Abstract
Quantum criticality accounts for the unconventional physics that develops in the vicinity of the critical point of a second-order quantum phase transition [1]. It is characterized by the power law divergence of the correlation length \(\xi \) as a non-thermal parameter g approaches a critical value \(g_c\): \(\xi \propto |g-g_c|^{-\nu }\), where \(\nu \) is called a critical exponent. The concept of quantum criticality provides a powerful universal framework to describe some of the most fascinating strongly correlated electrons phenomena, including heavy fermions [2] or high-\(T_C\) superconductivity [3].
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Notes
- 1.
The classification that follows is the same for classical phase transitions, one just has to replace the non-thermal parameter g by T.
- 2.
For instance, the \(J\longrightarrow \infty \) fixed point in the 1CK model is not a quantum critical point.
- 3.
Some strongly correlated materials have displayed a signature of quantum criticality up to 700 K [12].
- 4.
It is argued in [6] that in general, the prefactor of a critical power law as \(T_\mathrm{{co}}\propto \Delta J^2\) can be different on each side of a quantum critical point. The reason for such an anisotropy is unclear to us.
- 5.
This is possible since they remain approximately equal. The typical difference between \(G_1\) and \(G_3\) can be observed on the diagonal of the diagram, from the similar difference between \(G_2\) and \(G_{1,3}\).
- 6.
To be precise, we plot \(G_2^{T \gg T_K}(T/T_K(\tau _2))\) versus \(G_1^{T \gg T_K}(T/T_K(\tau _1))\), where \(G^{T \gg T_K}(T/T_K) = {19,24}\, G_K \ln ^{-2}(T/{0.0037}T_K)\) is the tunnel regime of the universal curve (see Fig. 3.14a), and where \(T_K(\tau _1)\) and \(T_K(\tau _2)\) correspond to the \(T_K(\tau )\) in the inset of the same figure.
- 7.
For example, see the Fig. 3 of [30], where the conductance of a QPC in series with an ohmic resistor of resistance \(R \approx {26}\,\mathrm{k\Omega } \approx R_K\) does not drop at low temperature in the limit of ballistic transmission \(\tau _\infty \longrightarrow 1\).
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Iftikhar, Z. (2018). Quantum Phase Transition in Multi-channel Kondo Systems. In: Charge Quantization and Kondo Quantum Criticality in Few-Channel Mesoscopic Circuits. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-94685-6_4
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