arXiv subjects

Li-Mei Chen

Publications and source records attributed to Li-Mei Chen.

6 recordsLinked to original sources

arXiv2024

Quantum entanglement and non-Hermiticity in free-fermion systems

This topical review article reports rapid progress on the generalization and application of entanglement in non-Hermitian free-fermion quantum systems. We begin by examining the realization of non-Hermitian quantum systems through the Lindblad master equation, alongside a review of typical non-Hermitian free-fermion systems that exhibit unique features. A pedagogical discussion is provided on the relationship between entanglement quantities and the correlation matrix in Hermitian systems. Building on this foundation, we focus on how entanglement concepts are extended to non-Hermitian systems from their Hermitian free-fermion counterparts, with a review of the general properties that emerge. Finally, we highlight various concrete studies, demonstrating that entanglement entropy remains a powerful diagnostic tool for characterizing non-Hermitian physics. The entanglement spectrum also reflects the topological characteristics of non-Hermitian topological systems, while unique non-Hermitian entanglement behaviors are also discussed. The review is concluded with several future directions. Through this review, we hope to provide a useful guide for researchers who are interested in entanglement in non-Hermitian quantum systems.

quant-ph↗

arXiv2023

Measuring entanglement entropy and its topological signature for phononic systems

Entanglement entropy is a fundamental concept with rising importance in different fields ranging from quantum information science, black holes to materials science. In complex materials and systems, entanglement entropy provides insight into the collective degrees of freedom that underlie the systems' complex behaviours. As well-known predictions, the entanglement entropy exhibits area laws for systems with gapped excitations, whereas it follows the Gioev-Klich-Widom scaling law in gapless fermion systems. Furthermore, the entanglement spectrum provides salient characterizations of topological phases and phase transitions beyond the conventional paradigms. However, many of these fundamental predictions have not yet been confirmed in experiments due to the difficulties in measuring entanglement entropy in physical systems. Here, we report the experimental verification of the above predictions by probing the nonlocal correlations in phononic systems. From the pump-probe responses in phononic crystals, we obtain the entanglement entropy and entanglement spectrum for phononic systems with the fermion filling analog. With these measurements, we verify the Gioev-Klich-Widom scaling law of entanglement entropy for various quasiparticle dispersions in one- and two-dimensions. Moreover, we observe the salient signatures of topological phases in the entanglement spectrum and entanglement entropy which unveil an unprecedented probe of topological phases without relying on the bulk-boundary correspondence. The progress here opens a frontier where entanglement entropy serves as an important experimental tool in the study of emergent phases and phase transitions which can be generalized to non-Hermitian and other unconventional regimes.

quant-ph↗

arXiv2023

Chiral spin liquid in a $\mathbb{Z}_3$ Kitaev model

We study a $\mathbb{Z}_3$ Kitaev model on the honeycomb lattice with nearest neighbor interactions. Based on matrix product state simulations and symmetry considerations, we find evidence that, with ferromagnetic isotropic couplings, the model realizes a chiral spin liquid, characterized by a possible $\mathrm{U}(1)_{12}$ chiral topological order. This is supported by simulations on both cylinder and strip geometries. On infinitely long cylinders with various widths, scaling analysis of entanglement entropy and maximal correlation length suggests that the model has a gapped 2D bulk. The topological entanglement entropy is extracted and found to be in agreement with the $\mathrm{U}(1)_{12}$ topological order. On infinitely long strips with moderate widths, we find the model is critical with a central charge consistent with the chiral edge theory of the $\mathrm{U}(1)_{12}$ topological phase. We conclude by discussing several open questions.

