### Abstract

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 deviation from the maximal value that grows with the square root of the volume of the system. Exact numerical results for highly excited eigenstates of a particle number conserving quantum chaotic model indicate that the bound is saturated with increasing system size.

Original language | English (US) |
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Article number | 220603 |

Journal | Physical Review Letters |

Volume | 119 |

Issue number | 22 |

DOIs | |

State | Published - Nov 29 2017 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Physical Review Letters*,

*119*(22), [220603]. https://doi.org/10.1103/PhysRevLett.119.220603

}

*Physical Review Letters*, vol. 119, no. 22, 220603. https://doi.org/10.1103/PhysRevLett.119.220603

**Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians.** / Vidmar, Lev; Rigol, Marcos.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians

AU - Vidmar, Lev

AU - Rigol, Marcos

PY - 2017/11/29

Y1 - 2017/11/29

N2 - 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 deviation from the maximal value that grows with the square root of the volume of the system. Exact numerical results for highly excited eigenstates of a particle number conserving quantum chaotic model indicate that the bound is saturated with increasing system size.

AB - 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 deviation from the maximal value that grows with the square root of the volume of the system. Exact numerical results for highly excited eigenstates of a particle number conserving quantum chaotic model indicate that the bound is saturated with increasing system size.

UR - http://www.scopus.com/inward/record.url?scp=85037683434&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85037683434&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.119.220603

DO - 10.1103/PhysRevLett.119.220603

M3 - Article

C2 - 29286792

AN - SCOPUS:85037683434

VL - 119

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 22

M1 - 220603

ER -