Z3 Parafermion in the Double Charge Kondo Model

Karki, D.  B.; Boulat, Edouard; Pouse, Winston; Goldhaber-Gordon, David; Mitchell, Andrew K.; Mora, Christophe

doi:10.1103/physrevlett.130.146201

Z3 Parafermion in the Double Charge Kondo Model

Journal Article · Thu Apr 06 00:00:00 EDT 2023 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.130.146201· OSTI ID:2002886

Karki, D. B. ^[1]; ^[2]; Pouse, Winston ^[3]; ^[4]; ^[5]; ^[2]

Beijing Academy of Quantum Information Sciences, Beijing (China); Argonne National Laboratory (ANL), Argonne, IL (United States); SLAC
Univ. of Paris (France); Centre National de la Recherche Scientifique (CNRS) (France)
Stanford Univ., CA (United States); SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States); Stanford Univ., CA (United States)
University College Dublin (Ireland)

Quantum impurity models with frustrated Kondo interactions can support quantum critical points with fractionalized excitations. Recent experiments [arXiv:2108.12691] on a circuit containing two coupled metal-semiconductor islands exhibit transport signatures of such a critical point. Here we show using bosonization that the double charge-Kondo model describing the device can be mapped in the Toulouse limit to a sine-Gordon model. Its Bethe-ansatz solution shows that a Z₃ parafermion emerges at the critical point, characterized by a fractional $$\frac{1}{2}$$ln(3) residual entropy, and scattering fractional charges e/3. Finally, we also present full numerical renormalization group calculations for the model and show that the predicted behavior of conductance is consistent with experimental results.

View Accepted Manuscript (DOE)

Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: Irish Research Council; USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 2002886

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 14 Vol. 130; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (79)

