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 J r u n g ≫ 1 ), 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.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 J r u n g ≫ 1 ), 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.

arXiv:2409.17062SciPost Physics CoreNov 20, 20248 citations

Quantum Entanglement Theory

Michigan State University Press eBooksJan 1, 20260 citations

Non-hermitian Density Matrices from Time-like Entanglement and Wormholes

Jonathan Harper, Taishi Kawamoto, Ryota Maeda +2 more

We extensively explore the connections between time-like entanglement and non-hermitian density matrices in quantum many-body systems. We classify setups where we encounter non-hermitian density matrices into two types: one is due to causal influences under unitary evolutions, and the other is due to non-unitary evolutions in non-hermitian systems. We provide various examples of these setups including interacting harmonic oscillators, two dimensional conformal field theories and holographic dualities. In them, we compute the time-like entanglement entropy and imagitivity, which measures how much density matrices are non-hermitian. In both two classes, typical holographic examples are given by traversable AdS wormholes. We explain how causal influences in a wormhole dual to a pair of non-hermitian quantum systems is possible even without interactions between them. We argue that to realize a traversable wormhole we need not only ordinary quantum entanglement but also time-like entanglement.We extensively explore the connections between time-like entanglement and non-hermitian density matrices in quantum many-body systems. We classify setups where we encounter non-hermitian density matrices into two types: one is due to causal influences under unitary evolutions, and the other is due to non-unitary evolutions in non-hermitian systems. We provide various examples of these setups including interacting harmonic oscillators, two dimensional conformal field theories and holographic dualities. In them, we compute the time-like entanglement entropy and imagitivity, which measures how much density matrices are non-hermitian. In both two classes, typical holographic examples are given by traversable AdS wormholes. We explain how causal influences in a wormhole dual to a pair of non-hermitian quantum systems is possible even without interactions between them. We argue that to realize a traversable wormhole we need not only ordinary quantum entanglement but also time-like entanglement.

hep-thCross-listedarXiv:2512.13800Physical review. D/Physical review. D.Dec 17, 20251 citation

Defectiveness and anomaly from non-Hermitian perturbations in topological quantum states

Wang Xiao-Ran, Su-Peng Kou

Topological quantum states are important research fields in condensed matter physics, which can be divided into two categories: (1) symmetry-protected topological states (SPTs) with short-range entanglement and (2) symmetry-enriched topological states (SETs) with long-range entanglement. Recently, research on non-Hermitian topological quantum states (SPTs and SETs) has become a hot topic. In this review paper, we discuss the theory for non-Hermitian topological insulators—a particular type of SPTs and that for non-Hermitian Z $_2$ topological orders—a particular type of SETs based on the progress of our research group.These theories would help understand the physics of non-Hermitian topological quantum states.Topological quantum states are important research fields in condensed matter physics, which can be divided into two categories: (1) symmetry-protected topological states (SPTs) with short-range entanglement and (2) symmetry-enriched topological states (SETs) with long-range entanglement. Recently, research on non-Hermitian topological quantum states (SPTs and SETs) has become a hot topic. In this review paper, we discuss the theory for non-Hermitian topological insulators—a particular type of SPTs and that for non-Hermitian Z$_2$ topological orders—a particular type of SETs based on the progress of our research group.These theories would help understand the physics of non-Hermitian topological quantum states.

Zhongguo kexue. Wulixue Lixue TianwenxueMar 7, 20221 citation

Quantum entanglement and its applications

Shengjun Wu

Jan 1, 20030 citations

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topological orders—a particular type of SETs based on the progress of our research group.These theories would help understand the physics of non-Hermitian topological quantum states.