Walking behavior induced by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetry breaking in a non-Hermitian <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X

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 of how non-Hermiticity affects quantum criticality. In this context, we consider a non-Hermitian system consisting of an <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>X</a:mi><a:mi>Y</a:mi></a:mrow></a:math> model with a complex-valued four-state clock interaction that may or may not have parity-time-reversal (<b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi mathvariant="script">PT</b:mi></b:math>) symmetry. When the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi mathvariant="script">PT</d:mi></d:math> symmetry is broken, and time-evolution becomes nonunitary, 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 <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>d</f:mi></f:math>-dimensional renormalization group equations, we obtain that the unconventional behavior in the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mi mathvariant="script">PT</g:mi></g:math> broken regime follows from the collision of two fixed points in the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mi>d</i:mi><i:mo>→</i:mo><i:mn>2</i:mn></i:mrow></i:math> limit, leading to walking behavior or pseudocriticality. For <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:mi>d</j:mi><j:mo>=</j:mo><j:mn>2</j:mn><j:mo>+</j:mo><j:mn>1</j:mn></j:mrow></j:math> the near critical behavior is characterized by a correlation length exponent <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:mi>ν</k:mi><k:mo>=</k:mo><k:mn>3</k:mn><k:mo>/</k:mo><k:mn>8</k:mn></k:mrow></k:math>, a value smaller than the mean-field one. These results are in sharp contrast with the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mi mathvariant="script">PT</l:mi></l:math>-symmetric case where only one fixed point arises for <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"><n:mrow><n:mn>2</n:mn><n:mo>&lt;</n:mo><n:mi>d</n:mi><n:mo>&lt;</n:mo><n:mn>4</n:mn></n:mrow></n:math> and in <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"><o:mrow><o:mi>d</o:mi><o:mo>=</o:mo><o:mn>1</o:mn><o:mo>+</o:mo><o:mn>1</o:mn></o:mrow></o:math> three lines of fixed points occur with a continuously varying critical exponent <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"><p:mi>ν</p:mi></p:math>. Published by the American Physical Society 2024