusive bath coupling, we find an enhancement of the dephasing rate, but at second order we find a rephasing contribution. Our results differ qualitatively from those obtained via self-consistent calculations and are relevant in two different contexts. First, in the search for precursors to many-body localization in the ergodic phase. Second, our results provide a mechanism for the enhancement of dephasing at low temperatures in spin SU(2)-symmetric quantum wires, beyond the Altshuler-Aronov-Khmelnitsky result. The enhancement is possible due to the amplification of the triplet-channel interaction strength, and provides an additional mechanism that could contribute to the experimentally observed low-temperature saturation of the dephasing time.
We develop a novel eikonal expansion for the Cooperon to study the effect of space- and time-dependent electric fields on the dephasing rate of disordered conductors. For randomly fluctuating fields with arbitrary covariance we derive a general expression for the dephasing rate which is free of infrared divergencies in reduced dimensions. For time-dependent external fields with finite wavelength and sufficiently small amplitude we show that the dephasing rate is proportional to the square root of the electromagnetic power coupled into the system, in agreement with data by Wang and Lindelof [Ph…
The resistivity of disordered metallic layer sandwiched by two ferromagnetic layers at low-temperature is investigated theoretically. It is shown that the magnetic field acting at the interface does not affect the classical Boltzmann resistivity but causes a dephasing among electrons in the presence of the spin-orbit interaction, suppressing the anti-localization due to the spin-orbit interaction. The dephasing turns out to be stronger in the case where the magnetization of the two layers is parallel, contributing to a positive magnetoresistance close to a switching field at low temperature.
We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. The conductivity at finite temperature is nonzero only because of inelastic electron-electron scattering. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. We calculate the relevant dephasing rate, which for spinless electrons is governed by the interplay of electron-electron interaction and disorder, thus vanishing in the clean limit.
We study transport properties of a disordered tight-binding model (XX spin chain) in the presence of dephasing. Focusing on diffusive behavior in the thermodynamic limit at high energies, we analytically derive the dependence of conductivity on dephasing and disorder strengths. As a function of dephasing, conductivity exhibits a single maximum at the optimal dephasing strength. The scaling of the position of this maximum with disorder strength is different for small and large disorder. In addition, we study periodic disorder for which we find a resonance phenomenon, with conductivity having tw…
We study dephasing by electron interactions in a small disordered quasi-one dimensional (1D) ring weakly coupled to leads. We use an influence functional for quantum Nyquist noise to describe the crossover for the dephasing time $\Tph (T)$ from diffusive or ergodic 1D ($ \Tph^{-1} \propto T^{2/3}, T^{1}$) to 0D behavior ($\Tph^{-1} \propto T^{2}$) as $T$ drops below the Thouless energy. The crossover to 0D, predicted earlier for 2D and 3D systems, has so far eluded experimental observation. The ring geometry holds promise of meeting this longstanding challenge, since the crossover manifests it…
We have systematically investigated the low-temperature electron dephasing times $τ_ϕ$ in more than 40 three-dimensional polycrystalline impure metals with distinct material characteristics. In all cases, a saturation of the dephasing time is observed below about a (few) degree(s) Kelvin, depending on samples. The value of the saturated dephasing time $τ_0$ [$\equiv τ_ϕ(T \to 0 {\rm K})$] falls basically in the range 0.005 to 0.5 ns for all samples. Particularly, we find that $τ_0$ scales with the electron diffusion constant $D$ as $τ_0 \sim D^{- α}$, with $α$ close to or slightly larger than …
Dephasing of spins is a major roadblock to scaling up the size of quantum computing systems. We explore the possibility of utilizing highly disordered environments which are in the Many-Body Localized phase to arrest this dephasing. We embedded 2 `special' spins in such a highly disordered environment of Heisenberg spins to act as the target qubits and use the long-time value of the spin-spin correlator $\langle \vecσ_i \cdot \vecσ_j\rangle$ as an order parameter to quantify the transition between the thermal and MBL phases of this system. It is seen that the dephasing between spins, as encode…
We calculate the Nyquist noise contribution to the dephasing rate 1/τ_{nn}(omega, T) of disordered conductors in d dimensions in the regime where the frequency omega is larger than the temperature T. For systems with a continuous spectrum we find at zero temperature $1/ tau_{nn} (omega, 0) propto nu_d^{-1} (omega / D)^{d/2}, which agrees qualitatively with the inelastic quasiparticle scattering rate. Here nu_d is d-dimensional density of states, and D is the diffusion coefficient. Because at zero frequency and finite temperatures 1 / tau_{nn} (0, T) propto [ T / (nu_d {D}^{d/2})]^{2 / (4-d)} f…
Many-body localization is a fascinating theoretical concept describing the intricate interplay of quantum interference, i.e. localization, with many-body interaction induced dephasing. Numerous computational tests and also several experiments have been put forward to support the basic concept. Typically, averages of time-dependent global observables have been considered, such as the charge imbalance. We here investigate within the disordered spin-less Hubbard ($t-V$) model how dephasing manifests in time dependent variances of observables. We find that after quenching a Néel state the local ch…
The conduction electrons' dephasing rate, $τ_ϕ^{-1}$, is expected to vanish with the temperature. A very intriguing apparent saturation of this dephasing rate in several systems was recently reported at very low temperatures. The suggestion that this represents dephasing by zero-point fluctuations has generated both theoretical and experimental controversies. We start by proving that the dephasing rate must vanish at the $T\to 0$ limit, unless a large ground state degeneracy exists. This thermodynamic proof includes most systems of relevance and it is valid for any determination of $τ_ϕ$ from …
