arXiv subjects

Lucas Hackl

Publications and source records attributed to Lucas Hackl.

At least 19 recordsLinked to original sources

arXiv2026

Probing Spacetime Topology and Superposition with Accelerated Detectors

We study entanglement harvested by Unruh DeWitt detectors following Rindler trajectories in compactified and superposed Minkowski spacetime. We consider different directions of acceleration (both parallel and antiparallel), separation between detectors and direction of spatial compactification mutually perpendicular to each other. Using the standard entanglement harvesting protocol, we analyze how these features influence the extracted correlations. When detector separation is perpendicular to the direction of acceleration, the harvested entanglement is uniformly suppressed due to increased spacelike separation. Compactification enhances field correlations leading to an increased concurrence and an extended harvesting range at higher accelerations. Additionally, we show that spacetime superposition introduces interference effects that further enlarge the entanglement harvesting region in parameter space, particularly in the high acceleration regime. We also find that the effect of antiparallel acceleration yielding significantly higher entanglement than parallel acceleration prevails in compactified and superposed spacetime.

gr-qc↗

arXiv2026

Typical entanglement in anyon chains: Page curves beyond Lie group symmetries

We study bipartite entanglement statistics in one-dimensional anyon chains, whose Hilbert spaces are constrained by fusion rules of unitary pre-modular categories. Our setup generalizes previous frameworks on symmetry-resolved entanglement entropy for non-abelian Lie group symmetries to the setting of quantum groups. We derive analytical expressions for the average anyonic entanglement entropy and its variance. Surprisingly, despite the constrained Hilbert space structure, the large $L$ expansion has no universal $O(\sqrt{L})$ or $O(1)$ symmetry-type corrections except for a subleading topological correction term that produces a Page curve asymmetry. We further show that the variance decays exponentially with system size, establishing the typicality. Numerical simulations of the integrable and quantum-chaotic golden chain Hamiltonian show that chaotic mid-spectrum eigenstates match the Haar-random predictions, supporting the use of eigenstate entanglement as a diagnostic of quantum chaos. Our results establish the anyonic Page curve as an appropriate chaotic benchmark in topological many-body systems and connect anyonic entanglement to Page-type universality in quantum many-body physics.

quant-ph↗

arXiv2026

Representation theory of inhomogeneous Gaussian unitaries

Gaussian unitaries, generated by quadratic Hamiltonians, are fundamental in quantum optics and continuous-variable computing. Their structures correspond to symplectic (bosons) and orthogonal (fermions) groups, but physical realizations give rise to their respective double covers, introducing phase and sign ambiguities. The homogeneous (quadratic-only) case has been resolved through a parameterization constructed in a recent work [arXiv:2409.11628]. We extend the previous framework to inhomogeneous Gaussian unitaries parameterized by $(M,z,\Psi)$. The Baker-Campbel-Hausdorff formula allows us then to factor any Gaussian unitary into a squeezing and a displacement transformation, from which we derive the group multiplication law.

quant-ph↗

arXiv2025

Random matrix prediction of average entanglement entropy in non-Abelian symmetry sectors

We study the average bipartite entanglement entropy of Haar-random pure states in quantum many-body systems with global $\mathrm{SU}(2)$ symmetry, constrained to fixed total spin $J$ and magnetization $J_z = 0$. Focusing on spin-$\tfrac12$ lattices and subsystem fractions $f < \frac{1}{2}$, we derive a asymptotic expression for the average entanglement entropy up to constant order in the system volume $V$. In addition to the expected leading volume law term, we prove the existence of a $\frac{1}{2}\log V$ finite-size correction resulting from the scaling of the Clebsch-Gordon coefficients and compute explicitly the $O(1)$ contribution reflecting angular-momentum coupling within magnetization blocks. Our analysis uses features of random matrix ensembles and provides a fully analytical treatment for arbitrary spin densities, thereby extending Page type results to non-Abelian sectors and clarifying how $\mathrm{SU}(2)$ symmetry shapes average entanglement.

quant-ph↗

arXiv2025

Average entanglement entropy of a small subsystem in a constrained pure Gaussian state ensemble

