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}
}
https://doi.org/10.1103/PhysRevX.5.021017
Web of Science
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