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| Format: | Preprint |
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2024
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| Accès en ligne: | https://arxiv.org/abs/2404.17373 |
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| _version_ | 1866929619117015040 |
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| author | Naichuk, Eduard Brink, Jeroen van den Nogueira, Flavio S. |
| author_facet | Naichuk, Eduard Brink, Jeroen van den Nogueira, Flavio S. |
| contents | A quantum system governed by a non-Hermitian Hamiltonian may exhibit zero temperature phase transitions that are driven by interactions, just as its Hermitian counterpart, raising the fundamental question how non-Hermiticity affects quantum criticality. In this context we consider a non-Hermitian system consisting of an $\rm XY$ model with a complex-valued four-state clock interaction that may or may not have parity-time-reversal ($\mathcal{PT}$) symmetry. When the $\mathcal{PT}$ symmetry is broken, and time-evolution becomes non-unitary, a scaling behavior similar to the Berezinskii-Kosterlitz-Thouless phase transition ensues, but in a highly unconventional way, as the line of fixed points is absent. From the analysis of the $d$-dimensional RG equations, we obtain that the unconventional behavior in the $\mathcal{PT}$ broken regime follows from the collision of two fixed points in the $d\to 2$ limit, leading to walking behavior or pseudocriticality. For $d=2+1$ the near critical behavior is characterized by a correlation length exponent $ν=3/8$, a value smaller than the mean-field one. These results are in sharp contrast with the $\mathcal{PT}$-symmetric case where only one fixed point arises for $2<d<4$ and in $d=1+1$ three lines of fixed points occur with a continuously varying critical exponent $ν$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17373 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Walking behavior induced by $\mathcal{PT}$ symmetry breaking in a non-Hermitian $\rm XY$ model with clock anisotropy Naichuk, Eduard Brink, Jeroen van den Nogueira, Flavio S. Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory A quantum system governed by a non-Hermitian Hamiltonian may exhibit zero temperature phase transitions that are driven by interactions, just as its Hermitian counterpart, raising the fundamental question how non-Hermiticity affects quantum criticality. In this context we consider a non-Hermitian system consisting of an $\rm XY$ model with a complex-valued four-state clock interaction that may or may not have parity-time-reversal ($\mathcal{PT}$) symmetry. When the $\mathcal{PT}$ symmetry is broken, and time-evolution becomes non-unitary, a scaling behavior similar to the Berezinskii-Kosterlitz-Thouless phase transition ensues, but in a highly unconventional way, as the line of fixed points is absent. From the analysis of the $d$-dimensional RG equations, we obtain that the unconventional behavior in the $\mathcal{PT}$ broken regime follows from the collision of two fixed points in the $d\to 2$ limit, leading to walking behavior or pseudocriticality. For $d=2+1$ the near critical behavior is characterized by a correlation length exponent $ν=3/8$, a value smaller than the mean-field one. These results are in sharp contrast with the $\mathcal{PT}$-symmetric case where only one fixed point arises for $2<d<4$ and in $d=1+1$ three lines of fixed points occur with a continuously varying critical exponent $ν$. |
| title | Walking behavior induced by $\mathcal{PT}$ symmetry breaking in a non-Hermitian $\rm XY$ model with clock anisotropy |
| topic | Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.17373 |