Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1905.01144 · Journal of Statistical Mechanics Theory and Experiment

Entanglement Hamiltonians in 1D free lattice models after a global quantum quench

Giuseppe Di Giulio, Raúl Arias, Erik Tonni C

Published Dec 1, 2019• 57 citations
arXivHTMLPDF

Abstract

Abstract We study the temporal evolution of the entanglement Hamiltonian of an interval after a global quantum quench in 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 contours for the entanglement entropies. The temporal evolution of these contours for the entanglement entropy is studied, also by employing existing conformal field theory results for the semi-infinite line and the quasi-particle picture for the global quench.

DOI
10.1088/1742-5468/ab4e8f

Related papers

Entanglement Hamiltonians in 1D free lattice models after a global quantum quench

Giuseppe Di Giulio, Raúl Arias, Erik Tonni C

We study the temporal evolution of the entanglement hamiltonian of an interval after a global quantum quench in 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 contours for the entanglement entropies. The temporal evolution of these contours for the entanglement entropy is studied, also by employing existing conformal field theory results for the semi-infinite line and the quasi-particle picture for the global quench.

•Nov 1, 2019•61 citations

Entanglement evolution after a global quench across a conformal defect

Luca Capizzi, Viktor Eisler

We study the evolution of entanglement after a global quench in a one-dimensional quantum system with a localized impurity. For systems described by a conformal field theory, the entanglement entropy between the two regions separated by the defect grows linearly in time. Introducing the notion of boundary twist fields, we show how the slope of this growth can be related to the effective central charge that emerges in the study of ground-state entropy in the presence of the defect. On the other hand, we also consider a particular lattice realization of the quench in a free-fermion chain with a conformal defect. Starting from a gapped initial state, we obtain the slope via a quasiparticle ansatz and observe small discrepancies between the field theory and lattice results, which persist even in the limit of a vanishing gap.

arXiv:2209.03297•SciPost Physics•Apr 13, 2023•14 citations

Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems

Erik Tonni C, Javier Rodríguez-Laguna, Germán Sierra

Abstract 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 the same boundary condition is imposed at the endpoints. A contour function for the entanglement entropies corresponding to this configuration is also considered, being closely related to the entanglement hamiltonian. The analytic expressions obtained by considering the curved spacetime which characterises the rainbow model have been checked against numerical data for the rainbow chain, finding an excellent agreement.

arXiv:1712.03557•Journal of Statistical Mechanics Theory and Experiment•Apr 1, 2018•107 citations

Entanglement Hamiltonians for non-critical quantum chains

Viktor Eisler, Giuseppe Di Giulio, Erik Tonni C +1 more

Abstract 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 criticality, the longer-range couplings, although small, lead to a more complex picture. A comparison between the exact spectra and entanglement entropies and those resulting from the dominant terms in the Hamiltonian is also reported.

arXiv:2007.01804•Journal of Statistical Mechanics Theory and Experiment•Oct 1, 2020•43 citations

Entanglement Hamiltonians for non-criticalquantum chains

Viktor Eisler, Giuseppe Di Giulio, Erik Tonni C +1 more

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 criticality, the longer-range couplings, although small, lead to a more complex picture. A comparison between the exact spectra and entanglement entropies and those resulting from the dominant terms in the Hamiltonian is also reported.

•Jan 1, 2020•29 citations

A contour for the entanglement entropies in harmonic lattices

Andrea Coser, Cristiano De Nobili, Erik Tonni C

Abstract We construct a contour function for the entanglement entropies in generic harmonic lattices. In one spatial dimension, numerical analysis are performed by considering harmonic chains with either periodic or Dirichlet boundary conditions. In the massless regime and for some configurations where the subsystem is a single interval, the numerical results for the contour function are compared to the inverse of the local weight function which multiplies the energy-momentum tensor in the corresponding entanglement hamiltonian, found through conformal field theory methods, and a good agreement is observed. A numerical analysis of the contour function for the entanglement entropy is performed also in a massless harmonic chain for a subsystem made by two disjoint intervals.

arXiv:1701.08427•Journal of Physics A Mathematical and Theoretical•Jun 13, 2017•68 citations
Abstract We study the temporal evolution of the entanglement Hamiltonian of an interval after a global quantum quench in 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 contours for the entanglement entropies. The temporal evolution of these contours for the entanglement entropy is studied, also by employing existing conformal field theory results for the semi-infinite line and the quasi-particle picture for the global quench.
We study the temporal evolution of the entanglement hamiltonian of an interval after a global quantum quench in 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 contours for the entanglement entropies. The temporal evolution of these contours for the entanglement entropy is studied, also by employing existing conformal field theory results for the semi-infinite line and the quasi-particle picture for the global quench.
We study the evolution of entanglement after a global quench in a one-dimensional quantum system with a localized impurity. For systems described by a conformal field theory, the entanglement entropy between the two regions separated by the defect grows linearly in time. Introducing the notion of boundary twist fields, we show how the slope of this growth can be related to the effective central charge that emerges in the study of ground-state entropy in the presence of the defect. On the other hand, we also consider a particular lattice realization of the quench in a free-fermion chain with a conformal defect. Starting from a gapped initial state, we obtain the slope via a quasiparticle ansatz and observe small discrepancies between the field theory and lattice results, which persist even in the limit of a vanishing gap.
Abstract 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 the same boundary condition is imposed at the endpoints. A contour function for the entanglement entropies corresponding to this configuration is also considered, being closely related to the entanglement hamiltonian. The analytic expressions obtained by considering the curved spacetime which characterises the rainbow model have been checked against numerical data for the rainbow chain, finding an excellent agreement.
Abstract 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 criticality, the longer-range couplings, although small, lead to a more complex picture. A comparison between the exact spectra and entanglement entropies and those resulting from the dominant terms in the Hamiltonian is also reported.
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 criticality, the longer-range couplings, although small, lead to a more complex picture. A comparison between the exact spectra and entanglement entropies and those resulting from the dominant terms in the Hamiltonian is also reported.
Abstract We construct a contour function for the entanglement entropies in generic harmonic lattices. In one spatial dimension, numerical analysis are performed by considering harmonic chains with either periodic or Dirichlet boundary conditions. In the massless regime and for some configurations where the subsystem is a single interval, the numerical results for the contour function are compared to the inverse of the local weight function which multiplies the energy-momentum tensor in the corresponding entanglement hamiltonian, found through conformal field theory methods, and a good agreement is observed. A numerical analysis of the contour function for the entanglement entropy is performed also in a massless harmonic chain for a subsystem made by two disjoint intervals.