Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator
Abstract
Topological Kondo insulators are strongly correlated materials where itinerant electrons hybridize with localized spins, giving rise to a topologically nontrivial band structure. Here, we use nonperturbative bosonization and renormalization-group techniques to study theoretically a one-dimensional topological Kondo insulator, described as a Kondo-Heisenberg model, where the Heisenberg spin-1/2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p-wave channel (i.e., a strongly correlated version of the prototypical Tamm-Schockley model).We derive and solve renormalization-group equations at two-loop order in the Kondo parameter, and find that, at half filling, the charge degrees of freedom in the Hubbard chain acquire a Mott gap, even in the case of a noninteracting conduction band (Hubbard parameter U = 0). Furthermore, at low enough temperatures, the system maps onto a spin-1/2 ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-1 chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-1/2 end states for chains with open boundary conditions. In conclusion, our analysis allows us to derive an insightful connection between topological Kondo insulators in one spatial dimensionmore »
- Authors:
- Publication Date:
- Research Org.:
- Univ. of Maryland, College Park, MD (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1182821
- Alternate Identifier(s):
- OSTI ID: 1452836
- Grant/Contract Number:
- SC0001911
- Resource Type:
- Published Article
- Journal Name:
- Physical Review. X
- Additional Journal Information:
- Journal Name: Physical Review. X Journal Volume: 5 Journal Issue: 2; Journal ID: ISSN 2160-3308
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Lobos, Alejandro M., Dobry, Ariel O., and Galitski, Victor. Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator. United States: N. p., 2015.
Web. doi:10.1103/PhysRevX.5.021017.
Lobos, Alejandro M., Dobry, Ariel O., & Galitski, Victor. Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator. United States. https://doi.org/10.1103/PhysRevX.5.021017
Lobos, Alejandro M., Dobry, Ariel O., and Galitski, Victor. Fri .
"Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator". United States. https://doi.org/10.1103/PhysRevX.5.021017.
@article{osti_1182821,
title = {Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator},
author = {Lobos, Alejandro M. and Dobry, Ariel O. and Galitski, Victor},
abstractNote = {Topological Kondo insulators are strongly correlated materials where itinerant electrons hybridize with localized spins, giving rise to a topologically nontrivial band structure. Here, we use nonperturbative bosonization and renormalization-group techniques to study theoretically a one-dimensional topological Kondo insulator, described as a Kondo-Heisenberg model, where the Heisenberg spin-1/2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p-wave channel (i.e., a strongly correlated version of the prototypical Tamm-Schockley model).We derive and solve renormalization-group equations at two-loop order in the Kondo parameter, and find that, at half filling, the charge degrees of freedom in the Hubbard chain acquire a Mott gap, even in the case of a noninteracting conduction band (Hubbard parameter U = 0). Furthermore, at low enough temperatures, the system maps onto a spin-1/2 ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-1 chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-1/2 end states for chains with open boundary conditions. In conclusion, our analysis allows us to derive an insightful connection between topological Kondo insulators in one spatial dimension and the well-known physics of the Haldane chain, showing that the ground state of the former is qualitatively different from the predictions of the naive mean-field theory.},
doi = {10.1103/PhysRevX.5.021017},
journal = {Physical Review. X},
number = 2,
volume = 5,
place = {United States},
year = {2015},
month = {5}
}
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevX.5.021017
https://doi.org/10.1103/PhysRevX.5.021017
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 6 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Topological Kondo Insulators
journal, March 2010
- Dzero, Maxim; Sun, Kai; Galitski, Victor
- Physical Review Letters, Vol. 104, Issue 10
Rigorous results on valence-bond ground states in antiferromagnets
journal, August 1987
- Affleck, Ian; Kennedy, Tom; Lieb, Elliott H.
- Physical Review Letters, Vol. 59, Issue 7
Topological insulators and superconductors
journal, October 2011
- Qi, Xiao-Liang; Zhang, Shou-Cheng
- Reviews of Modern Physics, Vol. 83, Issue 4
Spin Gap in a Doped Kondo Chain
journal, August 1997
- Sikkema, Arnold E.; Affleck, Ian; White, Steven R.
- Physical Review Letters, Vol. 79, Issue 5
Time reversal polarization and a adiabatic spin pump
journal, November 2006
- Fu, Liang; Kane, C. L.
