We consider the entanglement properties of free fermions in one dimension and review an approach which relates the problem to the solution of a certain differential equation. The single-particle eigenfunctions of the entanglement Hamiltonian are then seen to be spheroidal functions or generalizations of them. The analytical results for the eigenvalue spectrum agree with those obtained by other methods. In the continuum case, there are close connections to random matrix theory.
We calculate the ground state entanglement entropy between two heterogeneous parts of a free fermion chain. The two parts could be XX chains with different parameters or an XX half chain connected with a quantum Ising half chain. It is shown that logarithmic behavior holds if the two parts are conformally critical. In other cases, area law holds with abundant convergence behaviors. In particular, when XX chain at Lifshitz point is connected with a conformally or Lifshitz critical part, entanglement entropy converges algebraically with a fractional subleading index.
We study the entanglement Hamiltonian for fermionic hopping models on rings and open chains and determine single-particle spectra, eigenfunctions and the form in real space. For the chain, we find a commuting operator as for the ring and compare with its properties in both cases. In particular, a scaling relation between the eigenvalues is found for large systems. We also show how the commutation property carries over to the critical transverse Ising model.
The entanglement entropy of free fermions with a Fermi surface is known to obey a logarithmic scaling and violate the area law in all dimensions. Here, we would like to see how temperature affects the logarithmic scaling behavior. To this end, we compute the entanglement negativity of free fermions using the fermionic partial transpose developed in our earlier paper [Phys. Rev. B 95, 165101 (2017)]. In one dimension, we analytically derive the leading order term in the finite-temperature entanglement negativity and show how the entanglement negativity indicates a crossover from a quantum entan…
We study the entanglement entropy of the quantum trajectories of a free fermion chain under continuous monitoring of local occupation numbers. We propose a simple theory for entanglement entropy evolution from disentangled and highly excited initial states. It is based on generalized hydrodynamics and the quasi-particle pair approach to entanglement in integrable systems. We test several quantitative predictions of the theory against extensive numerics and find good agreement. In particular, the volume law entanglement is destroyed by the presence of arbitrarily weak measurement.
Entanglement spectrum and magic in higher-dimensional free fermionic systems
Universität zu Köln（科隆大学）；Scuola Superiore Meridionale（南方高等学院）；INFN Sezione di Napoli（那不勒斯 INFN 分部）；SISSA（国际高等研究学院）；INFN Sezione di Trieste（的里雅斯特 INFN 分部）
We study the entanglement entropy of free fermions in 2d in the presence of a partially transmitting interface that splits Minkowski space into two half-spaces. We focus on the case of a single interval that straddles the defect, and compute its entanglement entropy in three limits: Perturbing away from the fully transmitting and fully reflecting cases, and perturbing in the amount of asymmetry of the interval about the defect. Using these results within the setup of the Poincaré patch of AdS$_2$ statically coupled to a zero temperature flat space bath, we calculate the effect of a partially t…
Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations
在最近的一篇文章T。Grover [Phys. Rev. Lett. 111，130402（2013）]介绍了一种在辅助场量子蒙特卡罗算法领域中计算Renyi纠缠熵的简单方法。在这里，我们进一步发展这种方法，并提供一个稳定的计划来计算高阶Renyi熵和扩展访问纠缠谱。该方法在相关拓扑绝缘体系统上进行了测试。
Entanglement in finite and semi-infinite free Fermionic chains is studied. A parallel is drawn with the analysis of time and band limiting in signal processing. It is shown that a tridiagonal matrix commuting with the entanglement Hamiltonian can be found using the algebraic Heun operator construct in instances when there is an underlying bispectral problem. Cases corresponding to the Lie algebras $\mathfrak{su}(2)$ and $\mathfrak{su}(1,1)$ as well as to the q-deformed algebra $\mathfrak{so}_q(3)$ at $q$ a root of unity are presented.
We present a simple construction for a tridiagonal matrix $T$ that commutes with the hopping matrix for the entanglement Hamiltonian ${\cal H}$ of open finite free-Fermion chains associated with families of discrete orthogonal polynomials. It is based on the notion of algebraic Heun operator attached to bispectral problems, and the parallel between entanglement studies and the theory of time and band limiting. As examples, we consider Fermionic chains related to the Chebychev, Krawtchouk and dual Hahn polynomials. For the former case, which corresponds to a homogeneous chain, the outcome of ou…
Free Fermions on vertices of distance-regular graphs are considered. Bipartition are defined by taking as one part all vertices at a given distance from a reference vertex. The ground state is constructed by filling all states below a certain energy. Borrowing concepts from time and band limiting problems, algebraic Heun operators and Terwilliger algebras, it is shown how to obtain, quite generally, a block tridiagonal matrix that commutes with the entanglement Hamiltonian. The case of the Hadamard graphs is studied in details within that framework and the existence of the commuting matrix is …
In this paper we present the detailed calculation of a new modular Hamiltonian, namely that of a chiral fermion on a circle at non-zero temperature. We provide explicit results for an arbitrary collection of intervals, which we discuss at length by checking against known results in different limits and by computing the associated modular flow. We also compute the entanglement entropy, and we obtain a simple expression for it which appears to be more manageable than those already existing in the literature.
