M. Dalmonte, V. Eisler, M. Falconi, B. Vermersch
We review results about entanglement (or modular) Hamiltonians of quantum many-body systems in field theory and statistical mechanics models, as well as recent applications in the context of quantum information and quantum simulation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Sudden change in entanglement Hamiltonian: Phase diagram of an Ising entanglement Hamiltonian
本文通过研究1D Ising纠缠哈密顿量的相图，澄清了纠缠哈密顿量与原始哈密顿量关系的长期争议，发现即使存在奇异性，Li-Haldane-Poilblanc猜想依然成立。
Entanglement Hamiltonian and orthogonal polynomials
本文研究了具有特定非均匀性的自由费米子链的纠缠哈密顿量，通过引入与Askey方案离散正交多项式相关的单粒子本征态，构造了与纠缠哈密顿量精确对易的算符，并证明该算符可作为局部逆温度有效近似纠缠谱和熵。
In this paper, we review how to obtain the central charge of a critical entanglement Hamiltonian through the nested entanglement entropy which was first introduced in [J. Lou et al. PRB 84, 245128 (2011)]. The critical phenomena of the entanglement Hamiltonian can be identified by the central charge obtained by the nested entanglement entropy. We review our previous studies[J. Lou et al. PRB 84, 245128 (2011), S. Tanaka et al. PRA 87, 214401 (2013)] in which we investigated certain entanglement nature of two-dimensional valence-bond-solid (VBS) state and quantum hard-square models on square an…
We introduce the concept of entanglement features of unitary gates, as a collection of exponentiated entanglement entropies over all bipartitions of input and output channels. We obtained the general formula for time-dependent $n$th-Renyi entanglement features for unitary gates generated by random Hamiltonian. In particular, we propose an Ising formulation for the 2nd-Renyi entanglement features of random Hamiltonian dynamics, which admits a holographic tensor network interpretation. As a general description of entanglement properties, we show that the entanglement features can be applied to s…
In this work, we study the time evolution of the entanglement hamiltonian during the process of thermalization in a (1+1)-dimensional conformal field theory (CFT) after a quantum quench from a special class of initial states. In particular, we focus on a subsystem which is a finite interval at the end of a semi-infinite line. Based on conformal mappings, the exact forms of both entanglement hamiltonian and entanglement spectrum of the subsystem can be obtained. Aside from various interesting features, it is found that in the infinite time limit the entanglement hamiltonian and entanglement spe…
Entanglement Hamiltonian in the non-Hermitian SSH model
本文研究了非厄米特SSH链中纠缠哈密顿量的特性，发现临界点处存在新的虚化学势项，导致负纠缠熵。
We study the ground-state entanglement Hamiltonian of several disjoint intervals for the massless Dirac fermion on the half-line. Its structure consists of a local part and a bi-local term that couples each point to another one in each other interval. The bi-local operator can be either diagonal or mixed in the fermionic chiralities and it is sensitive to the boundary conditions. The knowledge of such entanglement Hamiltonian is the starting point to evaluate the negativity Hamiltonian, i.e. the logarithm of the partially transposed reduced density matrix, which is an operatorial characterisat…
Inhomogeneous quantum critical systems in one spatial dimension have been studied by using conformal field theory in static curved backgrounds. Two interesting examples are the free fermion gas in the harmonic trap and the inhomogeneous XX spin chain called rainbow chain. For conformal field theories defined on static curved spacetimes characterised by a metric which is Weyl equivalent to the flat metric, with the Weyl factor depending only on the spatial coordinate, we study the entanglement hamiltonian and the entanglement spectrum of an interval adjacent to the boundary of a segment where t…
Recent numerical advances in the field of strongly correlated electron systems allow the calculation of the entanglement spectrum and entropies for interacting fermionic systems. An explicit determination of the entanglement (modular) Hamiltonian has proven to be a considerably more difficult problem, and only a few results are available. We introduce a technique to directly determine the entanglement Hamiltonian of interacting fermionic models by means of auxiliary field quantum Monte Carlo simulations. We implement our method on the one-dimensional Hubbard chain partitioned into two segments…
