The study of entanglement in the symmetry sectors of a theory has recently attracted a lot of attention since it provides better understanding of some aspects of quantum many-body systems. In this paper, we extend this analysis to the case of non-Hermitian models, in which the reduced density matrix $ρ_A$ may be non-positive definite and the entanglement entropy negative or even complex. Here we examine in detail the symmetry-resolved entanglement in the ground state of the non-Hermitian Su-Schrieffer-Heeger chain at the critical point, a model that preserves particle number and whose scaling limit is a $bc$-ghost non-unitary CFT. By combining bosonization techniques in the field theory and exact lattice numerical calculations, we analytically derive the charged moments of $ρ_A$ and $|ρ_A|$. From them, we can understand the origin of the non-positiveness of $ρ_A$ and naturally define a positive-definite reduced density matrix in each charge sector, which gives a well-defined symmetry-resolved entanglement entropy. As byproduct, we also obtain the analytical distribution of the critical entanglement spectrum.
Entanglement entropy is a powerful tool in characterizing universal features in quantum many-body systems. In quantum chaotic Hermitian systems, typical eigenstates have near maximal entanglement with very small fluctuations. Here, we show that for Hamiltonians displaying non-Hermitian many-body quantum chaos, modeled by the Ginibre ensemble, the entanglement entropy of typical eigenstates is greatly suppressed. The entropy does not grow with the Hilbert space dimension for sufficiently large systems and the fluctuations are of equal order. We derive the novel entanglement spectrum that has in…
The excess entanglement resulting from exciting a finite number of quasiparticles above the ground state of a free integrable quantum field theory has been investigated quite extensively in the literature. It has been found that it takes a very simple form, depending only on the number of excitations and their statistics. There is now mounting evidence that such formulae also apply to interacting and even higher-dimensional quantum theories. In this paper we study the entanglement content of such zero-density excited states focusing on the symmetry resolved entanglement, that is on 1+1D quantu…
The presence of a global internal symmetry in a quantum many-body system is reflected in the fact that the entanglement between its subparts is endowed with an internal structure, namely it can be decomposed as sum of contributions associated to each symmetry sector. The symmetry resolution of entanglement measures provides a formidable tool to probe the out-of-equilibrium dynamics of quantum systems. Here, we study the time evolution of charge-imbalance-resolved negativity after a global quench in the context of free-fermion systems, complementing former works for the symmetry-resolved entang…
We investigate the symmetry resolution of entanglement in the presence of long-range couplings. To this end, we study the symmetry-resolved entanglement entropy in the ground state of a fermionic chain that has dimerised long-range hoppings with power-like decaying amplitude -- a long-range generalisation of the Su-Schrieffer-Heeger model. This is a system that preserves the number of particles. The entropy of each symmetry sector is calculated via the charged moments of the reduced density matrix. We exploit some recent results on block Toeplitz determinants generated by a discontinuous symbo…
The study of the entanglement dynamics plays a fundamental role in understanding the behaviour of many-body quantum systems out of equilibrium. In the presence of a globally conserved charge, further insights are provided by the knowledge of the resolution of entanglement in the various symmetry sectors. Here, we carry on the program we initiated in [Phys. Rev. B 103, L041104 (2021)], for the study of the time evolution of the symmetry resolved entanglement in free fermion systems. We complete and extend our derivations also by defining and quantifying a symmetry resolved mutual information. T…
We develop a general approach to compute the symmetry-resolved Rényi and von Neumann entanglement entropies (SREE) of thermodynamic macrostates in interacting integrable systems. Our method is based on a combination of the thermodynamic Bethe ansatz and the Gärtner-Ellis theorem from large deviation theory. We derive an explicit simple formula for the von Neumann SREE, which we show to coincide with the thermodynamic Yang-Yang entropy of an effective macrostate determined by the charge sector. Focusing on the XXZ Heisenberg spin chain, we test our result against iTEBD calculations for thermal …
Symmetry Resolved Entanglement Entropy: Equipartition under Driven and Non-unitary Evolution in a Compact Boson CFT
SISSA and INFN Sezione di Trieste（的里雅斯特国际高等研究学院和意大利国家核物理研究所的里雅斯特分部）；Theory Division, Saha Institute of Nuclear Physics, A CI of Homi Bhabha National Institute（萨哈核物理研究所理论部，霍米·巴哈国家研究所附属机构）
Detecting Symmetry-Resolved Entanglement: A Quantum Monte Carlo Approach
Fudan University（复旦大学）；Shanghai Qizhi Institute and Shanghai Artificial Intelligence Laboratory（上海琦智研究院和上海人工智能实验室）；The Chinese University of Hong Kong（香港中文大学）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Hefei National Laboratory（合肥国家实验室）；Julius-Maximilians-Universität Würzburg（维尔茨堡大学）；Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS)（上海数学与交叉学科研究院）