We study transport properties of anisotropic Heisenberg model in a disordered magnetic field experiencing dephasing due to external degrees of freedom. In the absence of dephasing the model can display, depending on parameter values, the whole range of possible transport regimes: ideal ballistic conduction, diffusive, or ideal insulating behavior. We show that the presence of dephasing induces normal diffusive transport in a wide range of parameters. We also analyze the dependence of spin conductivity on the dephasing strength. In addition, by analyzing the decay of spin-spin correlation funct…
In a recent paper, Phys. Rev. Lett. 81, 1074 (1998), Golubev and Zaikin (GZ) found that ``zero-point fluctuations of electrons'' contribute to the dephasing rate extracted from the magnetoresistance. As a result, the dephasing rate remains finite at zero temperature. GZ claimed that their results ``agree well with the experimental data''. We point out that the GZ results are incompatible with (i) conventional perturbation theory of the effects of interaction on weak localization (WL), and (ii) with the available experimental data. More detailed criticism of GZ findings can be found in cond-mat…
This paper is intended to demonstrate that there is no need to revise the existing theory of the transport properties of disordered conductors in the so-called weak localization regime. In particular, we demonstrate explicitly that recent attempts to justify theoretically that the dephasing rate (extracted from the magnetoresistance) remains finite at zero temperature are based on the profoundly incorrect calculation. This demonstration is based on a straightforward evaluation of the effect of the electron-electron interaction on the weak localization correction to the conductivity of disorder…
The effect of an in-plane magnetic field upon open quasi-two-dimensional electron and hole systems is investigated in terms of the carrier ground-state spectrum. The magnetic field, classified as weak from the viewpoint of correlation between size parameters of classical electron motion and the gate potential spatial profile is shown to efficiently cut off extended modes from the spectrum and to change singularly the mode density of states (MDOS). The reduction in the number of current-carrying modes, right up to zero in magnetic fields of moderate strength, can be viewed as the cause of magne…
In two dimensions (2D), dephasing by a bath cuts off Anderson localization that would otherwise occur at any energy density for fermions with disorder. For an isolated system with short-range interactions, the system can be its own bath, exhibiting diffusive (non-Markovian) thermal density fluctuations. We recast the dephasing of weak localization due to a diffusive bath as a self-interacting polymer loop. We investigate the critical behavior of the loop in $d=4-ε$ dimensions, and find a nontrivial fixed point corresponding to a temperature $T^* \sim ε>0$ where the dephasing time diverges. Ass…
Conduction electrons in disordered metals and heavily doped semiconductors at low temperatures preserve their phase coherence for a long time: phase relaxation time $τ_ϕ$ can be orders of magnitude longer than the momentum relaxation time. The large difference in these time scales gives rise to well known effects of weak localization, such as anomalous magnetoresistance. Among other interesting characteristics, study of these effects provide quantitative information on the dephasing rate $1/τ_ϕ$. This parameter is of fundamental interest: the relation between $\hbar/τ_ϕ$ and the temperature $T…
The Lindblad dynamics with dephasing in the bulk and magnetization-driving at the two boundaries is studied for the quantum spin chain with random fields $h_j$ and couplings $J_j$ (that can be either uniform or random). In the regime of strong disorder in the random fields, or in the regime of strong bulk-dephasing, the effective dynamics can be mapped onto a classical Simple Symmetric Exclusion Process with quenched disorder in the diffusion coefficient associated to each bond. The properties of the corresponding Non-Equilibrium-Steady-State in each disordered sample between the two reservoir…
We study the spreading of single-site excitations in one-dimensional disordered Klein-Gordon chains with tunable nonlinearity $|u_{l}|^σ u_{l}$ for different values of $σ$. We perform extensive numerical simulations where wave packets are evolved a) without and, b) with dephasing in normal mode space. Subdiffusive spreading is observed with the second moment of wave packets growing as $t^α$. The dependence of the numerically computed exponent $α$ on $σ$ is in very good agreement with our theoretical predictions both for the evolution of the wave packet with and without dephasing (for $σ\geq 2$…
In this work I will discuss some numerical results on the stability of the many-body localized phase to thermal inclusions. The work simplifies a recent proposal by Morningstar et al. [arXiv:2107.05642] and studies small disordered spin chains which are perturbatively coupled to a Markovian bath. The critical disorder for avalanche stability of the canonical disordered Heisenberg chain is shown to exceed W>20. In stark contrast to the Anderson insulator, the avalanche threshold drifts considerably with system size, with no evidence of saturation in the studied regime. I will argue that the res…
We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime when bulk dephasing is present. We find that while dephasing always renders the transport diffusive, there is nonetheless a remnant of the diffusive to sub-diffusive transition found in a system without dephasing manifested in the behaviour of the diffusion constant with the dephasing strength. By studying finite-size effects we show numerically and theoretically that this feature is caused by the competition between large crossover length scales associated to disorder and dephasing that control the…