We consider ensembles of pure Gaussian states parametrized by single-mode marginals and (optionally) specific mode-mode correlations. Such ensembles provide a model for the final states when isolated quantum systems thermalize, as they can reproduce thermal properties locally, while being globally pure. By an analysis using real replicas and the coherent state representation of Gaussian states we show that the average entanglement entropy of a small subsystem is the same as the von Neumann entropy of a mixed Gaussian state with the same marginals, but no correlations. Finally, we discuss how these ensembles provide a model for Hawking radiation assuming unitary evolution, and discuss some of their properties in relations to the Page curve of Hawking radiation.

quant-ph↗

arXiv2025

Adiabatic vacua from linear complex structures

Adiabatic vacua play a central role in quantum fields in cosmological spacetimes, where they serve as distinguished initial conditions and as reference states for the renormalization of observables. In this paper we introduce new methods based on linear complex structures which provide a powerful tool for determining adiabatic vacua. The new methods generalize both the standard WKB appoach and the Lewis-Riesenfeld invariants, and allow us to study the problem of many coupled bosonic degrees of freedom with general quadratic time-dependent Hamiltonian. We show that the adiabatic number operator and the adiabatic vacuum of finite order can be expressed in terms of the adiabatic complex structure of the same order. We compare our results to standard techniques which apply only to a single degree of freedom, and comment on its applicability to problems in quantum fields in cosmological spacetimes, many-body systems and quantum thermodynamics, where the Hamiltonian is time dependent with slowly-changing parameters.

gr-qc↗

arXiv2024

Average mutual information for random fermionic Gaussian quantum states

Studying the typical entanglement entropy of a bipartite system when averaging over different ensembles of pure quantum states has been instrumental in different areas of physics, ranging from many-body quantum chaos to black hole evaporation. We extend such analysis to open quantum systems and mixed states, where we compute the typical mutual information in a bipartite system averaged over the ensemble of mixed Gaussian states with a fixed spectrum. Tools from random matrix theory and determinantal point processes allow us to compute arbitrary k-point correlation functions of the singular values of the corresponding complex structure in a subsystem for a given spectrum in the full system. In particular, we evaluate the average von Neumann entropy in a subsystem based on the level density and the average mutual information. Those results are given for finite system size as well as in the thermodynamic limit.

quant-ph↗

arXiv2024

Entanglement harvesting in quantum superposed spacetime

We investigate the phenomenon of entanglement harvesting for a spacetime in quantum superposition, using two Unruh-DeWitt detectors interacting with a quantum scalar field where the spacetime background is modeled as a superposition of two quotient Minkowski spaces which are not related by diffeomorphisms. Our results demonstrate that the superposed nature of spacetime induces interference effects that can significantly enhance entanglement for both twisted and untwisted field. We compute the concurrence, which quantifies the harvested entanglement, as function of the energy gap of detectors and their separation. We find that it reaches its maximum when we condition the final spacetime superposition state to match the initial spacetime state. Notably, for the twisted field, the parameter region without entanglement exhibits a significant deviation from that observed in classical Minkowski space or a single quotient Minkowski space.

gr-qc↗

arXiv2024

Finite complexity of the de Sitter vacuum

The ER=EPR conjecture states that quantum entanglement between boundary degrees of freedom leads to the emergence of bulk spacetime itself. Although this has been tested extensively in String Theory for asymptotically anti-de Sitter spacetimes, its implications for an accelerating universe, such as our own, remain less explored. Assuming a cosmic version of ER=EPR for de Sitter space, we explore computational complexity corresponding to long-range entanglement responsible for bulk states on spacelike hypersurfaces. Rather remarkably, we find that the complexity (per unit volume) of the Euclidean vacuum, as an entangled state over two boundary CFT vacua, is finite both in the UV and the IR, which provides additional evidence for cosmic ER=EPR. Our result seems to be a universal feature of spacetimes with horizons and, moreover, hints at new features of the thermofield double state for studying thermalization of any quantum system.

hep-th↗

arXiv2024

Representation theory of Gaussian unitary transformations for bosonic and fermionic systems

Gaussian unitary transformations are generated by quadratic Hamiltonians, i.e., Hamiltonians containing quadratic terms in creations and annihilation operators, and are heavily used in many areas of quantum physics, ranging from quantum optics and condensed matter theory to quantum information and quantum field theory in curved spacetime. They are known to form a representation of the metaplectic and spin group for bosons and fermions, respectively. These groups are the double covers of the symplectic and special orthogonal group, respectively, and our goal is to analyze the behavior of the sign ambiguity that one needs to deal with when moving between these groups and their double cover. We relate this sign ambiguity to expectation values of the form $\langle 0|\exp{(-i\hat{H})}|0\rangle$, where $|0\rangle$ is a Gaussian state and $\hat{H}$ an arbitrary quadratic Hamiltonian. We provide closed formulas for $\langle 0|\exp{(-i\hat{H})}|0\rangle$ and show how we can efficiently describe group multiplications in the double cover without the need of going to a faithful representation on an exponentially large or even infinite-dimensional space. Our construction relies on an explicit parametrization of these two groups (metaplectic, spin) in terms of symplectic and orthogonal group elements together with a twisted U(1) group.

