Evidence for spontaneous breaking of a continuous symmetry at a non-conformal quantum critical point in one dimension
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arXiv
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| Natura: | Preprint |
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2025
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| author | Flores-Calderón, R. Zündel, M. |
| author_facet | Flores-Calderón, R. Zündel, M. |
| contents | In this work, we present evidence for the spontaneous breaking of a continuous symmetry in a nearest-neighbour interacting spin-1 chain tuned to a quantum critical point at $T=0$ between two XY quasi-long-range order phases differing by the spontaneous breaking of a $\mathbb{Z}_2$ symmetry. Despite the one-dimensional nature of the system, which typically prevents such a continuous symmetry breaking due to the Hohenberg-Mermin-Wagner theorem, the presence of a Berry phase term in the quantum model allows us to observe, using matrix product state methods, a finite perpendicular magnetization. Moreover, the quasi-long-range decay of the correlation function becomes truly long-range order, and the dynamical structure factor displays a characteristic Bragg peak together with sharp gapless modes. Our results imply the quantum phase transition has an anomalous dimension of $η\simeq 1$ together with the dynamical critical exponent $z\simeq 3/2$, known from the Kardar-Parisi-Zhang universality class in one dimension. We perform a perturbative renormalization group calculation about the upper critical dimension $d_c=2$ that we could close at second loop order. We find an interacting fixed point with critical exponents distinct from the Ising ones. Together, our findings suggest the nature of the fixed point to be non-perturbative. We propose a field-theory that we believe to improve the quantitative results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09097 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Evidence for spontaneous breaking of a continuous symmetry at a non-conformal quantum critical point in one dimension Flores-Calderón, R. Zündel, M. Statistical Mechanics Quantum Gases Strongly Correlated Electrons Mathematical Physics In this work, we present evidence for the spontaneous breaking of a continuous symmetry in a nearest-neighbour interacting spin-1 chain tuned to a quantum critical point at $T=0$ between two XY quasi-long-range order phases differing by the spontaneous breaking of a $\mathbb{Z}_2$ symmetry. Despite the one-dimensional nature of the system, which typically prevents such a continuous symmetry breaking due to the Hohenberg-Mermin-Wagner theorem, the presence of a Berry phase term in the quantum model allows us to observe, using matrix product state methods, a finite perpendicular magnetization. Moreover, the quasi-long-range decay of the correlation function becomes truly long-range order, and the dynamical structure factor displays a characteristic Bragg peak together with sharp gapless modes. Our results imply the quantum phase transition has an anomalous dimension of $η\simeq 1$ together with the dynamical critical exponent $z\simeq 3/2$, known from the Kardar-Parisi-Zhang universality class in one dimension. We perform a perturbative renormalization group calculation about the upper critical dimension $d_c=2$ that we could close at second loop order. We find an interacting fixed point with critical exponents distinct from the Ising ones. Together, our findings suggest the nature of the fixed point to be non-perturbative. We propose a field-theory that we believe to improve the quantitative results. |
| title | Evidence for spontaneous breaking of a continuous symmetry at a non-conformal quantum critical point in one dimension |
| topic | Statistical Mechanics Quantum Gases Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2511.09097 |