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:cond-mat/0602077 · Physical Review A

Entanglement scaling in critical two-dimensional fermionic and bosonic systems

Thomas Barthel, Ming-Chiang Chung, Ulrich Schollwöck

Published Aug 29, 2006• 182 citations
arXivHTMLPDF

Abstract

We relate the reduced density matrices of quadratic fermionic and bosonic models to their Green's function matrices in a unified way and calculate the scaling of the entanglement entropy of finite systems in an infinite universe exactly. For critical fermionic two-dimensional (2D) systems at $T=0$, two regimes of scaling are identified: generically, we find a logarithmic correction to the area law with a prefactor dependence on the chemical potential that confirms earlier predictions based on the Widom conjecture. If, however, the Fermi surface of the critical system is zero-dimensional, then we find an area law with a sublogarithmic correction. For a critical bosonic 2D array of coupled oscillators at $T=0$, our results show that the entanglement entropy follows the area law without corrections.

DOI
10.1103/physreva.74.022329

Related papers

Scaling behavior of entanglement in two- and three-dimensional free-fermion systems

Weifei Li, Letian Ding, Rong Yu +2 more

Exactly solving a spinless fermionic system in two and three dimensions, we investigate the scaling behavior of the block entropy in critical and noncritical phases. The scaling of the block entropy crucially depends on the nature of the excitation spectrum of the system and on the topology of the Fermi surface. Noticeably, in the critical phases the scaling violates the area law and acquires a logarithmic correction only when a well-defined Fermi surface exists in the system. When the area law is violated, we accurately verify a conjecture for the prefactor of the logarithmic correction, proposed by D. Gioev and I. Klich [Phys. Rev. Lett. 96, 100503 (2006)].

arXiv:quant-ph/0602094•Physical Review B•Aug 17, 2006•122 citations

Statistics Dependence of the Entanglement Entropy

M. Cramer, Jens Eisert, Martin Bodo Plenio

The entanglement entropy of a distinguished region of a quantum many-body system reflects the entanglement in its pure ground state. Here we establish scaling laws for this entanglement in critical quasifree fermionic and bosonic lattice systems, without resorting to numerical means. We consider the setting of D-dimensional half-spaces which allows us to exploit a connection to the one-dimensional case. Intriguingly, we find a difference in the scaling properties depending on whether the system is bosonic-where an area law is proven to hold-or fermionic where we determine a logarithmic correction to the area law, which depends on the topology of the Fermi surface. We find Lifshitz quantum phase transitions accompanied with a nonanalyticity in the prefactor of the leading order term.

arXiv:quant-ph/0611264•Physical Review Letters•May 31, 2007•87 citations

Entanglement in strongly fluctuating quantum many-body states

Weifei Li

In this thesis, the scaling behavior of entanglement is investigated in quantum systems with strongly fluctuating ground states. We relate the reduced density matrices of quadratic fermionic and bosonic models to their Green's function matrices in a unified way, and calculate exactly the scaling of the entanglement entropy of finite systems in an infinite universe. In these systems, we observe quantum phase transition by tuning the parameters of the Hamiltonian. Our study shows that although in one dimension there is a unique relation between the quantum phase transition and the scaling behavior of entanglement, this is not necessarily true in higher dimensions.

•Jan 1, 2015•0 citations

Entropic area law for Fermions

Wolf, M M

We investigate the scaling of the entanglement entropy in an infinite translational invariant Fermionic system of any spatial dimension. The states under consideration are ground states and excitations of tight-binding Hamiltonians with arbitrary interactions. We show that the entropy of a finite region typically scales with the area of the surface times a logarithmic correction. The latter can be traced back to the criticality of the models. The relation between the entanglement entropy and the structure of the Fermi surface is discussed, and it is proven, that the presented scaling law holds whenever the Fermi surface is finite. This is in particular true for all ground states of Hamiltonians with finite range interactions.

•Mar 29, 2005•1 citation

Universal finite-size corrections of the entanglement entropy of quantum ladders and the entropic area law

J. C. Xavier, Flávia B. Ramos

We investigate the finite-size corrections of the entanglement entropy of critical ladders and propose a conjecture for its scaling behaviour. The conjecture is verified for free fermions, for Heisenberg ladders, and for quantum Ising ladders. Our results support that the prefactor of the logarithmic correction of the entanglement entropy of critical ladder models is universal and is associated with the central charge of the one-dimensional version of the models and with the number of branches associated with gapless excitations. Our results suggest that it is possible to infer whether there is a violation of the entropic area law in two-dimensional critical systems by analyzing the scaling behaviour of the entanglement entropy of ladder systems, which are easier to deal with.

arXiv:1406.4849•Journal of Statistical Mechanics Theory and Experiment•Oct 21, 2014•6 citations