quant-ph↗

arXiv2023

Random pure Gaussian states and Hawking radiation

A black hole evaporates by Hawking radiation. Each mode of that radiation is thermal. If the total state is nevertheless to be pure, modes must be entangled. Estimating the minimum size of this entanglement has been an important outstanding issue. We develop a new theory of constrained random symplectic transformations, based on that the total state is pure and Gaussian with given marginals. In the random constrained symplectic model we then compute the distribution of mode-mode correlations, from which we bound mode-mode entanglement. Modes of frequency much larger than $\frac{k_B T_{H}(t)}{\hbar}$ are not populated at time $t$ and drop out of the analysis. Among the other modes we find that correlations and hence entanglement between relatively thinly populated modes (early-time high-frequency modes and/or late modes of any frequency) to be strongly suppressed. Relatively highly populated modes (early-time low-frequency modes) can on the other hand be strongly correlated, but a detailed analysis reveals that they are nevertheless very unlikely to be entangled. Our analysis hence establishes that restoring unitarity after a complete evaporation of a black hole does not require any significant quantum entanglement between any pair of Hawking modes. Our analysis further gives exact general expressions for the distribution of mode-mode correlations in random, pure, Gaussian states with given marginals, which may have applications beyond black hole physics.

gr-qc↗

arXiv2023

Typical entanglement entropy in systems with particle-number conservation

We calculate the typical bipartite entanglement entropy $\langle S_A\rangle_N$ in systems containing indistinguishable particles of any kind as a function of the total particle number $N$, the volume $V$, and the subsystem fraction $f=V_A/V$, where $V_A$ is the volume of the subsystem. We expand our result as a power series $\langle S_A\rangle_N=a f V+b\sqrt{V}+c+o(1)$, and find that $c$ is universal (i.e., independent of the system type), while $a$ and $b$ can be obtained from a generating function characterizing the local Hilbert space dimension. We illustrate the generality of our findings by studying a wide range of different systems, e.g., bosons, fermions, spins, and mixtures thereof. We provide evidence that our analytical results describe the entanglement entropy of highly excited eigenstates of quantum-chaotic spin and boson systems, which is distinct from that of integrable counterparts.

quant-ph↗

arXiv2023

Probing Hilbert space fragmentation and the block inverse participation ratio

We consider a family of quantum many-body Hamiltonians that show exact Hilbert space fragmentation in certain limits. The question arises whether fragmentation has implications for Hamiltonians in the vicinity of the subset defined by these exactly fragmented models, in particular in the thermodynamic limit. We attempt to illuminate this issue by considering distinguishable classes of transitional behavior between fragmented and nonfragmented regimes and employing a set of numerical observables that indicate this transition. As one of these observables we present a modified inverse participation ratio (IPR) that is designed to capture the emergence of fragmented block structures. We compare this block IPR to other definitions of inverse participation ratios, as well as to the more traditional measures of level-spacing statistics and entanglement entropy. In order to resolve subtleties that arise in the numerics, we use perturbation theory around the fragmented limit as a basis for defining an effective block structure. We find that our block IPR predicts a boundary between fragmented and nonfragmented regimes that is compatible with results based on level statistics and bipartite entanglement. A scaling analysis indicates that a finite region around the exactly fragmented limit is dominated by effects of approximate fragmentation, even in the thermodynamic limit, and suggests that fragmentation constitutes a phase. We provide evidence for the universality of our approach by applying it to a different family of Hamiltonians, that features a fragmented limit due to emergent dipole conservation.