Topological Entanglement Entropy from the Holographic Partition Function Fendley, Paul; Fisher, Matthew P. A.; Nayak, Chetan Journal of Statistical Physics, Vol. 126, Issue 6 https://doi.org/10.1007/s10955-006-9275-8	journal	January 2007
Exact solution of a massless scalar field with a relevant boundary interaction Fendley, P.; Saleur, H.; Warner, N. P. Nuclear Physics B, Vol. 430, Issue 3 https://doi.org/10.1016/0550-3213(94)90160-0	journal	November 1994
Quantum brownian motion on a triangular lattice and boundary conformal field theory Affleck, Ian; Oshikawa, Masaki; Saleur, Hubert Nuclear Physics B, Vol. 594, Issue 3 https://doi.org/10.1016/S0550-3213(00)00499-5	journal	February 2001
The Kondo Problem to Heavy Fermions Hewson, Alexander Cyril https://doi.org/10.1017/CBO9780511470752	book	January 1993
Kondo effect in a single-electron transistor Goldhaber-Gordon, D.; Shtrikman, Hadas; Mahalu, D. Nature, Vol. 391, Issue 6663, p. 156-159 https://doi.org/10.1038/34373	journal	January 1998
Kondo resonance in a single-molecule transistor Liang, Wenjie; Shores, Matthew P.; Bockrath, Marc Nature, Vol. 417, Issue 6890 https://doi.org/10.1038/nature00790	journal	June 2002
Observation of the two-channel Kondo effect Potok, R. M.; Rau, I. G.; Shtrikman, Hadas Nature, Vol. 446, Issue 7132 https://doi.org/10.1038/nature05556	journal	March 2007
Universal Fermi liquid crossover and quantum criticality in a mesoscopic system Keller, A. J.; Peeters, L.; Moca, C. P. Nature, Vol. 526, Issue 7572 https://doi.org/10.1038/nature15261	journal	October 2015
Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states Iftikhar, Z.; Jezouin, S.; Anthore, A. Nature, Vol. 526, Issue 7572 https://doi.org/10.1038/nature15384	journal	October 2015
An order parameter for impurity systems at quantum criticality Bayat, Abolfazl; Johannesson, Henrik; Bose, Sougato Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms4784	journal	May 2014
Emergent SU(4) Kondo physics in a spin–charge-entangled double quantum dot Keller, A. J.; Amasha, S.; Weymann, I. Nature Physics, Vol. 10, Issue 2 https://doi.org/10.1038/nphys2844	journal	December 2013
Non-equilibrium singlet–triplet Kondo effect in carbon nanotubes Paaske, J.; Rosch, A.; Wölfle, P. Nature Physics, Vol. 2, Issue 7 https://doi.org/10.1038/nphys340	journal	July 2006
In situ click chemistry generation of cyclooxygenase-2 inhibitors Bhardwaj, Atul; Kaur, Jatinder; Wuest, Melinda Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-016-0009-6	journal	February 2017
Quantum simulation of an exotic quantum critical point in a two-site charge Kondo circuit Pouse, Winston; Peeters, Lucas; Hsueh, Connie L. Nature Physics, Vol. 19, Issue 4 https://doi.org/10.1038/s41567-022-01905-4	journal	January 2023
Kondo effect in real metals Nozières, Ph.; Blandin, A. Journal de Physique, Vol. 41, Issue 3 https://doi.org/10.1051/jphys:01980004103019300	journal	January 1980
Exotic Kondo effects in metals: Magnetic ions in a crystalline electric field and tunnelling centres Cox, D. L.; Zawadowski, A. Advances in Physics, Vol. 47, Issue 5 https://doi.org/10.1080/000187398243500	journal	September 1998
Impurity quantum phase transitions Vojta, Matthias Philosophical Magazine, Vol. 86, Issue 13-14 https://doi.org/10.1080/14786430500070396	journal	May 2006
Parafermionic edge zero modes in Z _n -invariant spin chains Fendley, Paul Journal of Statistical Mechanics: Theory and Experiment, Vol. 2012, Issue 11 https://doi.org/10.1088/1742-5468/2012/11/P11020	journal	November 2012
Bethe ansatz solution of the topological Kondo model Altland, A.; Béri, B.; Egger, R. Journal of Physics A: Mathematical and Theoretical, Vol. 47, Issue 26 https://doi.org/10.1088/1751-8113/47/26/265001	journal	June 2014
Anyons in multichannel Kondo systems Lopes, Pedro L. S.; Affleck, I.; Sela, E. Physical Review B, Vol. 101, Issue 8 https://doi.org/10.1103/PhysRevB.101.085141	journal	February 2020
Isolating Kondo anyons for topological quantum computation Komijani, Yashar Physical Review B, Vol. 101, Issue 23 https://doi.org/10.1103/PhysRevB.101.235131	journal	June 2020
Multi-impurity chiral Kondo model: Correlation functions and anyon fusion rules Gabay, Dor; Han, Cheolhee; Lopes, Pedro L. S. Physical Review B, Vol. 105, Issue 3 https://doi.org/10.1103/PhysRevB.105.035151	journal	January 2022
