Quantum spin liquid in spin 1/2 J1-J2 Heisenberg model on square lattice

Many-variable variational Monte Carlo study combined with quantum-number projections

Satoshi Morita, Ryui Kaneko, Masatoshi Imada

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Abstract

The nature of quantum spin liquids is studied for the spin-1/2 antiferromagnetic Heisenberg model on a square lattice containing exchange interactions between nearest-neighbor sites, J1, and those between next-nearest-neighbor sites, J2. We perform variational Monte Carlo simulations together with the quantum-number-projection technique and clarify the phase diagram in the ground state together with its excitation spectra. We obtain the nonmagnetic phase in the region 0.4 < J2/J1 ≤ 0.6 sandwiched by the staggered and stripe antiferromagnetic (AF) phases. Our direct calculations of the spin gap support the notion that the triplet excitation from the singlet ground state is gapless in the range of 0.4 < J2/J1 ≤ 0.5, while the gapped valence-bond-crystal (VBC) phase is stabilized for 0.5 < J2/J1 ≤ 0.6. The VBC order is likely to have the columnar symmetry with a spontaneous symmetry breaking of the C4v symmetry. The power-law behaviors of the spin-spin and dimer-dimer correlation functions in the gapless region are consistent with the emergence of the algebraic quantum-spin-liquid phase (critical phase). The exponent of the spin correlation <S(0)S(r )i &∝ 1/rz+η at a long distance r appears to increase from z + η ∼ 1 at J2/J1 ∼ 0.4 toward the continuous transition to the VBC phase at J1/J1 ∼ 0.5. Our results, however, do not fully exclude the possibility of a direct quantum transition between the staggered AF and VBC phases with a wide critical region and deconfined criticality.

Original languageEnglish
Article number024720
JournalJournal of the Physical Society of Japan
Volume84
Issue number2
DOIs
Publication statusPublished - 2015 Feb 15
Externally publishedYes

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quantum numbers
projection
liquids
valence
crystals
dimers
ground state
symmetry
atomic energy levels
broken symmetry
liquid phases
phase diagrams
exponents
excitation
simulation
interactions

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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abstract = "The nature of quantum spin liquids is studied for the spin-1/2 antiferromagnetic Heisenberg model on a square lattice containing exchange interactions between nearest-neighbor sites, J1, and those between next-nearest-neighbor sites, J2. We perform variational Monte Carlo simulations together with the quantum-number-projection technique and clarify the phase diagram in the ground state together with its excitation spectra. We obtain the nonmagnetic phase in the region 0.4 < J2/J1 ≤ 0.6 sandwiched by the staggered and stripe antiferromagnetic (AF) phases. Our direct calculations of the spin gap support the notion that the triplet excitation from the singlet ground state is gapless in the range of 0.4 < J2/J1 ≤ 0.5, while the gapped valence-bond-crystal (VBC) phase is stabilized for 0.5 < J2/J1 ≤ 0.6. The VBC order is likely to have the columnar symmetry with a spontaneous symmetry breaking of the C4v symmetry. The power-law behaviors of the spin-spin and dimer-dimer correlation functions in the gapless region are consistent with the emergence of the algebraic quantum-spin-liquid phase (critical phase). The exponent of the spin correlation <S(0)S(r )i &∝ 1/rz+η at a long distance r appears to increase from z + η ∼ 1 at J2/J1 ∼ 0.4 toward the continuous transition to the VBC phase at J1/J1 ∼ 0.5. Our results, however, do not fully exclude the possibility of a direct quantum transition between the staggered AF and VBC phases with a wide critical region and deconfined criticality.",
author = "Satoshi Morita and Ryui Kaneko and Masatoshi Imada",
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T2 - Many-variable variational Monte Carlo study combined with quantum-number projections

AU - Morita, Satoshi

AU - Kaneko, Ryui

AU - Imada, Masatoshi

PY - 2015/2/15

Y1 - 2015/2/15

N2 - The nature of quantum spin liquids is studied for the spin-1/2 antiferromagnetic Heisenberg model on a square lattice containing exchange interactions between nearest-neighbor sites, J1, and those between next-nearest-neighbor sites, J2. We perform variational Monte Carlo simulations together with the quantum-number-projection technique and clarify the phase diagram in the ground state together with its excitation spectra. We obtain the nonmagnetic phase in the region 0.4 < J2/J1 ≤ 0.6 sandwiched by the staggered and stripe antiferromagnetic (AF) phases. Our direct calculations of the spin gap support the notion that the triplet excitation from the singlet ground state is gapless in the range of 0.4 < J2/J1 ≤ 0.5, while the gapped valence-bond-crystal (VBC) phase is stabilized for 0.5 < J2/J1 ≤ 0.6. The VBC order is likely to have the columnar symmetry with a spontaneous symmetry breaking of the C4v symmetry. The power-law behaviors of the spin-spin and dimer-dimer correlation functions in the gapless region are consistent with the emergence of the algebraic quantum-spin-liquid phase (critical phase). The exponent of the spin correlation <S(0)S(r )i &∝ 1/rz+η at a long distance r appears to increase from z + η ∼ 1 at J2/J1 ∼ 0.4 toward the continuous transition to the VBC phase at J1/J1 ∼ 0.5. Our results, however, do not fully exclude the possibility of a direct quantum transition between the staggered AF and VBC phases with a wide critical region and deconfined criticality.

AB - The nature of quantum spin liquids is studied for the spin-1/2 antiferromagnetic Heisenberg model on a square lattice containing exchange interactions between nearest-neighbor sites, J1, and those between next-nearest-neighbor sites, J2. We perform variational Monte Carlo simulations together with the quantum-number-projection technique and clarify the phase diagram in the ground state together with its excitation spectra. We obtain the nonmagnetic phase in the region 0.4 < J2/J1 ≤ 0.6 sandwiched by the staggered and stripe antiferromagnetic (AF) phases. Our direct calculations of the spin gap support the notion that the triplet excitation from the singlet ground state is gapless in the range of 0.4 < J2/J1 ≤ 0.5, while the gapped valence-bond-crystal (VBC) phase is stabilized for 0.5 < J2/J1 ≤ 0.6. The VBC order is likely to have the columnar symmetry with a spontaneous symmetry breaking of the C4v symmetry. The power-law behaviors of the spin-spin and dimer-dimer correlation functions in the gapless region are consistent with the emergence of the algebraic quantum-spin-liquid phase (critical phase). The exponent of the spin correlation <S(0)S(r )i &∝ 1/rz+η at a long distance r appears to increase from z + η ∼ 1 at J2/J1 ∼ 0.4 toward the continuous transition to the VBC phase at J1/J1 ∼ 0.5. Our results, however, do not fully exclude the possibility of a direct quantum transition between the staggered AF and VBC phases with a wide critical region and deconfined criticality.

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