Typical entanglement entropy in systems with particle-number conservation

Abstract

We calculate the typical bipartite entanglement entropy $⟨S_A{⟩}_N$ 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 $⟨S_A{⟩}_N=afV+b\sqrt{V}+c+o(1)$, 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.

23+6 pages, 8+1 figures

References in corpus (44)

• Area laws for the entanglement entropy - a review
• Topological entanglement entropy
• Aspects of Holographic Entanglement Entropy
• Entanglement spectrum of a topological phase in one dimension
• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Does a single eigenstate encode the full Hamiltonian?
• Quantitative entanglement witnesses
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• Subsystem ETH
• Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
• Entanglement entropy of excited states
• The microscopic origin of thermodynamic entropy in isolated systems
• Entanglement and matrix elements of observables in interacting integrable systems
• Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians
• Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
• Universality in volume law entanglement of pure quantum states
• Statistical properties of the spectrum the extended Bose-Hubbard model
• Renyi Entropy of Chaotic Eigenstates
• Volume Law and Quantum Criticality in the Entanglement Entropy of Excited Eigenstates of the Quantum Ising Model
• Weak and strong typicality in quantum systems
• Quantum Entanglement of the Sachdev-Ye-Kitaev Models
• Two-component Structure in the Entanglement Spectrum of Highly Excited States
• Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians
• Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems
• Structure of chaotic eigenstates and their entanglement entropy
• Entanglement Across a Transition to Quantum Chaos
• Universal eigenstate entanglement of chaotic local Hamiltonians
• Typical entanglement entropy in the presence of a center: Page curve and its variance
• The Page Curve for Fermionic Gaussian States
• Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models
• Entanglement in ground and excited states of gapped fermion systems and their relationship with fermi surface and thermodynamic equilibrium properties
• Bound states and entanglement in the excited states of quantum spin chains
• Symmetry-resolved Page curves
• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians
• Eigenstate Gibbs Ensemble in Integrable Quantum Systems
• Bipartite entanglement entropy of the excited states of the free fermions and the harmonic oscillators
• Characterizing complexity of many-body quantum dynamics by higher-order eigenstate thermalization
• On integrable Hamiltonians for higher spin XXZ chain
• Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians
• Quantifying quantum chaos through microcanonical distributions of entanglement
• Information measures for a local quantum phase transition: Lattice fermions in a one-dimensional harmonic trap
• Average pure-state entanglement entropy in spin systems with SU(2) symmetry
• Probing Hilbert space fragmentation and the block inverse participation ratio

Cited by in corpus (7)

• Symmetry breaking in chaotic many-body quantum systems at finite temperature
• Non-Abelian entanglement asymmetry in random states
• Subsystem entropy in 2d CFT and KdV ETH
• Onset of Quantum Chaos and Ergodicity in Spin Systems with Highly Degenerate Hilbert Spaces
• Entanglement patterns of quantum chaotic Hamiltonians with a scalar U(1) charge
• Average Rényi Entanglement Entropy in Gaussian Boson Sampling
• Average entanglement entropy of a small subsystem in a constrained pure Gaussian state ensemble