Sign-problem-free effective models of triangular lattice quantum antiferromagnets
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866918136934039552 |
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| author | Shackleton, Leyna Sachdev, Subir |
| author_facet | Shackleton, Leyna Sachdev, Subir |
| contents | The triangular lattice antiferromagnet with $S=1/2$ spins and nearest neighbor interactions is known to have long-range antiferromagnetic order, with nearest-neighbor spins at an angle of 120 degrees. Numerical studies of quantum phases proximate to this state have been limited to small systems because the of the sign-problem in Monte Carlo simulations in imaginary time. We propose an effective lattice model for quantum fluctuations of the antiferromagnetic order, and a sign-problem free Monte Carlo algorithm, enabling studies in large systems sizes. The model is a $\mathbb{Z}_2$ gauge theory coupled to gauge-charged scalars which have a relativistic dispersion in the continuum limit. Crucially, the gauge theory is odd, i.e. there is a static, background $\mathbb{Z}_2$ gauge charge on each site, accounting for the Berry phases of the half-odd-integer spins on each site. We present results of simulations on lattices of sizes up to $36 \times 36 \times 36$. Along with the antiferromagnetically ordered phase, our phase diagram has a valence bond solid state with a $\sqrt{12} \times \sqrt{12}$ unit cell, and a gapped $\mathbb{Z}_2$ spin liquid. Deconfined critical points or phases in intermediate regions are not ruled out by our present simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01572 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sign-problem-free effective models of triangular lattice quantum antiferromagnets Shackleton, Leyna Sachdev, Subir Strongly Correlated Electrons The triangular lattice antiferromagnet with $S=1/2$ spins and nearest neighbor interactions is known to have long-range antiferromagnetic order, with nearest-neighbor spins at an angle of 120 degrees. Numerical studies of quantum phases proximate to this state have been limited to small systems because the of the sign-problem in Monte Carlo simulations in imaginary time. We propose an effective lattice model for quantum fluctuations of the antiferromagnetic order, and a sign-problem free Monte Carlo algorithm, enabling studies in large systems sizes. The model is a $\mathbb{Z}_2$ gauge theory coupled to gauge-charged scalars which have a relativistic dispersion in the continuum limit. Crucially, the gauge theory is odd, i.e. there is a static, background $\mathbb{Z}_2$ gauge charge on each site, accounting for the Berry phases of the half-odd-integer spins on each site. We present results of simulations on lattices of sizes up to $36 \times 36 \times 36$. Along with the antiferromagnetically ordered phase, our phase diagram has a valence bond solid state with a $\sqrt{12} \times \sqrt{12}$ unit cell, and a gapped $\mathbb{Z}_2$ spin liquid. Deconfined critical points or phases in intermediate regions are not ruled out by our present simulations. |
| title | Sign-problem-free effective models of triangular lattice quantum antiferromagnets |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2311.01572 |