- Physical Review B, Vol. 74, Issue 19
Quantum phase diagram of the half filled Hubbard model with bond-charge interaction
journal, February 2011
- Dobry, A. O.; Aligia, A. A.
- Nuclear Physics B, Vol. 843, Issue 3
Quantum Spin Hall Insulator State in HgTe Quantum Wells
journal, November 2007
- Konig, M.; Wiedmann, S.; Brune, C.
- Science, Vol. 318, Issue 5851, p. 766-770
New approach to the mixed-valence problem
journal, March 1984
- Coleman, Piers
- Physical Review B, Vol. 29, Issue 6
Surface electronic structure of the topological Kondo-insulator candidate correlated electron system SmB6
journal, December 2013
- Neupane, M.; Alidoust, N.; Xu, S-Y.
- Nature Communications, Vol. 4, Issue 1
Antiferromagnetic spin ladders: Crossover between spin S =1/2 and S =1 chains
journal, April 1996
- Shelton, D. G.; Nersesyan, A. A.; Tsvelik, A. M.
- Physical Review B, Vol. 53, Issue 13
Mean-field theory of intermediate valence/heavy fermion systems
journal, January 1987
- Newns, D. M.; Read, N.
- Advances in Physics, Vol. 36, Issue 6
Dimerized phase of ionic Hubbard models
journal, March 2005
- Aligia, A. A.; Batista, C. D.
- Physical Review B, Vol. 71, Issue 12
A topological Dirac insulator in a quantum spin Hall phase
journal, April 2008
- Hsieh, D.; Qian, D.; Wray, L.
- Nature, Vol. 452, Issue 7190, p. 970-974
Finite wave vector pairing in doped two-leg ladders
journal, May 2012
- Robinson, N. J.; Essler, F. H. L.; Jeckelmann, E.
- Physical Review B, Vol. 85, Issue 19
On the solution of the Coqblin-Schreiffer Hamiltonian by the large-N expansion technique
journal, June 1983
- Read, N.; Newns, D. M.
- Journal of Physics C: Solid State Physics, Vol. 16, Issue 17
Zero-modes and thermodynamics of disordered ladders
journal, February 1999
- Gogolin, Alexander O.; Nersesyan, Alexander A.; Tsvelik, Alexei M.
- Nuclear Physics B, Vol. 540, Issue 3
Low-temperature surface conduction in the Kondo insulator SmB
journal, November 2013
- Wolgast, Steven; Kurdak, Çağlıyan; Sun, Kai
- Physical Review B, Vol. 88, Issue 18
classification of quantum spin Hall systems: An approach using time-reversal invariance
journal, May 2009
- Roy, Rahul
- Physical Review B, Vol. 79, Issue 19, Article No. 195321
Periodic table for topological insulators and superconductors
conference, January 2009
- Kitaev, Alexei; Lebedev, Vladimir; Feigel’man, Mikhail
- ADVANCES IN THEORETICAL PHYSICS: Landau Memorial Conference, AIP Conference Proceedings
Evidence for Helical Edge Modes in Inverted Quantum Wells
journal, September 2011
- Knez, Ivan; Du, Rui-Rui; Sullivan, Gerard
- Physical Review Letters, Vol. 107, Issue 13
Bosonization for beginners - refermionization for experts
journal, November 1998
- von Delft, Jan; Schoeller, Herbert
- Annalen der Physik, Vol. 7, Issue 4
Electron Localization in the Insulating State
journal, January 1999
- Resta, Raffaele; Sorella, Sandro
- Physical Review Letters, Vol. 82, Issue 2
Mixed valence as an almost broken symmetry
journal, April 1987
- Coleman, Piers
- Physical Review B, Vol. 35, Issue 10
Hybridization, Inter-Ion Correlation, and Surface States in the Kondo Insulator
journal, February 2013
- Zhang, Xiaohang; Butch, N. P.; Syers, P.
- Physical Review X, Vol. 3, Issue 1
Edge states in Schwinger-boson mean-field theory of low-dimensional quantum antiferromagnets
journal, May 1993
- Ng, T. K.