In the context of ground states of quantum many-body systems, the locality of entanglement between connected regions of space is directly tied to the locality of the corresponding entanglement Hamiltonian: the latter is dominated by local, few-body terms. In this work, we introduce the negativity Hamiltonian as the (non hermitian) effective Hamiltonian operator describing the logarithm of the partial transpose of a many-body system. This allows us to address the connection between entanglement and operator locality beyond the paradigm of bipartite pure systems. As a first step in this directio…
Entanglement is central to our understanding of many-body quantum matter. In particular, the entanglement spectrum, as eigenvalues of the reduced density matrix of a subsystem, provides a unique footprint of properties of strongly correlated quantum matter from detection of topological order to characterisation of quantum critical systems. However, direct experimental measurement of the entanglement spectrum has so far remained elusive due to lack of direct experimental probes. Here we show that the entanglement spectrum of the ground state of a broad class of Hamiltonians becomes directly acc…
Entanglement Hamiltonian after a local quench
本文利用共形场论研究一维自由费米子局部连接淬火后的纠缠哈密顿量动力学，给出左右行分量对应不同权重函数的局域表达式，并通过晶格数值计算验证了理论预测。
Entanglement or modular Hamiltonians play a crucial role in the investigation of correlations in quantum field theories. In particular, in 1+1 space-time dimensions, the spectra of entanglement Hamiltonians of conformal field theories (CFTs) for certain geometries are related to the spectra of the physical Hamiltonians of corresponding boundary CFTs. As a result, conformal invariance allows exact computation of the spectra of the entanglement Hamiltonians for these models. In this work, we perform this computation of the spectrum of the entanglement Hamiltonian for the free compactified boson …
The eigenstate entanglement entropy has been recently shown to be a powerful tool to distinguish integrable from generic quantum-chaotic models. In integrable models, a unique feature of the average eigenstate entanglement entropy (over all Hamiltonian eigenstates) is that the volume-law coefficient depends on the subsystem fraction. Hence, it deviates from the maximal (subsystem fraction independent) value encountered in quantum-chaotic models. Using random matrix theory for quadratic Hamiltonians, we obtain a closed-form expression for the average eigenstate entanglement entropy as a functio…
We prove that the entanglement entropy of any pure initial state of a bipartite bosonic quantum system grows linearly in time with respect to the dynamics induced by any unstable quadratic Hamiltonian. The growth rate does not depend on the initial state and is equal to the sum of certain Lyapunov exponents of the corresponding classical dynamics. This paper generalizes the findings of [Bianchi et al., JHEP 2018, 25 (2018)], which proves the same result in the special case of Gaussian initial states. Our proof is based on a recent generalization of the strong subadditivity of the von Neumann e…
Entanglement Hamiltonian of a nonrelativistic Fermi gas
该研究针对任意维度非相对论自由费米气体基态球形区域的纠缠哈密顿量，分解为径向形式后揭示其谱与线性势跃迁链的对应关系，验证共形场论预测的适用范围，指出其仅在一维渐近精确。
2D Hamiltonians with exotic bipartite and topological entanglement
本文提出两类可精确求解的二维局域哈密顿量模型，其基态为带框环构型的加权叠加，分别展示非局域来源的面积律纠缠（拓扑纠缠熵随子系统尺寸变化）和体积律纠缠，挑战传统纠缠标度观念。
In this Letter we study the effect of topological zero modes on entanglement Hamiltonians and entropy of free chiral fermion systems in (1+1)d. We show how Riemann-Hilbert solutions combined with finite rank perturbation theory allow us to obtain explicit expressions for entanglement Hamiltonians. We consider both chiral Majorana and Dirac fermions, and explore the effects of boundary conditions (periodic/anti-periodic for Majorana and generic for Dirac) and associated zero modes on entanglement. In the periodic sector, we derive explicitly the non-local contribution to the entanglement Hamilt…
Entanglement Hamiltonian of two disjoint blocks in the harmonic chain
该论文研究谐振子链基态中两个不相交块的纠缠哈密顿量，推导大质量下在位与最近邻项的解析形式，并分析零质量极限下的耦合结构及纠缠谱。
Entanglement Hamiltonian for inhomogeneous free fermions
本文研究了非均匀化学势下一维自由费米子基态的纠缠哈密顿量，发现共形场论预测的 Bisognano-Wichmann 形式被非相对论模型继承，并提供了纠缠谱的极佳近似。
Quasiparticle Picture for Entanglement Hamiltonians in Higher Dimensions
本研究利用准粒子图像，结合维度约化与推广分析，得到二维及以上自由费米子系统量子猝灭后流体动力学尺度下非平衡纠缠哈密顿量的弹道尺度解析表达式，并通过多初始构型数值验证其高精度。
