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Gapped spin liquid phase in the J1-J2 Heisenberg model by a Bosonic resonating valence-bond ansatz
Strongly Correlated Electrons · Submitted 17 May 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In contrast to the RVB ansatz based on Schwinger Fermions, the representation based on Schwinger Bosons, supplemented by a variational Monte Carlo technique enforcing the exact projection onto the physical subspace, is able to describe a fully gapped spin liquid in the strongly frustrated regime.
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The abstract, sentence by sentence
We study the ground-state phase diagram of the spin-1/2 J1-J2 Heisenberg model on the square lattice with an accurate Bosonic resonating valence-bond (RVB) wave function. In contrast to the RVB ansatz based on Schwinger Fermions, the representation based on Schwinger Bosons, supplemented by a variational Monte Carlo technique enforcing the exact projection onto the physical subspace, is able to describe a fully gapped spin liquid in the strongly frustrated regime. In particular, a fully symmetric Z2 spin liquid is stable between two antiferromagnetic phases; a continuous transition at J2=0.4J1, when the Marshall sign rule begins to be essentially violated, and a first-order transition around J2=0.6J1 are present. Most importantly, the triplet gap is found to have a non-monotonic behavior, reaching a maximum around J2=0.51J1, when the lowest spinon excitation moves from the \Gamma to the M point, i.e., k=(\pi,0).
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the ground-state phase diagram of the spin-1/2 J1-J2 Heisenberg model on the square lattice with an accurate Bosonic resonating valence-bond (RVB) wave function. | contribution 0.98 | 0.95 | 0.06 | asserted 0.85 |
| s1 | In contrast to the RVB ansatz based on Schwinger Fermions, the representation based on Schwinger Bosons, supplemented by a variational Monte Carlo technique enforcing the exact projection onto the physical subspace, is able to describe a fully gapped spin liquid in the strongly frustrated regime. | result 0.43 | 0.75 | 0.55 | asserted 1.00 |
| s2 | In particular, a fully symmetric Z2 spin liquid is stable between two antiferromagnetic phases; a continuous transition at J2=0.4J1, when the Marshall sign rule begins to be essentially violated, and a first-order transition around J2=0.6J1 are present. | result 1.00 | 0.91 | 0.36 | asserted 1.00 |
| s3 | Most importantly, the triplet gap is found to have a non-monotonic behavior, reaching a maximum around J2=0.51J1, when the lowest spinon excitation moves from the \Gamma to the M point, i.e., k=(\pi,0). | result 1.00 | 0.95 | 0.19 | asserted 1.00 |
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The paper
Original abstract
We study the ground-state phase diagram of the spin-1/2 J1-J2 Heisenberg model on the square lattice with an accurate Bosonic resonating valence-bond (RVB) wave function. In contrast to the RVB ansatz based on Schwinger Fermions, the representation based on Schwinger Bosons, supplemented by a variational Monte Carlo technique enforcing the exact projection onto the physical subspace, is able to describe a fully gapped spin liquid in the strongly frustrated regime. In particular, a fully symmetric Z2 spin liquid is stable between two antiferromagnetic phases; a continuous transition at J2=0.4J1, when the Marshall sign rule begins to be essentially violated, and a first-order transition around J2=0.6J1 are present. Most importantly, the triplet gap is found to have a non-monotonic behavior, reaching a maximum around J2=0.51J1, when the lowest spinon excitation moves from the \Gamma to the M point, i.e., k=(\pi,0).
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2 arXiv papers cite this in 2 sentences
Papers whose main result relates to this one's
States a conflicting result 2 papers
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By direct calculations of the spin gap in the frustrated Heisenberg model on the square lattice, with nearest- ($J_1$) and next-nearest-neighbor ($J_2$) super-exchange couplings, we provide a solid evidence that the spin-liquid phase in the frustrated regime $0.45 \lesssim J_2/J_1 \lesssim 0.6$ is gapless.
Direct evidence for a gapless $Z_2$ spin liquid by frustrating N\'eel antiferromagnetism · 0.90
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We do not find clear evidence for spin gapped phases within the present approximation.
Ferromagnetic frustrated spin systems on the square lattice: a Schwinger boson study · 0.82
What it cites · 4 sentences without a confident label
Compares with 1 paper
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Despite that these outcomes are in good agreement with recent DMRG calculations of Ref. [ref] , the gapless Dirac-type Fermionic RVB ansatz remains slightly more accurate at the variational level in the highly-frustrated regime.
Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model · Conclusions · 0.99
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