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Auteurs principaux: Naichuk, Eduard, Brink, Jeroen van den, Nogueira, Flavio S.
Format: Preprint
Publié: 2024
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Accès en ligne:https://arxiv.org/abs/2404.17373
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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