This arXiv repository is a bundle of two closely related papers. Abstract of the first paper: In systems governed by "chaotic" local Hamiltonians, we conjecture the universality of eigenstate entanglement (defined as the average entanglement entropy of all eigenstates) by proposing an exact formula for its dependence on the subsystem size. This formula is derived from an analytical argument based on a plausible assumption, and is supported by numerical simulations. Abstract of the second paper: In systems governed by chaotic local Hamiltonians, the first paper conjectured the universality of t…
We study the temporal evolution of the entanglement hamiltonian of an interval after a global quantum quenchin free lattice models in one spatial dimension. In a harmonic chain we explore a quench of the frequency parameter. In a chain of free fermions at half filling we consider the evolution of the ground state of a fully dimerised chain through the homogeneous hamiltonian. We focus on critical evolution hamiltonians. The temporal evolutions of the gaps in the entanglement spectrum are analysed. The entanglement hamiltonians in these models are characterised by matrices that provide also con…
Entanglement Hamiltonian and effective temperature of non-Hermitian quantum spin ladders
本文利用双正交基下的微扰理论解析研究非厄米自旋梯的纠缠哈密顿量与能谱，发现在强耦合极限下其形式近似于重整化单链哈密顿量，从而可定义有效温度，为非厄米多体系统有限温度性质研究提供新途径。
The time evolution of entanglement tracks how information propagates in interacting quantum systems. We study entanglement entropy in CFT$_2$ with a time-dependent Hamiltonian. We perturb by operators with time-dependent source functions and use the replica trick to calculate higher order corrections to entanglement entropy. At first order, we compute the correction due to a metric perturbation in AdS$_3$/CFT$_2$ and find agreement on both sides of the duality. Past first order, we find evidence of a universal structure of entanglement propagation to all orders. The central feature is that int…
Measurement-induced entanglement Hamiltonian
该研究分析无限跳跃链经部分投影测量后的基态纠缠哈密顿量，揭示其局域逆温度、化学势的特性，表明纠缠哈密顿量含比对应熵更多的测量结果信息。
A powerful perspective in understanding non-equilibrium quantum dynamics is through the time evolution of its entanglement content. Yet apart from a few guiding principles for the entanglement entropy, to date, not much else is known about the refined characters of entanglement propagation. Here, we unveil signatures of the entanglement evolving and information propagation out-of-equilibrium, from the view of entanglement Hamiltonian. As a prototypical example, we study quantum quench dynamics of a one-dimensional Bose-Hubbard model by means of time-dependent density-matrix renormalization gro…
The modular (or entanglement) Hamiltonian correspondent to the half-space-bipartition of a quantum state uniquely characterizes its entanglement properties. However, in the context of lattice models, its explicit form is analytically known only for the Ising chain and certain free theories in one-dimension. In this work, we provide a throughout investigation of entanglement Hamiltonians in lattice models obtained via the Bisognano-Wichmann theorem, which provides an explicit functional form for the entanglement Hamiltonian itself in quantum field theory. Our study encompasses a variety of one-…
Entanglement Hamiltonian for the massless Dirac field on a segment with an inhomogeneous background
研究非均匀背景下段上无质量狄拉克场的纠缠哈密顿量，给出局部与双局部项之和的显式形式，并通过彩虹链模型验证了与格点数值结果的极好一致性。
We enumerate the cases in 2d conformal field theory where the logarithm of the reduced density matrix (the entanglement or modular hamiltonian) may be written as an integral over the energy-momentum tensor times a local weight. These include known examples and new ones corresponding to the time-dependent scenarios of a global and local quench. In these latter cases the entanglement hamiltonian depends on the momentum density as well as the energy density. In all cases the entanglement spectrum is that of the appropriate boundary CFT. We emphasize the role of boundary conditions at the entangli…
On the Bisognano-Wichmann entanglement Hamiltonian of nonrelativistic fermions
本文针对一维半无限自由非相对论费米子，利用两点关联与本征函数 ansatz，证明其基态纠缠哈密顿量在连续与晶格中均具有精确的 Bisognano–Wichmann 形式。
We show that a proportionality between the entanglement Hamiltonian and the Hamiltonian of a subsystem exists near the limit of maximal entanglement under certain conditions. Away from that limit, solvable models show that the coupling range differs in both quantities and allow to investigate the effect.
