Nonlinear ac conductivity of interacting one-dimensional electron systems

Rosenow, Bernd; Nattermann, Thomas

doi:10.1103/physrevb.73.085103

Cited by 15 publications

(14 citation statements)

References 26 publications

(48 reference statements)

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“…In the presence of dissipation, the system is always "thermal" at sufficiently long times, in the sense that localization is destroyed [26]. In general, the system will reach a steady state, in which the energy gained from the drive is balanced by the energy lost to the bath [66]. Here, in addition to the drive amplitude and frequency, the dissipation rate γ (computed, e.g., using the Golden Rule [26]) is crucial.…”

Section: Discussionmentioning

confidence: 99%

Regimes of heating and dynamical response in driven many-body localized systems

2016

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We explore the response of many-body localized (MBL) systems to periodic driving of arbitrary amplitude, focusing on the rate at which they exchange energy with the drive. To this end, we introduce an infinite-temperature generalization of the effective "heating rate" in terms of the spread of a random walk in energy space. We compute this heating rate numerically and estimate it analytically in various regimes. When the drive amplitude is much smaller than the frequency, this effective heating rate is given by linear response theory with a coefficient that is proportional to the optical conductivity; in the opposite limit, the response is nonlinear and the heating rate is a nontrivial power law of time. We discuss the mechanisms underlying this crossover in the MBL phase. We comment on implications for the subdiffusive thermal phase near the MBL transition, and for response in imperfectly isolated MBL systems.

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Section: Discussionmentioning

confidence: 99%

Regimes of heating and dynamical response in driven many-body localized systems

2016

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“…Coupling to the spin bath does not appreciably change this linear-response result in the regime W s ω T . However, it does affect the nature of the steady-state response [23]. When dissipation is absent, linear response only occurs as a transient, on timescales short compared with the field amplitude t 1/(ξ q E).…”

Section: Charge Transportmentioning

confidence: 99%

“…Previous investigations of transport in SILLs [21] have focused on single-impurity problems, rather than the case of a finite density of quenched impurities that is pertinent to localization physics. Hopping conductivity (both d.c. and a.c.) in Luttinger liquids has been recast in terms of effective two-level systems [22,23] and pinned charge-density waves [24][25][26][27][28], but those prior works all assumed the existence of a "perfect bath" capable of placing any hopping process on-shell; this is in marked contrast to the narrowbandwidth bath, natural in the SILL context, that we consider here. The phenomenology of "narrow bath" disordered systems was studied in [14] but there the focus was on developing a mean-field approach to the MBL transition, rather than on transport properties.…”

Section: Introductionmentioning

confidence: 99%

Spin-catalyzed hopping conductivity in disordered strongly interacting quantum wires

Parameswaran

Gopalakrishnan

2017

Phys. Rev. B

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In one-dimensional electronic systems with strong repulsive interactions, charge excitations propagate much faster than spin excitations. Such systems therefore have an intermediate temperature range [termed the "spin-incoherent Luttinger liquid" (SILL) regime] where charge excitations are "cold" (i.e., have low entropy) whereas spin excitations are "hot." We explore the effects of chargesector disorder in the SILL regime in the absence of external sources of equilibration. We argue that the disorder localizes all charge-sector excitations; however, spin excitations are protected against full localization, and act as a heat bath facilitating charge and energy transport on asymptotically long timescales. The charge, spin, and energy conductivities are widely separated from one another. The dominant carriers of energy in much of the SILL regime are neither charge nor spin excitations, but neutral "phonon" modes, which undergo an unconventional form of hopping transport that we discuss. We comment on the applicability of these ideas to experiments and numerical simulations.

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“…(3.1) is for weak external fields much smaller than the extension E s /e 0 E 0 of the instanton. The domain wall energy per unit length is given by E s /v eff , and in contrast to the disordered case 14 , the spontaneous formation of instantons due to quantum fluctuations needs not be considered as the domain wall energy is spatially constant in the present model. Hence, the instanton action can be expressed in terms of the domain wall position X(y) as…”

Section: Instantonsmentioning

confidence: 98%

Nonlinear AC conductivity of one-dimensional Mott insulators

Rosenow

2008

J. Stat. Mech.

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We discuss a semiclassical calculation of low energy charge transport in one-dimensional (1d) insulators with a focus on Mott insulators, whose charge degrees of freedom are gapped due to the combination of short range interactions and a periodic lattice potential. Combining RG and instanton methods, we calculate the nonlinear ac conductivity and interpret the result in terms of multi-photon absorption. We compare the result of the semiclassical calculation for interacting systems to a perturbative, fully quantum mechanical calculation of multi-photon absorption in a 1d band insulator and find good agreement when the number of simultaneously absorbed photons is large. * On leave from the

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Nonlinear ac conductivity of interacting one-dimensional electron systems

Cited by 15 publications

References 26 publications

Regimes of heating and dynamical response in driven many-body localized systems

Regimes of heating and dynamical response in driven many-body localized systems

Spin-catalyzed hopping conductivity in disordered strongly interacting quantum wires

Nonlinear AC conductivity of one-dimensional Mott insulators

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