Target space entanglement in quantum mechanics of fermions and matrices

Abstract

We consider entanglement of first-quantized identical particles by adopting an algebraic approach. In particular, we investigate fermions whose wave functions are given by the Slater determinants, as for singlet sectors of one-matrix models. We show that the upper bounds of the general Rényi entropies are $N\log 2$ for $N$ particles or an $N\times N$ matrix. We compute the target space entanglement entropy and the mutual information in a free one-matrix model. We confirm the area law: the single-interval entropy for the ground state scales as $\frac{1}{3}\log N$ in the large $N$ model. We obtain an analytical $\mathcal{O}(N^0)$ expression of the mutual information for two intervals in the large $N$ expansion.

arXiv comment28 pages + appendices, 4 figures; v2: typos corrected

References in corpus (39)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• M Theory As A Matrix Model: A Conjecture
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Aspects of Holographic Entanglement Entropy
• Entropy and Area
• A Covariant Holographic Entanglement Entropy Proposal
• Calculation of reduced density matrices from correlation functions
• Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
• Quantum corrections to holographic entanglement entropy
• Entanglement entropy in free quantum field theory
• Probing entanglement in a many-body-localized system
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• The Ryu-Takayanagi Formula from Quantum Error Correction
• The entanglement of indistinguishable particles shared between two parties
• Entanglement entropy of two disjoint intervals in conformal field theory
• Quantum tensor product structures are observable-induced
• Remarks on entanglement entropy for gauge fields
• A subsystem-independent generalization of entanglement
• Bipartite Fluctuations as a Probe of Many-Body Entanglement
• Symmetry-resolved entanglement in many-body systems
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• A hole-ographic spacetime
• The entanglement entropy of one-dimensional gases
• Symmetry resolved entanglement in free fermionic systems
• Entanglement and Particle Identity: A Unifying Approach
• Entanglement, Particle Identity and the GNS Construction: A Unifying Approach
• Holographic Holes in Higher Dimensions
• Operationally accessible entanglement of one dimensional spinless fermions
• Algebraic Approach to Entanglement and Entropy
• Entanglement entropy in two dimensional string theory
• Bulk entanglement entropy in perturbative excited states
• Geometric Entropy of Nonrelativistic Fermions and Two Dimensional Strings
• Gauge Invariant Target Space Entanglement in D-Brane Holography
• Bulk Entanglement Entropy and Matrices
• Areas and entropies in BFSS/gravity duality
• A proof of the Shepp-Olkin entropy concavity conjecture
• Quantum Quench in Non-relativistic Fermionic Field Theory: Harmonic traps and 2d String Theory
• Double-Trace Deformations and Entanglement Entropy in AdS
• Entanglement entropy for free scalar fields in AdS

Cited by in corpus (8)

• Entanglement in the Quantum Hall Matrix Model
• Matrix Entanglement
• Finiteness of Entanglement Entropy in Collective Field Theory
• Dress code for infrared safe scattering in QED
• Target space entanglement in a matrix model for the bubbling geometry
• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics
• Target space entanglement in quantum mechanics of fermions at finite temperature