We consider the entanglement Hamiltonian for an interval in a chain of free fermions in its ground state and show that the lattice expression goes over into the conformal one if one includes the hopping to distant neighbours in the continuum limit. For an infinite chain, this can be done analytically for arbitrary fillings and is shown to be the consequence of the particular structure of the entanglement Hamiltonian, while for finite rings or temperatures the result is based on numerical calculations.
In past work we introduced a method which allows for exact computations of entanglement Hamiltonians. The method relies on computing the resolvent for the projected (on the entangling region) Green's function using a solution to the Riemann-Hilbert problem combined with finite rank perturbation theory. Here we analyze in detail several examples involving excited states of chiral fermions (Dirac and Majorana) on a spatial circle. We compute the exact entanglement Hamiltonians and an exact formula for the change in entanglement entropy due to the introduction of a particle above the Dirac sea. F…
We show that the subregion entanglement Hamiltonians of excited eigenstates of a quantum many-body system are approximately linear combinations of subregionally (quasi)local approximate conserved quantities, with relative commutation errors $\mathcal{O}\left(\frac{\text{subregion boundary area}}{\text{subregion volume}}\right)$. By diagonalizing an entanglement Hamiltonian superdensity matrix (EHSM) for an ensemble of eigenstates, we can obtain these conserved quantities as the EHSM eigen-operators with nonzero eigenvalues. For free fermions, we find the number of nonzero EHSM eigenvalues is c…
Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders
本研究针对耦合量子自旋链的广延纠缠性质开展数值研究，对比了以往低一维纠缠切割的研究范式，分析了无隙与自发对称破缺情形下的纠缠哈密顿量，并用共形场论确定无隙情形的普适行为，为广延纠缠物理的系统探索提供范式起点。
Entanglement Hamiltonians and the quasiparticle picture
针对非平衡多体量子系统缺乏微观模型解析结果的问题，本文将准粒子图像应用于算符，推导出非相互作用费米子模型量子淬火后在弹道标度区域有效的纠缠哈密顿量解析公式，为量子光学实验工程化EH奠定基础。
Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum
研究二维正方形-八边形晶格各向同性模型在量子临界点和聂尔相中的纠缠谱，发现M形磁子模式及长程相互作用的涌现，揭示世界线 confinement/deconfinement 机制。
We study the entanglement Hamiltonian for finite intervals in infinite quantum chains for two different free-particle systems: coupled harmonic oscillators and fermionic hopping models with dimerization. Working in the ground state, the entanglement Hamiltonian describes again free bosons or fermions and is obtained from the correlation functions via high-precision numerics for up to several hundred sites. Far away from criticality, the dominant on-site and nearest-neighbour terms have triangular profiles that can be understood from the analytical results for a half-infinite interval. Near cri…
We study the time evolution of the entanglement entropy in bosonic systems with time-independent, or time-periodic, Hamiltonians. In the first part, we focus on quadratic Hamiltonians and Gaussian initial states. We show that all quadratic Hamiltonians can be decomposed into three parts: (a) unstable, (b) stable, and (c) metastable. If present, each part contributes in a characteristic way to the time-dependence of the entanglement entropy: (a) linear production, (b) bounded oscillations, and (c) logarithmic production. In the second part, we use numerical calculations to go beyond Gaussian st…
We study the continuum limit of the entanglement Hamiltonian of a sphere for the massless scalar field in its ground state by employing the lattice model defined through the discretisation of the radial direction. In two and three spatial dimensions and for small values of the total angular momentum, we find numerical results in agreement with the corresponding ones derived from the entanglement Hamiltonian predicted by conformal field theory. When the mass parameter in the lattice model is large enough, the dominant contributions come from the on-site and the nearest-neighbour terms, whose we…
