Resonating quantum three-coloring wave functions for the kagome quantum antiferromagnet

Hitesh J. Changlani, Sumiran Pujari, Chia Min Chung, Bryan K. Clark

Research output: Contribution to journalArticle

Abstract

Motivated by the recent discovery of a macroscopically degenerate exactly solvable point of the spin-1/2XXZ model for Jz/J=-1/2 on the kagome lattice [H. J. Changlani Phys. Rev. Lett. 120, 117202 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.117202] - a result that holds for arbitrary magnetization - we develop an exact mapping between its exact "quantum three-coloring" wave functions and the characteristic localized and topological magnons. This map, involving "resonating two-color loops," is developed to represent exact many-body ground state wave functions for special high magnetizations. Using this map we show that these exact ground state solutions are valid for any Jz/J≥-1/2. This demonstrates the equivalence of the ground-state wave function of the Ising, Heisenberg, and XY regimes all the way to the Jz/J=-1/2 point for these high magnetization sectors. In the hardcore bosonic language, this means that a certain class of exact many-body solutions, previously argued to hold for purely repulsive interactions (Jz≥0), actually hold for attractive interactions as well, up to a critical interaction strength. For the case of zero magnetization, where the ground state is not exactly known, we perform density matrix renormalization group calculations. Based on the calculation of the ground state energy and measurement of order parameters, we provide evidence for a lack of any qualitative change in the ground state on finite clusters in the Ising (Jz J), Heisenberg (Jz=J), and XY (Jz=0) regimes, continuing adiabatically to the vicinity of the macroscopically degenerate Jz/J=-1/2 point. These findings offer a framework for recent results in the literature and also suggest that the Jz/J=-1/2 point is an unconventional quantum critical point whose vicinity may contain the key to resolving the spin-1/2 kagome problem.

Original languageEnglish (US)
Article number104433
JournalPhysical Review B
Volume99
Issue number10
DOIs
StatePublished - Mar 27 2019

Fingerprint

Coloring
Wave functions
Ground state
wave functions
ground state
Magnetization
magnetization
interactions
magnons
equivalence
critical point
sectors
Color
color

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Resonating quantum three-coloring wave functions for the kagome quantum antiferromagnet. / Changlani, Hitesh J.; Pujari, Sumiran; Chung, Chia Min; Clark, Bryan K.

In: Physical Review B, Vol. 99, No. 10, 104433, 27.03.2019.

Research output: Contribution to journalArticle

Changlani, Hitesh J. ; Pujari, Sumiran ; Chung, Chia Min ; Clark, Bryan K. / Resonating quantum three-coloring wave functions for the kagome quantum antiferromagnet. In: Physical Review B. 2019 ; Vol. 99, No. 10.
@article{48854af80fbe45b8b51f24ed238e09dd,
title = "Resonating quantum three-coloring wave functions for the kagome quantum antiferromagnet",
abstract = "Motivated by the recent discovery of a macroscopically degenerate exactly solvable point of the spin-1/2XXZ model for Jz/J=-1/2 on the kagome lattice [H. J. Changlani Phys. Rev. Lett. 120, 117202 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.117202] - a result that holds for arbitrary magnetization - we develop an exact mapping between its exact {"}quantum three-coloring{"} wave functions and the characteristic localized and topological magnons. This map, involving {"}resonating two-color loops,{"} is developed to represent exact many-body ground state wave functions for special high magnetizations. Using this map we show that these exact ground state solutions are valid for any Jz/J≥-1/2. This demonstrates the equivalence of the ground-state wave function of the Ising, Heisenberg, and XY regimes all the way to the Jz/J=-1/2 point for these high magnetization sectors. In the hardcore bosonic language, this means that a certain class of exact many-body solutions, previously argued to hold for purely repulsive interactions (Jz≥0), actually hold for attractive interactions as well, up to a critical interaction strength. For the case of zero magnetization, where the ground state is not exactly known, we perform density matrix renormalization group calculations. Based on the calculation of the ground state energy and measurement of order parameters, we provide evidence for a lack of any qualitative change in the ground state on finite clusters in the Ising (Jz J), Heisenberg (Jz=J), and XY (Jz=0) regimes, continuing adiabatically to the vicinity of the macroscopically degenerate Jz/J=-1/2 point. These findings offer a framework for recent results in the literature and also suggest that the Jz/J=-1/2 point is an unconventional quantum critical point whose vicinity may contain the key to resolving the spin-1/2 kagome problem.",
author = "Changlani, {Hitesh J.} and Sumiran Pujari and Chung, {Chia Min} and Clark, {Bryan K.}",
year = "2019",
month = "3",
day = "27",
doi = "10.1103/PhysRevB.99.104433",
language = "English (US)",
volume = "99",
journal = "Physical Review B",
issn = "2469-9950",
publisher = "American Physical Society",
number = "10",

