Walking behavior induced by $\mathcal{PT}$ symmetry breaking in a non-Hermitian $\rm XY$ model with clock anisotropy

• URL: http://arxiv.org/abs/2404.17373v1
• Date: Fri, 26 Apr 2024 12:45:16 GMT
• Title: Walking behavior induced by $\mathcal{PT}$ symmetry breaking in a non-Hermitian $\rm XY$ model with clock anisotropy
• Authors: Eduard Naichuk, Jeroen van den Brink, Flavio S. Nogueira,
• Abstract summary: A quantum system governed by a non-Hermitian Hamiltonian may exhibit zero temperature phase transitions driven by interactions. We show that when the $mathcalPT$ symmetry is broken, and time-evolution becomes non-unitary, a scaling behavior similar to the Berezinskii-Kosterlitz-Thouless phase transition ensues.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $\nu=3/8$, 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 $\nu$.

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