Sampling reduced density matrix to extract fine levels of entanglement spectrum and restore entanglement Hamiltonian
本文提出一种低技术门槛的量子蒙特卡洛方案，用于精确提取约化密度矩阵，从而获得精细纠缠谱能级并恢复纠缠哈密顿量，适用于环境自由度巨大的系统。
We study the continuum limit of the entanglement hamiltonians of a block of consecutive sites in massless harmonic chains. This block is either in the chain on the infinite line or at the beginning of a chain on the semi-infinite line with Dirichlet boundary conditions imposed at its origin. The entanglement hamiltonians of the interval predicted by Conformal Field Theory for the massless scalar field are obtained in the continuum limit. We also study the corresponding entanglement spectra and the numerical results for the ratios of the gaps are compatible with the operator content of the Boun…
In a recent Letter [Phys. Rev. Lett. 125, 180604 (2020)], we introduced a closed-form analytic expression for the average bipartite von Neumann entanglement entropy of many-body eigenstates of random quadratic Hamiltonians. Namely, of Hamiltonians whose single-particle eigenstates have random coefficients in the position basis. A paradigmatic Hamiltonian for which the expression is valid is the quadratic Sachdev-Ye-Kitaev (SYK2) model in its Dirac fermion formulation. Here we show that the applicability of our result is much broader. Most prominently, it is also relevant for local Hamiltonians…
A critical state under weak measurement is not critical
本文通过场论映射证明弱测量使临界自由费米子的纠缠哈密顿量产生能隙并失去共形对称性，但其本征函数分布不变，从而解释了对数纠缠熵与有能隙纠缠哈密顿量共存的现象。
We investigate the behavior of entanglement-entropy on a broad scale, that is, a large class of systems, Hamiltonians and states describing the interaction of many degrees of freedom. It is one of our aims to show which general characteristics are responsible for the different types of quantitative behavior of entantglement-entropy. Our main lesson is that what really matters is the degree of degeneracy of the spectrum of certain nearby reference Hamiltonians. For calculational convenience we study primarily systems defined on large but finite regions of regular lattices. We show that general …
Deviation from maximal entanglement for mid-spectrum eigenstates of local Hamiltonians
针对局部哈密顿量的谱中部本征态，证明其平均纠缠熵与最大熵及热力学熵存在至少正常数偏差，揭示与随机态的差异。
Entanglement spectra (ES) for the critical SU(N) (2 <= N <= 4) spin chains and other integrable models of finite length are studied with the density matrix renormalization group method. For all models under investigation, the level spacings and the degeneracy structure of the ES are in excellent agreement with the spectra of the corner Hamiltonian, defined as the generator of the associated corner transfer matrix. The correspondence holds between the ES (n) at the n-th cut position from the edge of the spin model, and the corner Hamiltonian of length n, for all small values of n. The cut posit…
Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study
本文通过量子蒙特卡罗方法研究晶格-比森诺-维希曼形式在非平移不变系统中的应用，揭示了纠缠哈密顿量的重构方法及不同量子相变行为。
Recent advances in the field of strongly correlated electron systems allow to access the entanglement properties of interacting fermionic models, by means of Monte Carlo simulations. We briefly review the techniques used in this context to determine the entanglement entropies and correlations of the entanglement Hamiltonian. We further apply these methods to compute the spin two-point function of entanglement Hamiltonian for a stripe embedded into a correlated topological insulator. Further we discuss a recent method that allows an unbiased, numerically exact, direct determination of the entan…
In quantum statistical mechanics, it is of fundamental interest to understand how close the bipartite entanglement entropy of eigenstates of quantum chaotic Hamiltonians is to maximal. For random pure states in the Hilbert space, the average entanglement entropy is known to be nearly maximal, with a deviation that is, at most, a constant. Here we prove that, in a system that is away from half filling and divided in two equal halves, an upper bound for the average entanglement entropy of random pure states with a fixed particle number and normally distributed real coefficients exhibits a deviat…
