Entanglement Hamiltonian and effective temperature of non-Hermitian quantum spin ladders

Quantum entanglement plays a crucial role not only in understanding Hermitian many-body systems but also in offering valuable insights into non-Hermitian quantum systems. In this paper, we analytically investigate the entanglement Hamiltonian and entanglement energy spectrum of a non-Hermitian spin ladder using perturbation theory in the biorthogonal basis. Specifically, we examine the entanglement properties between coupled non-Hermitian quantum spin chains. In the strong coupling limit ( J_\mathrm{rung}\gg1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mstyle mathvariant="normal"> <mml:mi>r</mml:mi> <mml:mi>u</mml:mi> <mml:mi>n</mml:mi> <mml:mi>g</mml:mi> </mml:mstyle> </mml:msub> <mml:mo>≫</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> ), first-order perturbation theory reveals that the entanglement Hamiltonian closely resembles the single-chain Hamiltonian with renormalized coupling strengths, allowing for the definition of an ad hoc temperature. Our findings provide new insights into quantum entanglement in non-Hermitian systems and offer a foundation for developing novel approaches for studying finite temperature properties in non-Hermitian quantum many-body systems.