cond-mat.str-el↗

arXiv2022

Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors

Non-orthogonality in non-Hermitian quantum systems gives rise to tremendous exotic quantum phenomena, which can be fundamentally traced back to non-unitarity and is much more fundamental and universal than complex energy spectrum. In this paper, we introduce an interesting quantity (denoted as $\eta$) as a new variant of the Petermann factor to directly and efficiently measure non-unitarity and the associated non-Hermitian physics. By tuning the model parameters of underlying non-Hermitian systems, we find that the discontinuity of both $\eta$ and its first-order derivative (denoted as $\partial \eta$) pronouncedly captures rich physics that is fundamentally caused by non-unitarity. More concretely, in the 1D non-Hermitian topological systems, two mutually orthogonal edge states that are respectively localized on two boundaries become non-orthogonal in the vicinity of discontinuity of $\eta$ as a function of the model parameter, which is dubbed ``edge state transition''. Through theoretical analysis, we identify that the appearance of edge state transition indicates the existence of exceptional points~(EPs) in topological edge states. Regarding the discontinuity of $\partial\eta$, we investigate a two-level non-Hermitian model and establish a connection between the points of discontinuity of $\partial \eta$ and EPs of bulk states. By studying this connection in more general lattice models, we find that some models have discontinuity of $\partial\eta$, implying the existence of EPs in bulk states.

quant-ph↗

arXiv2021

Quantum Entanglement of Non-Hermitian Quasicrystals

As a hallmark of pure quantum effect, quantum entanglement has provided unconventional routes to condensed matter systems. Here, from the perspective of quantum entanglement, we disclose exotic quantum physics in non-Hermitian quasicrystals. We present a class of experimentally realizable models for non-Hermitian quasicrystal chains, in which asymmetric hopping and complex potential coexist. We diagnose global phase diagram by means of entanglement from both real-space and momentum-space partition. By measuring entanglement entropy, we numerically determine the metal-insulator transition point. We combine real-space and momentum-space entanglement spectra to complementarily characterize the delocalization phase and the localization phase. Inspired by entanglement spectrum, we further analytically prove that a duality exists between the two phase regions. The transition point is self-dual and exact, further validating the numerical result from diagonalizing non-Hermitian matrices. Finally, we identify mobility edge by means of entanglement.

cond-mat.mes-hall↗

arXiv2020

Entanglement, non-Hermiticity, and duality

Usually duality process keeps energy spectrum invariant. In this paper, we provide a duality, which keeps entanglement spectrum invariant, in order to diagnose quantum entanglement of non-Hermitian non-interacting fermionic systems. We limit our attention to non-Hermitian systems with a complete set of biorthonormal eigenvectors and an entirely real energy spectrum. The original system has a reduced density matrix $\rho_\mathrm{o}$ and the real space is partitioned via a projecting operator $\mathcal{R}_{\mathrm o}$. After dualization, we obtain a new reduced density matrix $\rho_{\mathrm{d}}$ and a new real space projector $\mathcal{R}_{\mathrm d}$. Remarkably, entanglement spectrum and entanglement entropy keep invariant. Inspired by the duality, we defined two types of non-Hermitian models, upon $\mathcal R_{\mathrm{o}}$ is given. In type-I exemplified by the ``non-reciprocal model'', there exists at least one duality such that $\rho_{\mathrm{d}}$ is Hermitian. In other words, entanglement information of type-I non-Hermitian models with a given $\mathcal{R}_{\mathrm{o}}$ is entirely controlled by Hermitian models with $\mathcal{R}_{\mathrm{d}}$. As a result, we are allowed to apply known results of Hermitian systems to efficiently obtain entanglement properties of type-I models. On the other hand, the duals of type-II models, exemplified by ``non-Hermitian Su-Schrieffer-Heeger model'', are always non-Hermitian. For the practical purpose, the duality provides a potentially \textit{efficient} computation route to entanglement of non-Hermitian systems. Via connecting different models, the duality also sheds lights on either trivial or nontrivial role of non-Hermiticity played in quantum entanglement, paving the way to potentially systematic classification and characterization of non-Hermitian systems from the entanglement perspective.

cond-mat.mes-hall↗