Entanglement dynamics of many-body quantum states: sensitivity to system conditions and a hidden universality
研究不同量子态和哈密顿量在对称约束下的纠缠统计演变，揭示系统参数与纠缠熵的深层联系。
We consider free-fermion chains in the ground state and the entanglement Hamiltonian for a subsystem consisting of two separated intervals. In this case, one has a peculiar long-range hopping between the intervals in addition to the well-known and dominant short-range hopping. We show how the continuum expressions can be recovered from the lattice results for general filling and arbitrary intervals. We also discuss the closely related case of a single interval located at a certain distance from the end of a semi-infinite chain and the continuum limit for this problem. Finally, we show that for…
It is well known that in Anderson localized systems, starting from a random product state the entanglement entropy remains bounded at all times. However, we show that adding a single boundary term to an Anderson localized Hamiltonian leads to unbounded growth of entanglement. Our results imply that Anderson localization is not a local property. One cannot conclude that a subsystem has Anderson localized behavior without looking at the whole system, as a term that is arbitrarily far from the subsystem can affect the dynamics of the subsystem in such a way that the features of Anderson localizat…
We numerically study the evolution of spectral correlations in the entanglement Hamiltonian (EH) of non-interacting fermions in the Aubry-André-Harper (AAH) model. We analyze the time evolution of the EH spectrum in a nonequilibrium setting by studying several quantities: spectral distribution, level statistics, entanglement entropy, and spectral form factor (SFF) in the context of the delocalization-localization transition in the AAH model. It is observed that the SFF of the entanglement spectrum in the delocalized phase and at the phase-transition point evolves in three-time intervals. We ma…
Correlated many-body problems ubiquitously appear in various fields of physics such as condensed matter physics, nuclear physics, and statistical physics. However, due to the interplay of the large number of degrees of freedom, it is generically impossible to treat these problems from first principles. Thus the construction of a proper model, namely effective Hamiltonian, is essential. Here, we propose a simple scheme of constructing Hamiltonians from given energy or entanglement spectra with machine learning. We apply the proposed scheme to the Hubbard model at the half-filling, and compare t…
Entanglement dynamics after quenches with inhomogeneous Hamiltonians
研究不均匀哈密顿量下双区域系统的纠缠动力学，推导出在长时标极限下的纠缠熵公式，并通过数值模拟验证分析结果，发现强不均匀性抑制了输运和纠缠增长，但纠缠在中间时间仍持续增加。
We investigate the second quantization form of the entanglement Hamiltonian (EH) of various subregions for the ground-state of several interacting lattice fermions and spin models. The relation between the EH and the model Hamiltonian itself is an unsolved problem for the ground-state of generic local Hamiltonians. In this letter, we demonstrate that the EH is practically local and its dominant components are related to the terms present in the model Hamiltonian up to a smooth spatially varying temperature even for (a) discrete lattice systems, (b) systems with no emergent conformal or Lorentz…
Transport interpretation of entanglement Hamiltonian cumulants in integrable quantum quenches
该研究建立了纠缠哈密顿量累积量与守恒荷流累积量的联系，为纠缠动力学提供输运诠释，对自由、共形及相互作用可积系统的纠缠涨落给出统一描述。
Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system
通过新发展的量子蒙特卡洛方法研究自旋-1/2海森堡双层系统，发现纠缠哈密顿量中存在相关长程相互作用项并导致有限温度相变，从而揭示Li-Haldane-Poilblanc猜想忽略了必要修正。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。