Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories
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arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866929392732602368 |
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| author | Wei, Chenan Mkhitaryan, Vagharsh V. Sedrakyan, Tigran A. |
| author_facet | Wei, Chenan Mkhitaryan, Vagharsh V. Sedrakyan, Tigran A. |
| contents | We study the low-energy properties of the one-dimensional spin-1/2 XXZ chain with time-reversal symmetry-breaking pseudo-scalar chiral interaction and propose a phase diagram for the model. In the integrable case of the isotropic Heisenberg model with the chiral interaction, we employ the thermodynamic Bethe ansatz to find "chiralization", the response of the ground state versus the strength of the pseudo-scalar chiral interaction of a chiral Heisenberg chain. Unlike the magnetization case, the chirality of the ground state remains zero until the transition point corresponding to critical coupling $α_c=2J/π$ with $J$ being the antiferromagnetic spin-exchange interaction. The central-charge $c=1$ conformal field theories (CFTs) describe the two phases with zero and finite chirality. We show for this particular case and conjecture more generally for similar phase transitions that the difference between two emergent CFTs with identical central charges lies in the symmetry of their ground state (lightest weight) primary fields, i.e., the two phases are symmetry-enriched CFTs. At finite but small temperatures, the non-chiral Heisenberg phase acquires a finite chirality that scales with the temperature quadratically. We show that the finite-size effect around the transition point probes the transition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16660 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories Wei, Chenan Mkhitaryan, Vagharsh V. Sedrakyan, Tigran A. Strongly Correlated Electrons Statistical Mechanics Exactly Solvable and Integrable Systems We study the low-energy properties of the one-dimensional spin-1/2 XXZ chain with time-reversal symmetry-breaking pseudo-scalar chiral interaction and propose a phase diagram for the model. In the integrable case of the isotropic Heisenberg model with the chiral interaction, we employ the thermodynamic Bethe ansatz to find "chiralization", the response of the ground state versus the strength of the pseudo-scalar chiral interaction of a chiral Heisenberg chain. Unlike the magnetization case, the chirality of the ground state remains zero until the transition point corresponding to critical coupling $α_c=2J/π$ with $J$ being the antiferromagnetic spin-exchange interaction. The central-charge $c=1$ conformal field theories (CFTs) describe the two phases with zero and finite chirality. We show for this particular case and conjecture more generally for similar phase transitions that the difference between two emergent CFTs with identical central charges lies in the symmetry of their ground state (lightest weight) primary fields, i.e., the two phases are symmetry-enriched CFTs. At finite but small temperatures, the non-chiral Heisenberg phase acquires a finite chirality that scales with the temperature quadratically. We show that the finite-size effect around the transition point probes the transition. |
| title | Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories |
| topic | Strongly Correlated Electrons Statistical Mechanics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2312.16660 |