Universal Fermi liquid crossover and quantum criticality in a mesoscopic system

Keller, Andrew J.; Peeters, Lucas; Moca, Cătălin Paşcu; Weymann, Ireneusz; Mahalu, D.; Umansky, V.; Zaránd, Gergely; Goldhaber‐Gordon, David

doi:10.1038/nature15261

Cited by 114 publications

(108 citation statements)

References 43 publications

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“…Experimentally, signatures of the 2CK model have been observed in mesoscopic structures [26][27][28][29]. Still, the real-space entanglement structure and the imprints of the two distinct length scales ξ 2CK ∼ u/T 2CK and ξ * ∼ u/T * with u the spin velocity-implied by the known crossover energy scales T 2CK (2CK temperature) and T * (critical crossover in the channel-asymmetric case) [5, 23] − have not yet been unraveled.…”

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confidence: 99%

Entanglement structure of the two-channel Kondo model

et al. 2016

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Two electronic channels competing to screen a single impurity spin, as in the two-channel Kondo model, are expected to generate a ground state with nontrivial entanglement structure. We exploit a spin-chain representation of the two-channel Kondo model to probe the ground-state block entropy, negativity, tangle, and Schmidt gap, using a density matrix renormalization group approach. In the presence of symmetric coupling to the two channels we confirm field-theory predictions for the boundary entropy difference, ln(g UV /g IR ) = ln(2)/2, between the ultraviolet and infrared limits and the leading ln(x)/x impurity correction to the block entropy. The impurity entanglement, S imp , is shown to scale with the characteristic length ξ 2CK . We show that both the Schmidt gap and the entanglement of the impurity with one of the channels − as measured by the negativity− faithfully serve as order parameters for the impurity quantum phase transition appearing as a function of channel asymmetry, allowing for explicit determination of critical exponents, ν ≈ 2 and β ≈ 0.2. Remarkably, we find the emergence of tripartite entanglement only in the vicinity of the critical channel-symmetric point.Introduction.-The Kondo effect is one of the most intriguing effects in quantum many-body physics. At low temperatures, a localized magnetic impurity is screened by the conduction electrons leading to the formation of many-body entanglement. A generalization of the Kondo model was introduced by Nozières and Blandin [1], where another channel of electrons is also coupled to the impurity. This is the wellknown two-channel Kondo (2CK) model, for which various results were obtained using Bethe ansatz [2-4], conformal field theory [5, 6] (CFT), bosonization [7][8][9] and entanglement of formation [10]. This model is very different from the one-channel Kondo (1CK) model as the two channels compete to screen the spin-1/2 impurity, leading to an "overscreened" residual spin interacting with the electrons [5]. This leads to non-trivial properties including a residual zero-temperature impurity entropy and a logarithmic behavior of magnetic susceptibility and specific heat. However, channel symmetry is crucial; even the smallest asymmetry leads to screening of the impurity by the channel with the stronger coupling [1], and as the channel asymmetry is varied, an impurity quantum phase transition (IQPT) occurs at the symmetric point, corresponding to the 2CK model.Intensive research has been carried out to investigate the thermodynamics and the transport properties of the 2CK model [1-3, 5-9, 11-25]. Experimentally, signatures of the 2CK model have been observed in mesoscopic structures [26][27][28][29]. Still, the real-space entanglement structure and the imprints of the two distinct length scales ξ 2CK ∼ u/T 2CK and ξ * ∼ u/T * with u the spin velocity-implied by the known crossover energy scales T 2CK (2CK temperature) and T * (critical crossover in the channel-asymmetric case) [5, 23] − have not yet been unraveled. A way forward is to use a spi...

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Entanglement structure of the two-channel Kondo model

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“…The 2IKM and the 2CKM are the best examples of non-Fermi-liquid behavior generated by criticality [32][33][34]. There are also several experimental realizations for both the 2IKM [35][36][37] and the 2CKM [38][39][40][41].…”

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Scaling of Tripartite Entanglement at Impurity Quantum Phase Transitions

Bayat

2017

Phys. Rev. Lett.

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The emergence of a diverging length scale in many-body systems at a quantum phase transition implies that total entanglement has to reach its maximum there. In order to fully characterize this, one has to consider multipartite entanglement as, for instance, bipartite entanglement between individual particles fails to signal this effect. However, quantification of multipartite entanglement is very hard, and detecting it may not be possible due to the lack of accessibility to all individual particles. For these reasons it will be more sensible to partition the system into relevant subsystems, each containing a few to many spins, and study entanglement between those constituents as a coarse-grain picture of multipartite entanglement between individual particles. In impurity systems, famously exemplified by two-impurity and two-channel Kondo models, it is natural to divide the system into three parts, namely, impurities and the left and right bulks. By exploiting two tripartite entanglement measures, based on negativity, we show that at impurity quantum phase transitions the tripartite entanglement diverges and shows scaling behavior. While the critical exponents are different for each tripartite entanglement measure, they both provide very similar critical exponents for the two-impurity and the two-channel Kondo models, suggesting that they belong to the same universality class.

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“…Several low-dimensional systems, in fact, show interaction-induced phases of matter absent in higher dimensions. They include fractional quantum Hall states in two dimensions4, Tomonaga–Luttinger liquids in one-dimension (1D)5 and Kondo effects in zero-dimensional (0D) quantum dots (QDs)6. Here we demonstrate that analogous many-particle interactions dictate the 1D-to-0D dimensional crossover in low-dimensional semiconductors (Fig.…”

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Dimensional crossover in semiconductor nanostructures

McDonald

Chatterjee

et al. 2016

Nat Commun

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Recent advances in semiconductor nanostructure syntheses provide unprecedented control over electronic quantum confinement and have led to extensive investigations of their size- and shape-dependent optical/electrical properties. Notably, spectroscopic measurements show that optical bandgaps of one-dimensional CdSe nanowires are substantially (approximately 100 meV) lower than their zero-dimensional counterparts for equivalent diameters spanning 5–10 nm. But what, exactly, dictates the dimensional crossover of a semiconductor's electronic structure? Here we probe the one-dimensional to zero-dimensional transition of CdSe using single nanowire/nanorod absorption spectroscopy. We find that carrier electrostatic interactions play a fundamental role in establishing dimensional crossover. Moreover, the critical length at which this transition occurs is governed by the aspect ratio-dependent interplay between carrier confinement and dielectric contrast/confinement energies.

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Universal Fermi liquid crossover and quantum criticality in a mesoscopic system

Cited by 114 publications

References 43 publications

Entanglement structure of the two-channel Kondo model

Entanglement structure of the two-channel Kondo model

Scaling of Tripartite Entanglement at Impurity Quantum Phase Transitions

Dimensional crossover in semiconductor nanostructures

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