Theoretical Solid State Physics

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Tensor network approach for nonequilibrium steady-state transport through non-Fermi-liquid Kondo quantum dots

The description of interacting quantum impurity models in steady-state nonequilibrium presents a major challenge for computational many-particle methods: the numerical requirement of using a finite number of lead levels and the physical requirement of describing a truly open quantum system are seemingly incompatible. In a recent breakthrough, we have found a strategy that successfully bridges this gap, using Lindblad-driven discretized leads (LDDL) [1,2]: one couples auxiliary continuous reservoirs to the discretized lead levels and represents these additional reservoirs by  Lindblad terms in the Liouville equation. The resulting setup can be treated efficiently using state-of-the-art numerical tensor-network-based methods. Results of benchmark calculations are in excellent agreement with exact predictions for the nonequilibrium steady state conductance for exactly solvable interacting models.

The Master thesis topic will build on these results in either or both of two ways:

(i) Method development: Improve the efficiency of finding the nonequilibrium steady state, using various possible tensor network optimization strategies [3,4,5].

(ii) Application: use the new method to study nonequilibrium transport through more complex impurity models  exhibiting non-Fermi liquid physics (2- and 3-channel Kondo models), inspired by recent new experiments [6,7].

The master student would learn state-of-the-art tensor network methods to treat questions of direct relevance for experimental measurements of transport through quantum dots exhibiting very exotic behavior.


[1] F. Schwarz, M. Goldstein, A. Dorda, E. Arrigoni, A. Weichselbaum and J. von Delft
Lindblad-driven discretized leads for nonequilibrium steady-state transport in quantum impurity models: Recovering the continuum limit.
Phys. Rev. B 94, 155142 (2016)

[2] F. Schwarz, I. Weymann, J. von Delft and A. Weichselbaum
Nonequilibrium Steady-State Transport in Quantum Impurity Models: A Thermofield and Quantum Quench Approach Using Matrix Product States.
Phys. Rev. Lett. 121, 137702 (2018).

[3] J. Cui, J. I. Cirac and M. C. Banuls
Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems.
Phys. Rev. Lett. 114, 220601 (2015).

[4] A. H. Werner, D. Jaschke, P. Silvi, M. Kliesch, T. Calarco, J. Eisert and S. Montangero
Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems.
Phys. Rev. Lett. 116, 237201 (2016).

[5] E. Mascarenhas, H. Flayac and V. Savona
Matrix-product-operator approach to the nonequilibrium steady state of driven-dissipative quantum arrays.
Phys. Rev. A 92, 022116 (2015).

[6] Z. Iftikhar, S. Jezouin, A. Anthore, U. Gennser, F. Parmentier, A. Cavanna and F. Pierre
Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states
Nature 526, 233 (2015).

[7] Z. Iftikhar, A. Anthore, A. K. Mitchell, F. D. Parmentier, U. Gennser, A. Ouerghi, A. Cavanna, C. Mora, P. Simon and F. Pierre
Tunable quantum criticality and super-ballistic transport in a ``charge'' Kondo circuit.
Science 360, 1315-1320 (2018).