- Physical Review B, Vol. 47, Issue 17
Low-energy effective theories of the two-thirds filled Hubbard model on the triangular necklace lattice
journal, July 2014
- Janani, C.; Merino, J.; McCulloch, Ian P.
- Physical Review B, Vol. 90, Issue 3
Inhomogeneous superconducting phases in the frustrated Kondo-Heisenberg chain
journal, June 2013
- Dobry, Ariel; Jaefari, Akbar; Fradkin, Eduardo
- Physical Review B, Vol. 87, Issue 24
Topological insulators and superconductors: tenfold way and dimensional hierarchy
journal, June 2010
- Ryu, Shinsei; Schnyder, Andreas P.; Furusaki, Akira
- New Journal of Physics, Vol. 12, Issue 6
End states in a one-dimensional topological Kondo insulator in large- limit
journal, September 2014
- Alexandrov, Victor; Coleman, Piers
- Physical Review B, Vol. 90, Issue 11
Spin-liquid ground state of the half-filled Kondo lattice in one dimension
journal, August 1992
- Tsunetsugu, Hirokazu; Hatsugai, Yasuhiro; Ueda, Kazuo
- Physical Review B, Vol. 46, Issue 5
Hopes surface for exotic insulator
journal, December 2012
- Samuel Reich, Eugenie
- Nature, Vol. 492, Issue 7428
Exact Results for a 1D Kondo Lattice from Bosonization
journal, August 1996
- Zachar, Oron; Kivelson, S. A.; Emery, V. J.
- Physical Review Letters, Vol. 77, Issue 7
Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State
journal, April 1983
- Haldane, F. D. M.
- Physical Review Letters, Vol. 50, Issue 15
Images of Edge Current in Quantum Wells
journal, July 2014
- Spanton, Eric M.; Nowack, Katja C.; Du, Lingjie
- Physical Review Letters, Vol. 113, Issue 2
Haldane Phase in the Hubbard Model at 2/3-Filling for the Organic Molecular Compound
journal, December 2014
- Janani, C.; Merino, J.; McCulloch, I. P.
- Physical Review Letters, Vol. 113, Issue 26
Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order
journal, October 2009
- Gu, Zheng-Cheng; Wen, Xiao-Gang
- Physical Review B, Vol. 80, Issue 15
New method for the Anderson model
journal, July 1976
- Barnes, S. E.
- Journal of Physics F: Metal Physics, Vol. 6, Issue 7
Hidden × symmetry breaking in Haldane-gap antiferromagnets
journal, January 1992
- Kennedy, Tom; Tasaki, Hal
- Physical Review B, Vol. 45, Issue 1
Topological Order and the Quantum Spin Hall Effect
journal, September 2005
- Kane, C. L.; Mele, E. J.
- Physical Review Letters, Vol. 95, Issue 14, Article No. 146802
Surface Hall Effect and Nonlocal Transport in SmB6: Evidence for Surface Conduction
journal, November 2013
- Kim, D. J.; Thomas, S.; Grant, T.
- Scientific Reports, Vol. 3, Issue 1
Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices
journal, October 2011
- Soltan-Panahi, Parvis; Lühmann, Dirk-Sören; Struck, Julian
- Nature Physics, Vol. 8, Issue 1
Topological states in a ladder-like optical lattice containing ultracold atoms in higher orbital bands
journal, February 2013
- Li, Xiaopeng; Zhao, Erhai; Vincent Liu, W.
- Nature Communications, Vol. 4, Issue 1
Rise and fall of hidden string order of lattice bosons
journal, June 2008
- Berg, Erez; Dalla Torre, Emanuele G.; Giamarchi, Thierry
- Physical Review B, Vol. 77, Issue 24
Quantum Spin Hall Effect in Graphene
journal, November 2005
- Kane, C. L.; Mele, E. J.
- Physical Review Letters, Vol. 95, Issue 22
Colloquium: Topological insulators
journal, November 2010
- Hasan, M. Z.; Kane, C. L.
- Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067
Schwinger-boson mean-field theory for S=1 open spin chains
journal, April 1992
- Ng, T.
- Physical Review B, Vol. 45, Issue 14
Observation of a large-gap topological-insulator class with a single Dirac cone on the surface
journal, May 2009
- Xia, Y.; Qian, D.; Hsieh, D.
