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Title: 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 » 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.« less

Authors:
 [1];  [2];  [3]
  1. Univ. Nacional de Rosario and Instituto de Fisica Rosario, Rosario (Argentina); Univ. of Maryland, College Park, MD (United States)
  2. Univ. Nacional de Rosario and Instituto de Fisica Rosario, Rosario (Argentina)
  3. Univ. of Maryland, College Park, MD (United States); Monash Univ., Melbourne, VIC (Australia)
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 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}
}

Journal Article:
Free Publicly Available Full Text
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https://doi.org/10.1103/PhysRevX.5.021017

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Cited by: 14 works
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Works referenced in this record:

Topological Kondo Insulators
journal, March 2010


Rigorous results on valence-bond ground states in antiferromagnets
journal, August 1987


Field Theories of Condensed Matter Physics
book, January 2013


Topological insulators and superconductors
journal, October 2011


Spin Gap in a Doped Kondo Chain
journal, August 1997


Time reversal polarization and a Z 2 adiabatic spin pump
journal, November 2006


Quantum phase diagram of the half filled Hubbard model with bond-charge interaction
journal, February 2011


Quantum Spin Hall Insulator State in HgTe Quantum Wells
journal, November 2007


New approach to the mixed-valence problem
journal, March 1984


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
  • DOI: 10.1038/ncomms3991

Antiferromagnetic spin ladders: Crossover between spin S =1/2 and S =1 chains
journal, April 1996


Mean-field theory of intermediate valence/heavy fermion systems
journal, January 1987


Dimerized phase of ionic Hubbard models
journal, March 2005


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
  • DOI: 10.1038/nature06843

Finite wave vector pairing in doped two-leg ladders
journal, May 2012


On the solution of the Coqblin-Schreiffer Hamiltonian by the large-N expansion technique
journal, June 1983


Zero-modes and thermodynamics of disordered ladders
journal, February 1999


Scaling and Renormalization in Statistical Physics
book, January 2015


Low-temperature surface conduction in the Kondo insulator SmB 6
journal, November 2013


Topological Insulators and Topological Superconductors
book, January 2013


Z2classification of quantum spin Hall systems: An approach using time-reversal invariance
journal, May 2009


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
  • DOI: 10.1063/1.3149495

Evidence for Helical Edge Modes in Inverted InAs / GaSb Quantum Wells
journal, September 2011


Bosonization for beginners - refermionization for experts
journal, November 1998


Electron Localization in the Insulating State
journal, January 1999


Mixed valence as an almost broken symmetry
journal, April 1987


Hybridization, Inter-Ion Correlation, and Surface States in the Kondo Insulator SmB 6
journal, February 2013


Low-energy effective theories of the two-thirds filled Hubbard model on the triangular necklace lattice
journal, July 2014


Inhomogeneous superconducting phases in the frustrated Kondo-Heisenberg chain
journal, June 2013


Topological insulators and superconductors: tenfold way and dimensional hierarchy
journal, June 2010


End states in a one-dimensional topological Kondo insulator in large- N limit
journal, September 2014


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
  • DOI: 10.1103/PhysRevB.46.3175

Hopes surface for exotic insulator
journal, December 2012


Exact Results for a 1D Kondo Lattice from Bosonization
journal, August 1996


Images of Edge Current in InAs / GaSb Quantum Wells
journal, July 2014


Haldane Phase in the Hubbard Model at 2/3-Filling for the Organic Molecular Compound Mo 3 S 7 ( dmit ) 3
journal, December 2014


Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order
journal, October 2009


New method for the Anderson model
journal, July 1976


Hidden Z 2 × Z 2 symmetry breaking in Haldane-gap antiferromagnets
journal, January 1992


Z2 Topological Order and the Quantum Spin Hall Effect
journal, September 2005


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
  • DOI: 10.1038/srep03150

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
  • DOI: 10.1038/nphys2128

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
  • DOI: 10.1038/ncomms2523

Rise and fall of hidden string order of lattice bosons
journal, June 2008


Quantum Spin Hall Effect in Graphene
journal, November 2005


Colloquium: Topological insulators
journal, November 2010


Schwinger-boson mean-field theory for S=1 open spin chains
journal, April 1992


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
  • DOI: 10.1038/nphys1274

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
  • DOI: 10.1038/nmat3682

Pair-Density-Wave Correlations in the Kondo-Heisenberg Model
journal, September 2010


Topological Insulators in Three Dimensions
journal, March 2007


On the Surface States Associated with a Periodic Potential
journal, August 1939


Spin Order in One-Dimensional Kondo and Hund Lattices
journal, October 2004


Edge states in antiferromagnetic quantum spin chains
journal, July 1994


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
  • DOI: 10.1038/nphys1857

Magnetization and dimerization profiles of the cut two-leg spin ladder
journal, April 2002


Entanglement spectrum of a topological phase in one dimension
journal, February 2010


Staggered liquid phases of the one-dimensional Kondo-Heisenberg lattice model
journal, April 2001


Topological invariants of time-reversal-invariant band structures
journal, March 2007


One-dimensional electron gas interacting with a Heisenberg spin-1/2 chain
journal, June 2001


Shockley model description of surface states in topological insulators
journal, August 2012


Macroscopic polarization as a geometric quantum phase: Many-body formulation
journal, May 1994


Interaction Driven Subgap Spin Exciton in the Kondo Insulator SmB 6
journal, January 2015


Topological Pair-Density-Wave Superconducting States
journal, December 2014


Quantum phase diagram of the generalized ionic Hubbard model for AB n chains
journal, March 2006


Berry phase effects on electronic properties
journal, July 2010


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
  • DOI: 10.1007/BF01218021

Symmetry protection of topological phases in one-dimensional quantum spin systems
journal, February 2012


Works referencing / citing this record:

Symmetry-protected topological phase transition in one-dimensional Kondo lattice and its realization with ultracold atoms
journal, October 2017


Kramers doublet ground state in topological Kondo insulators
journal, February 2019


Kramers' doublet ground state in topological Kondo insulators
text, January 2018