Fractionalization and anyonic statistics in the integer quantum Hall collider Morel, Tom; Lee, June-Young M.; Sim, H. -S. Physical Review B, Vol. 105, Issue 7 https://doi.org/10.1103/PhysRevB.105.075433	journal	February 2022
Double-charge quantum island in the quasiballistic regime Karki, Deepak B.; Boulat, Edouard; Mora, Christophe Physical Review B, Vol. 105, Issue 24 https://doi.org/10.1103/PhysRevB.105.245418	journal	June 2022
Order fractionalization in a Kitaev-Kondo model Tsvelik, Alexei M.; Coleman, Piers Physical Review B, Vol. 106, Issue 12 https://doi.org/10.1103/PhysRevB.106.125144	journal	September 2022
Mapping of the two-channel Kondo problem to a resonant-level model Emery, V. J.; Kivelson, S. Physical Review B, Vol. 46, Issue 17 https://doi.org/10.1103/PhysRevB.46.10812	journal	November 1992
Transmission through barriers and resonant tunneling in an interacting one-dimensional electron gas Kane, C. L.; Fisher, Matthew P. A. Physical Review B, Vol. 46, Issue 23 https://doi.org/10.1103/PhysRevB.46.15233	journal	December 1992
Exact conformal-field-theory results on the multichannel Kondo effect: Single-fermion Green’s function, self-energy, and resistivity Affleck, Ian; Ludwig, Andreas W. W. Physical Review B, Vol. 48, Issue 10 https://doi.org/10.1103/PhysRevB.48.7297	journal	September 1993
Toulouse limit for the overscreened four-channel Kondo problem Fabrizio, M.; Gogolin, Alexander O. Physical Review B, Vol. 50, Issue 23 https://doi.org/10.1103/PhysRevB.50.17732	journal	December 1994
Coulomb blockade at almost perfect transmission Matveev, K. A. Physical Review B, Vol. 51, Issue 3 https://doi.org/10.1103/PhysRevB.51.1743	journal	January 1995
Tunneling and quantum noise in one-dimensional Luttinger liquids Chamon, C. de C.; Freed, D. E.; Wen, X. G. Physical Review B, Vol. 51, Issue 4 https://doi.org/10.1103/PhysRevB.51.2363	journal	January 1995
Theory of strong inelastic cotunneling Furusaki, A.; Matveev, K. A. Physical Review B, Vol. 52, Issue 23 https://doi.org/10.1103/PhysRevB.52.16676	journal	December 1995
Exact nonequilibrium transport through point contacts in quantum wires and fractional quantum Hall devices Fendley, P.; Ludwig, A. W. W.; Saleur, H. Physical Review B, Vol. 52, Issue 12 https://doi.org/10.1103/PhysRevB.52.8934	journal	September 1995
Spin precession and real-time dynamics in the Kondo model: Time-dependent numerical renormalization-group study Anders, Frithjof B.; Schiller, Avraham Physical Review B, Vol. 74, Issue 24 https://doi.org/10.1103/PhysRevB.74.245113	journal	December 2006
Quantum phase transition in quantum dot trimers Mitchell, Andrew K.; Jarrold, Thomas F.; Logan, David E. Physical Review B, Vol. 79, Issue 8 https://doi.org/10.1103/PhysRevB.79.085124	journal	February 2009
Two-channel Kondo physics in tunnel-coupled double quantum dots Jayatilaka, Frederic W.; Galpin, Martin R.; Logan, David E. Physical Review B, Vol. 84, Issue 11 https://doi.org/10.1103/PhysRevB.84.115111	journal	September 2011
Universal low-temperature crossover in two-channel Kondo models Mitchell, Andrew K.; Sela, Eran Physical Review B, Vol. 85, Issue 23 https://doi.org/10.1103/PhysRevB.85.235127	journal	June 2012
Conductance fingerprint of Majorana fermions in the topological Kondo effect Galpin, Martin R.; Mitchell, Andrew K.; Temaismithi, Jesada Physical Review B, Vol. 89, Issue 4 https://doi.org/10.1103/PhysRevB.89.045143	journal	January 2014
Generalized Wilson chain for solving multichannel quantum impurity problems Mitchell, Andrew K.; Galpin, Martin R.; Wilson-Fletcher, Samuel Physical Review B, Vol. 89, Issue 12 https://doi.org/10.1103/PhysRevB.89.121105	journal	March 2014
Fermion fractionalization to Majorana fermions in a dimerized Kitaev superconductor Wakatsuki, Ryohei; Ezawa, Motohiko; Tanaka, Yukio Physical Review B, Vol. 90, Issue 1 https://doi.org/10.1103/PhysRevB.90.014505	journal	July 2014
Quantum computing with parafermions Hutter, Adrian; Loss, Daniel Physical Review B, Vol. 93, Issue 12 https://doi.org/10.1103/PhysRevB.93.125105	journal	March 2016
Interleaved numerical renormalization group as an efficient multiband impurity solver Stadler, K. M.; Mitchell, A. K.; von Delft, J. Physical Review B, Vol. 93, Issue 23 https://doi.org/10.1103/PhysRevB.93.235101	journal	June 2016