- Nature Physics, Vol. 5, Issue 6, p. 398-402
Imaging currents in HgTe quantum wells in the quantum spin Hall regime
journal, June 2013
- Nowack, Katja C.; Spanton, Eric M.; Baenninger, Matthias
- Nature Materials, Vol. 12, Issue 9
Pair-Density-Wave Correlations in the Kondo-Heisenberg Model
journal, September 2010
- Berg, Erez; Fradkin, Eduardo; Kivelson, Steven A.
- Physical Review Letters, Vol. 105, Issue 14
Topological Insulators in Three Dimensions
journal, March 2007
- Fu, Liang; Kane, C. L.; Mele, E. J.
- Physical Review Letters, Vol. 98, Issue 10, Article No. 106803
On the Surface States Associated with a Periodic Potential
journal, August 1939
- Shockley, William
- Physical Review, Vol. 56, Issue 4
Spin Order in One-Dimensional Kondo and Hund Lattices
journal, October 2004
- Garcia, D. J.; Hallberg, K.; Alascio, B.
- Physical Review Letters, Vol. 93, Issue 17
Edge states in antiferromagnetic quantum spin chains
journal, July 1994
- Ng, Tai-Kai
- Physical Review B, Vol. 50, Issue 1
Evidence for orbital superfluidity in the P-band of a bipartite optical square lattice
journal, December 2010
- Wirth, Georg; Ölschläger, Matthias; Hemmerich, Andreas
- Nature Physics, Vol. 7, Issue 2
Magnetization and dimerization profiles of the cut two-leg spin ladder
journal, April 2002
- Lecheminant, P.; Orignac, E.
- Physical Review B, Vol. 65, Issue 17
Entanglement spectrum of a topological phase in one dimension
journal, February 2010
- Pollmann, Frank; Turner, Ari M.; Berg, Erez
- Physical Review B, Vol. 81, Issue 6
Staggered liquid phases of the one-dimensional Kondo-Heisenberg lattice model
journal, April 2001
- Zachar, Oron
- Physical Review B, Vol. 63, Issue 20
Topological invariants of time-reversal-invariant band structures
journal, March 2007
- Moore, J. E.; Balents, L.
- Physical Review B, Vol. 75, Issue 12, Article No. 121306(R)
One-dimensional electron gas interacting with a Heisenberg spin-1/2 chain
journal, June 2001
- Zachar, Oron; Tsvelik, Alexei M.
- Physical Review B, Vol. 64, Issue 3
Shockley model description of surface states in topological insulators
journal, August 2012
- Pershoguba, Sergey S.; Yakovenko, Victor M.
- Physical Review B, Vol. 86, Issue 7
Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model
journal, February 1983
- Haldane, F. D. M.
- Physics Letters A, Vol. 93, Issue 9
Macroscopic polarization as a geometric quantum phase: Many-body formulation
journal, May 1994
- Ortiz, Gerardo; Martin, Richard M.
- Physical Review B, Vol. 49, Issue 20
Interaction Driven Subgap Spin Exciton in the Kondo Insulator
journal, January 2015
- Fuhrman, W. T.; Leiner, J.; Nikolić, P.
- Physical Review Letters, Vol. 114, Issue 3
Topological Pair-Density-Wave Superconducting States
journal, December 2014
- Cho, Gil Young; Soto-Garrido, Rodrigo; Fradkin, Eduardo
- Physical Review Letters, Vol. 113, Issue 25
Quantum phase diagram of the generalized ionic Hubbard model for chains
journal, March 2006
- Torio, M. E.; Aligia, A. A.; Japaridze, G. I.
- Physical Review B, Vol. 73, Issue 11
Berry phase effects on electronic properties
journal, July 2010
- Xiao, Di; Chang, Ming-Che; Niu, Qian
- Reviews of Modern Physics, Vol. 82, Issue 3
Valence bond ground states in isotropic quantum antiferromagnets
journal, September 1988
- Affleck, Ian; Kennedy, Tom; Lieb, Elliott H.
- Communications in Mathematical Physics, Vol. 115, Issue 3
Symmetry protection of topological phases in one-dimensional quantum spin systems
journal, February 2012
- Pollmann, Frank; Berg, Erez; Turner, Ari M.
- Physical Review B, Vol. 85, Issue 7