cond-mat.str-el↗

arXiv2023

Average pure-state entanglement entropy in spin systems with SU(2) symmetry

We study the effect that the SU(2) symmetry, and the rich Hilbert space structure that it generates in lattice spin systems, has on the average entanglement entropy of highly excited eigenstates of local Hamiltonians and of random pure states. Focusing on the zero total magnetization sector ($J_z=0$) for different fixed total spin $J$, we argue that the average entanglement entropy of highly excited eigenstates of quantum-chaotic Hamiltonians and of random pure states has a leading volume-law term whose coefficient $s_A$ depends on the spin density $j=J/(\mathfrak{j}L)$, with $s_A(j \rightarrow 0)=\ln (2\mathfrak{j}+1)$ and $s_A(j \rightarrow 1)=0$, where $\mathfrak{j}$ is the microscopic spin. We provide numerical evidence that $s_A$ is smaller in highly excited eigenstates of integrable interacting Hamiltonians, which lends support to the expectation that the average eigenstate entanglement entropy can be used as a diagnostic of quantum chaos and integrability for Hamiltonians with non-Abelian symmetries. In the context of Hamiltonian eigenstates we consider spins $\mathfrak{j}=\frac12$ and $1$, while for our calculations based on random pure states we focus on the spin $\mathfrak{j}=\frac12$ case.

quant-ph↗

arXiv2022

Hilbert space fragmentation and interaction-induced localization in the extended Fermi-Hubbard model

We study Hilbert space fragmentation in the extended Fermi-Hubbard model with nearest and next-nearest-neighbor interactions. Using a generalized spin/mover picture and saddle point methods, we derive lower bounds for the scaling of the number of frozen states and for the size of the largest block preserved under the dynamics. We find fragmentation for strong nearest- and next-nearest-neighbor repulsions as well as for the combined case. Our results suggest that the involvement of next-nearest-neighbor repulsions leads to an increased tendency for localization. We then model the dynamics for larger systems using Markov simulations to test these findings and unveil in which interaction regimes the dynamics becomes spatially localized. In particular, we show that for strong nearest- and next-nearest-neighbor interactions random initial states will localize provided that the density of initial movers is sufficiently low.

cond-mat.str-el↗

arXiv2021

Volume-law entanglement entropy of typical pure quantum states

The entanglement entropy of subsystems of typical eigenstates of quantum many-body Hamiltonians has been recently conjectured to be a diagnostic of quantum chaos and integrability. In quantum chaotic systems it has been found to behave as in typical pure states, while in integrable systems it has been found to behave as in typical pure Gaussian states. In this tutorial, we provide a pedagogical introduction to known results about the entanglement entropy of subsystems of typical pure states and of typical pure Gaussian states. They both exhibit a leading term that scales with the volume of the subsystem, when smaller than one half of the volume of the system, but the prefactor of the volume law is fundamentally different. It is constant (and maximal) for typical pure states, and it depends on the ratio between the volume of the subsystem and of the entire system for typical pure Gaussian states. Since particle-number conservation plays an important role in many physical Hamiltonians, we discuss its effect on typical pure states and on typical pure Gaussian states. We prove that while the behavior of the leading volume-law terms does not change qualitatively, the nature of the subleading terms can change. In particular, subleading corrections can appear that depend on the square root of the volume of the subsystem. We unveil the origin of those corrections. Finally, we discuss the connection between the entanglement entropy of typical pure states and analytical results obtained in the context of random matrix theory, as well as numerical results obtained for physical Hamiltonians.

quant-ph↗

arXiv2021

Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states

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 entropy for bosonic quantum systems [De Palma et al., arXiv:2105.05627]. This technique allows us to extend our result to generic mixed initial states, with the squashed entanglement providing the right generalization of the entanglement entropy. We discuss several applications of our results to physical systems with (weakly) interacting Hamiltonians and periodically driven quantum systems, including certain quantum field theory models.

quant-ph↗

arXiv2021

Experimental proposal to probe the extended Pauli principle

All matter is made up of fermions -- one of the fundamental type of particles in nature. Fermions follow the Pauli exclusion principle, stating that two or more identical fermions cannot occupy the same quantum state. Antisymmetry of the fermionic wavefunction, however, implies additional constraints on the natural occupation numbers. These constraints depend on the dimensionality and purity of the system and have so far not been explored experimentally. Here, we propose an experiment in a system of multiple quantum dots capable of producing the highly entangled fermionic states necessary to reach the regime, where these additional constraints become dominant and can be probed. The type and strength of the required multi-fermion entanglement provides barriers to reaching deep into this regime. Transcending these barriers thus serves as a testing ground for the capabilities of future fermionic quantum information processing as well as quantum computer architectures based on fermionic states.

quant-ph↗