}

TY - JOUR

T1 - Resonating quantum three-coloring wave functions for the kagome quantum antiferromagnet

AU - Changlani, Hitesh J.

AU - Pujari, Sumiran

AU - Chung, Chia Min

AU - Clark, Bryan K.

PY - 2019/3/27

Y1 - 2019/3/27

N2 - Motivated by the recent discovery of a macroscopically degenerate exactly solvable point of the spin-1/2XXZ model for Jz/J=-1/2 on the kagome lattice [H. J. Changlani Phys. Rev. Lett. 120, 117202 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.117202] - a result that holds for arbitrary magnetization - we develop an exact mapping between its exact "quantum three-coloring" wave functions and the characteristic localized and topological magnons. This map, involving "resonating two-color loops," is developed to represent exact many-body ground state wave functions for special high magnetizations. Using this map we show that these exact ground state solutions are valid for any Jz/J≥-1/2. This demonstrates the equivalence of the ground-state wave function of the Ising, Heisenberg, and XY regimes all the way to the Jz/J=-1/2 point for these high magnetization sectors. In the hardcore bosonic language, this means that a certain class of exact many-body solutions, previously argued to hold for purely repulsive interactions (Jz≥0), actually hold for attractive interactions as well, up to a critical interaction strength. For the case of zero magnetization, where the ground state is not exactly known, we perform density matrix renormalization group calculations. Based on the calculation of the ground state energy and measurement of order parameters, we provide evidence for a lack of any qualitative change in the ground state on finite clusters in the Ising (Jz J), Heisenberg (Jz=J), and XY (Jz=0) regimes, continuing adiabatically to the vicinity of the macroscopically degenerate Jz/J=-1/2 point. These findings offer a framework for recent results in the literature and also suggest that the Jz/J=-1/2 point is an unconventional quantum critical point whose vicinity may contain the key to resolving the spin-1/2 kagome problem.

AB - Motivated by the recent discovery of a macroscopically degenerate exactly solvable point of the spin-1/2XXZ model for Jz/J=-1/2 on the kagome lattice [H. J. Changlani Phys. Rev. Lett. 120, 117202 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.117202] - a result that holds for arbitrary magnetization - we develop an exact mapping between its exact "quantum three-coloring" wave functions and the characteristic localized and topological magnons. This map, involving "resonating two-color loops," is developed to represent exact many-body ground state wave functions for special high magnetizations. Using this map we show that these exact ground state solutions are valid for any Jz/J≥-1/2. This demonstrates the equivalence of the ground-state wave function of the Ising, Heisenberg, and XY regimes all the way to the Jz/J=-1/2 point for these high magnetization sectors. In the hardcore bosonic language, this means that a certain class of exact many-body solutions, previously argued to hold for purely repulsive interactions (Jz≥0), actually hold for attractive interactions as well, up to a critical interaction strength. For the case of zero magnetization, where the ground state is not exactly known, we perform density matrix renormalization group calculations. Based on the calculation of the ground state energy and measurement of order parameters, we provide evidence for a lack of any qualitative change in the ground state on finite clusters in the Ising (Jz J), Heisenberg (Jz=J), and XY (Jz=0) regimes, continuing adiabatically to the vicinity of the macroscopically degenerate Jz/J=-1/2 point. These findings offer a framework for recent results in the literature and also suggest that the Jz/J=-1/2 point is an unconventional quantum critical point whose vicinity may contain the key to resolving the spin-1/2 kagome problem.

UR - http://www.scopus.com/inward/record.url?scp=85064136599&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064136599&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.99.104433

DO - 10.1103/PhysRevB.99.104433

M3 - Article

AN - SCOPUS:85064136599

VL - 99

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 10

M1 - 104433

ER -