Violation of the Entropic Area Law for Fermions

Michael M. Wolf

We investigate the scaling of the entanglement entropy in an infinite translational invariant fermionic system of any spatial dimension. The states under consideration are ground states and excitations of tight-binding Hamiltonians with arbitrary interactions. We show that the entropy of a finite region typically scales with the area of the surface times a logarithmic correction. Thus, in contrast with analogous bosonic systems, the entropic area law is violated for fermions. The relation between the entanglement entropy and the structure of the Fermi surface is discussed, and it is proven that the presented scaling law holds whenever the Fermi surface is finite. This is, in particular, true for all ground states of Hamiltonians with finite range interactions.

arXiv:quant-ph/0503219•Physical Review Letters•Jan 12, 2006•473 citations
We relate the reduced density matrices of quadratic fermionic and bosonic models to their Green's function matrices in a unified way and calculate the scaling of the entanglement entropy of finite systems in an infinite universe exactly. For critical fermionic two-dimensional (2D) systems at T=0T=0T=0, two regimes of scaling are identified: generically, we find a logarithmic correction to the area law with a prefactor dependence on the chemical potential that confirms earlier predictions based on the Widom conjecture. If, however, the Fermi surface of the critical system is zero-dimensional, then we find an area law with a sublogarithmic correction. For a critical bosonic 2D array of coupled oscillators at T=0T=0T=0, our results show that the entanglement entropy follows the area law without corrections.
Exactly solving a spinless fermionic system in two and three dimensions, we investigate the scaling behavior of the block entropy in critical and noncritical phases. The scaling of the block entropy crucially depends on the nature of the excitation spectrum of the system and on the topology of the Fermi surface. Noticeably, in the critical phases the scaling violates the area law and acquires a logarithmic correction only when a well-defined Fermi surface exists in the system. When the area law is violated, we accurately verify a conjecture for the prefactor of the logarithmic correction, proposed by D. Gioev and I. Klich [Phys. Rev. Lett. 96, 100503 (2006)].
The entanglement entropy of a distinguished region of a quantum many-body system reflects the entanglement in its pure ground state. Here we establish scaling laws for this entanglement in critical quasifree fermionic and bosonic lattice systems, without resorting to numerical means. We consider the setting of D-dimensional half-spaces which allows us to exploit a connection to the one-dimensional case. Intriguingly, we find a difference in the scaling properties depending on whether the system is bosonic-where an area law is proven to hold-or fermionic where we determine a logarithmic correction to the area law, which depends on the topology of the Fermi surface. We find Lifshitz quantum phase transitions accompanied with a nonanalyticity in the prefactor of the leading order term.
In this thesis, the scaling behavior of entanglement is investigated in quantum systems with strongly fluctuating ground states. We relate the reduced density matrices of quadratic fermionic and bosonic models to their Green's function matrices in a unified way, and calculate exactly the scaling of the entanglement entropy of finite systems in an infinite universe. In these systems, we observe quantum phase transition by tuning the parameters of the Hamiltonian. Our study shows that although in one dimension there is a unique relation between the quantum phase transition and the scaling behavior of entanglement, this is not necessarily true in higher dimensions.
We investigate the scaling of the entanglement entropy in an infinite translational invariant Fermionic system of any spatial dimension. The states under consideration are ground states and excitations of tight-binding Hamiltonians with arbitrary interactions. We show that the entropy of a finite region typically scales with the area of the surface times a logarithmic correction. The latter can be traced back to the criticality of the models. The relation between the entanglement entropy and the structure of the Fermi surface is discussed, and it is proven, that the presented scaling law holds whenever the Fermi surface is finite. This is in particular true for all ground states of Hamiltonians with finite range interactions.
We investigate the finite-size corrections of the entanglement entropy of critical ladders and propose a conjecture for its scaling behaviour. The conjecture is verified for free fermions, for Heisenberg ladders, and for quantum Ising ladders. Our results support that the prefactor of the logarithmic correction of the entanglement entropy of critical ladder models is universal and is associated with the central charge of the one-dimensional version of the models and with the number of branches associated with gapless excitations. Our results suggest that it is possible to infer whether there is a violation of the entropic area law in two-dimensional critical systems by analyzing the scaling behaviour of the entanglement entropy of ladder systems, which are easier to deal with.
We investigate the scaling of the entanglement entropy in an infinite translational invariant fermionic system of any spatial dimension. The states under consideration are ground states and excitations of tight-binding Hamiltonians with arbitrary interactions. We show that the entropy of a finite region typically scales with the area of the surface times a logarithmic correction. Thus, in contrast with analogous bosonic systems, the entropic area law is violated for fermions. The relation between the entanglement entropy and the structure of the Fermi surface is discussed, and it is proven that the presented scaling law holds whenever the Fermi surface is finite. This is, in particular, true for all ground states of Hamiltonians with finite range interactions.