Nontopological parafermions in a one-dimensional fermionic model with even multiplet pairing Mazza, Leonardo; Iemini, Fernando; Dalmonte, Marcello Physical Review B, Vol. 98, Issue 20 https://doi.org/10.1103/PhysRevB.98.201109	journal	November 2018
Kondo Decoherence: Finding the Right Spin Model for Iron Impurities in Gold and Silver Costi, T. A.; Bergqvist, L.; Weichselbaum, A. Physical Review Letters, Vol. 102, Issue 5 https://doi.org/10.1103/PhysRevLett.102.056802	journal	February 2009
Observation of the Underscreened Kondo Effect in a Molecular Transistor Roch, Nicolas; Florens, Serge; Costi, Theo A. Physical Review Letters, Vol. 103, Issue 19 https://doi.org/10.1103/PhysRevLett.103.197202	journal	November 2009
Exact Crossover Green Function in the Two-Channel and Two-Impurity Kondo Models Sela, Eran; Mitchell, Andrew K.; Fritz, Lars Physical Review Letters, Vol. 106, Issue 14 https://doi.org/10.1103/PhysRevLett.106.147202	journal	April 2011
Two-Channel Kondo Physics in Two-Impurity Kondo Models Mitchell, Andrew K.; Sela, Eran; Logan, David E. Physical Review Letters, Vol. 108, Issue 8 https://doi.org/10.1103/PhysRevLett.108.086405	journal	February 2012
Topological Kondo Effect with Majorana Fermions Béri, B.; Cooper, N. R. Physical Review Letters, Vol. 109, Issue 15 https://doi.org/10.1103/PhysRevLett.109.156803	journal	October 2012
Parafermions in an Interacting Nanowire Bundle Klinovaja, Jelena; Loss, Daniel Physical Review Letters, Vol. 112, Issue 24 https://doi.org/10.1103/PhysRevLett.112.246403	journal	June 2014
Universality and Scaling in a Charge Two-Channel Kondo Device Mitchell, A. K.; Landau, L. A.; Fritz, L. Physical Review Letters, Vol. 116, Issue 15 https://doi.org/10.1103/PhysRevLett.116.157202	journal	April 2016
Exact Nonequilibrium Transport in the Topological Kondo Effect Béri, B. Physical Review Letters, Vol. 119, Issue 2 https://doi.org/10.1103/PhysRevLett.119.027701	journal	July 2017
Charge Fractionalization in the Two-Channel Kondo Effect Landau, L. Aviad; Cornfeld, Eyal; Sela, Eran Physical Review Letters, Vol. 120, Issue 18 https://doi.org/10.1103/PhysRevLett.120.186801	journal	May 2018
Detecting the Universal Fractional Entropy of Majorana Zero Modes Sela, Eran; Oreg, Yuval; Plugge, Stephan Physical Review Letters, Vol. 123, Issue 14 https://doi.org/10.1103/PhysRevLett.123.147702	journal	October 2019
SO(5) Non-Fermi Liquid in a Coulomb Box Device Mitchell, Andrew K.; Liberman, Alon; Sela, Eran Physical Review Letters, Vol. 126, Issue 14 https://doi.org/10.1103/PhysRevLett.126.147702	journal	April 2021
Fractional Entropy of Multichannel Kondo Systems from Conductance-Charge Relations Han, Cheolhee; Iftikhar, Z.; Kleeorin, Yaakov Physical Review Letters, Vol. 128, Issue 14 https://doi.org/10.1103/PhysRevLett.128.146803	journal	April 2022
Solvable 3D Kondo Lattice Exhibiting Pair Density Wave, Odd-Frequency Pairing, and Order Fractionalization Coleman, Piers; Panigrahi, Aaditya; Tsvelik, Alexei Physical Review Letters, Vol. 129, Issue 17 https://doi.org/10.1103/PhysRevLett.129.177601	journal	October 2022
Entropy Measurement of a Strongly Coupled Quantum Dot Child, Timothy; Sheekey, Owen; Lüscher, Silvia Physical Review Letters, Vol. 129, Issue 22 https://doi.org/10.1103/PhysRevLett.129.227702	journal	November 2022
Manipulating Non-Abelian Anyons in a Chiral Multichannel Kondo Model Lotem, Matan; Sela, Eran; Goldstein, Moshe Physical Review Letters, Vol. 129, Issue 22 https://doi.org/10.1103/PhysRevLett.129.227703	journal	November 2022
Solution of the Multichannel Kondo Problem Andrei, N.; Destri, C. Physical Review Letters, Vol. 52, Issue 5 https://doi.org/10.1103/PhysRevLett.52.364	journal	January 1984
Low-Temperature Properties of the Two-Impurity Kondo Hamiltonian Jones, B. A.; Varma, C. M.; Wilkins, J. W. Physical Review Letters, Vol. 61, Issue 1 https://doi.org/10.1103/PhysRevLett.61.125	journal	July 1988
Exact critical theory of the two-impurity Kondo model Affleck, Ian; Ludwig, Andreas W. W. Physical Review Letters, Vol. 68, Issue 7 https://doi.org/10.1103/PhysRevLett.68.1046	journal	February 1992
Mapping the Critical Point of the Two-Impurity Kondo Model to a Two-Channel Problem Gan, Junwu Physical Review Letters, Vol. 74, Issue 13 https://doi.org/10.1103/PhysRevLett.74.2583	journal	March 1995
