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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-1/2 XXZ model for Jz/J = –1/2 on the kagome lattice —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 anymore » 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. Furthermore, 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.« less

Authors:
 [1];  [2];  [3];  [4]
+ Show Author Affiliations
  1. Florida State Univ., Tallahassee, FL (United States); National High Magnetic Field Lab., Tallahassee, FL (United States); Johns Hopkins Univ., Baltimore, MD (United States)
  2. Indian Inst. of Technology Bombay, Mumbai (India)
  3. Ludwig-Maximilians-Univ. Munchen (Germany)
  4. Univ. of Illinois at Urbana-Champaign, IL (United States)
Publication Date:
Research Org.:
Johns Hopkins Univ., Baltimore, MD (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1610024
Grant/Contract Number:  
FG02-08ER46544
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 99; Journal Issue: 10; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; materials science; physics; frustrated magnetism

Citation Formats

Changlani, Hitesh J., Pujari, Sumiran, Chung, Chia-Min, and Clark, Bryan K. Resonating quantum three-coloring wave functions for the kagome quantum antiferromagnet. United States: N. p., 2019. Web. doi:10.1103/physrevb.99.104433.
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Changlani, Hitesh J., Pujari, Sumiran, Chung, Chia-Min, & Clark, Bryan K. Resonating quantum three-coloring wave functions for the kagome quantum antiferromagnet. United States. https://doi.org/10.1103/physrevb.99.104433
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Changlani, Hitesh J., Pujari, Sumiran, Chung, Chia-Min, and Clark, Bryan K. Wed . "Resonating quantum three-coloring wave functions for the kagome quantum antiferromagnet". United States. https://doi.org/10.1103/physrevb.99.104433. https://www.osti.gov/servlets/purl/1610024.
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@article{osti_1610024,
title = {Resonating quantum three-coloring wave functions for the kagome quantum antiferromagnet},
author = {Changlani, Hitesh J. and Pujari, Sumiran and Chung, Chia-Min and Clark, Bryan K.},
abstractNote = {Motivated by the recent discovery of a macroscopically degenerate exactly solvable point of the spin-1/2 XXZ model for Jz/J = –1/2 on the kagome lattice —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. Furthermore, 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.},
doi = {10.1103/physrevb.99.104433},
journal = {Physical Review B},
number = 10,
volume = 99,
place = {United States},
year = {Wed Mar 27 00:00:00 EDT 2019},
month = {Wed Mar 27 00:00:00 EDT 2019}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1103/physrevb.99.104433
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Cited by: 15 works
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Figures / Tables:

Figure 1 Figure 1: Two representative three-colorings on the kagome lattice corresponding to the q = 0 and $\sqrt{3}$ × $\sqrt{3}$ solutions. The colors red, blue and green represent the classical 120° states or their quantum equivalents.
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    Works referencing / citing this record:

    Topological approach to quantum liquid ground states on geometrically frustrated Heisenberg antiferromagnets
    journal, January 2020

    • Pal, Santanu; Mukherjee, Anirban; Lal, Siddhartha
    • Journal of Physics: Condensed Matter, Vol. 32, Issue 16
    • DOI: 10.1088/1361-648x/ab670f
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      Figures / Tables found in this record:

      Figure 1 (p. 3)figure
      Figure 2 (p. 4)figure
      Figure 3 (p. 6)figure
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      Figure 5 (p. 7)figure
      Figure 6 (p. 7)figure
      Figure 7 (p. 8)figure
      Figure 8 (p. 9)figure
      Figure 9 (p. 9)figure
      Figure 10 (p. 10)figure
      Figure 11 (p. 13)figure
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