Exact Conductance through Point Contacts in the ν = 1 / 3 Fractional Quantum Hall Effect Fendley, P.; Ludwig, A. W. W.; Saleur, H. Physical Review Letters, Vol. 74, Issue 15 https://doi.org/10.1103/PhysRevLett.74.3005	journal	April 1995
Two-Channel Kondo Effect in a Modified Single Electron Transistor Oreg, Yuval; Goldhaber-Gordon, David Physical Review Letters, Vol. 90, Issue 13 https://doi.org/10.1103/PhysRevLett.90.136602	journal	April 2003
SU(4) Kondo Effect in Carbon Nanotubes Choi, Manh-Soo; López, Rosa; Aguado, Ramón Physical Review Letters, Vol. 95, Issue 6 https://doi.org/10.1103/PhysRevLett.95.067204	journal	August 2005
Kondo Resonances and Anomalous Gate Dependence in the Electrical Conductivity of Single-Molecule Transistors Yu, L. H.; Keane, Z. K.; Ciszek, J. W. Physical Review Letters, Vol. 95, Issue 25 https://doi.org/10.1103/PhysRevLett.95.256803	journal	December 2005
Sum-Rule Conserving Spectral Functions from the Numerical Renormalization Group Weichselbaum, Andreas; von Delft, Jan Physical Review Letters, Vol. 99, Issue 7 https://doi.org/10.1103/PhysRevLett.99.076402	journal	August 2007
Interplay between Kondo and Majorana Interactions in Quantum Dots Cheng, Meng; Becker, Michael; Bauer, Bela Physical Review X, Vol. 4, Issue 3 https://doi.org/10.1103/PhysRevX.4.031051	journal	September 2014
The renormalization group: Critical phenomena and the Kondo problem Wilson, Kenneth G. Reviews of Modern Physics, Vol. 47, Issue 4 https://doi.org/10.1103/RevModPhys.47.773	journal	October 1975
Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions Georges, Antoine; Kotliar, Gabriel; Krauth, Werner Reviews of Modern Physics, Vol. 68, Issue 1 https://doi.org/10.1103/RevModPhys.68.13	journal	January 1996
Non-Abelian anyons and topological quantum computation Nayak, Chetan; Simon, Steven H.; Stern, Ady Reviews of Modern Physics, Vol. 80, Issue 3 https://doi.org/10.1103/RevModPhys.80.1083	journal	September 2008
Numerical renormalization group method for quantum impurity systems Bulla, Ralf; Costi, Theo A.; Pruschke, Thomas Reviews of Modern Physics, Vol. 80, Issue 2 https://doi.org/10.1103/RevModPhys.80.395	journal	April 2008
Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices Mourik, V.; Zuo, K.; Frolov, S. M. Science, Vol. 336, Issue 6084 https://doi.org/10.1126/science.1222360	journal	April 2012
Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor Nadj-Perge, S.; Drozdov, I. K.; Li, J. Science, Vol. 346, Issue 6209 https://doi.org/10.1126/science.1259327	journal	October 2014
A Tunable Kondo Effect in Quantum Dots Cronenwett, S. M. Science, Vol. 281, Issue 5376 https://doi.org/10.1126/science.281.5376.540	journal	July 1998
The Kondo Effect in the Unitary Limit van der Wiel, W. G. Science, Vol. 289, Issue 5487 https://doi.org/10.1126/science.289.5487.2105	journal	September 2000
Tunable quantum criticality and super-ballistic transport in a “charge” Kondo circuit Iftikhar, Z.; Anthore, A.; Mitchell, A. K. Science, Vol. 360, Issue 6395 https://doi.org/10.1126/science.aan5592	journal	May 2018
Resistance Minimum in Dilute Magnetic Alloys Kondo, J. Progress of Theoretical Physics, Vol. 32, Issue 1, p. 37-49 https://doi.org/10.1143/PTP.32.37	journal	July 1964
Topological Phases with Parafermions: Theory and Blueprints Alicea, Jason; Fendley, Paul Annual Review of Condensed Matter Physics, Vol. 7, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031115-011336	journal	March 2016

Figures / Tables (3)

FIG. 1(p. 1)

FIG. 2(p. 3)

FIG. 3(p. 5)

Similar Records

A unified framework for the Kondo problem and for an impurity in a Luttinger liquid

Journal Article · Tue Oct 01 00:00:00 EDT 1996 · Journal of Statistical Physics · OSTI ID:468378

Frustrated Ising charge correlations in the kagome metal ScV 6 Sn 6

Journal Article · Mon Oct 14 20:00:00 EDT 2024 · Physical Review. B · OSTI ID:2478328

Quantum solitons and their classical relatives: Bethe Ansatz states in soliton sectors of the Sine--Gordon System

Journal Article · Wed Mar 31 23:00:00 EST 1982 · Ann. Phys. (N.Y.); (United States) · OSTI ID:5192807

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS

Z3 Parafermion in the Double Charge Kondo Model

Citation Formats

References (79)

Figures / Tables (3)

Similar Records

Related Subjects