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

Bulletin of the American Physical Society

Entanglement entropy at the quantum critical point of the 2D transverse field Ising model

Stephen Inglis, Roger G. Melko, Rajiv R. P. Singh, Anders W. Sandvik

Published Feb 29, 2012• 0 citations
OpenAlex

Related papers

Universal behavior of the entanglement entropy in 2D conformal quantum critical points and generalized quantum dimer models

Benjamin Hsu, Michael Mulligan, Eduardo Fradkin +1 more

Bulletin of the American Physical Society•Mar 17, 2009•0 citations

Entanglement Entropy in the Two-Dimensional Random Transverse Field Ising Model

Stephan Haas, Rong Yu, Hubert Saleur

Bulletin of the American Physical Society•Mar 13, 2008•0 citations

Logarithmic Terms in Entanglement Entropies of 2D Quantum Critical Points and Shannon Entropies of Spin Chains

Michael P. Zaletel, Jens Hjorleifur Bardarson, Joel E. Moore

Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the "Shannon entropy" of a 1D spin chain with open boundary conditions. The Shannon entropy of the XXZ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient ±0.25. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on the replica or Rényi index resulting from flows to different boundary conditions at the entanglement cut.

arXiv:1103.5452•Physical Review Letters•Jul 5, 2011•84 citations

Thermodynamic singularities in the entanglement entropy at a two-dimensional quantum critical point

Rajiv R. P. Singh, Roger G. Melko, J. Oitmaa

We study the bipartite entanglement entropy of the 2D transverse-field Ising model in the thermodynamic limit. Series expansions are developed for the Renyi entropy around both the small-field and large-field limits, allowing the separate calculation of the entanglement associated with lines and corners at the boundary between subsystems. Series extrapolations are used to extract power laws and logarithmic singularities as the quantum critical point is approached, giving access to new universal quantities. In 1D, we find excellent agreement with exact results as well as quantum Monte Carlo simulations. In 2D, we find compelling evidence that the entanglement at a corner is significantly different from a free boson field theory. These results demonstrate the power of the series expansion method for calculating entanglement entropy in interacting systems, a fact that will be particularly useful in searches for exotic quantum criticality in models with and without the sign problem.

arXiv:1204.1340•Physical Review B•Aug 6, 2012•54 citations

Finite-size scaling of entanglement entropy in the one-dimensional transverse field Ising model and the XX model

Haopeng Tian, Tianhao He, Xintian Wu

Physical review. B./Physical review. B•Sep 24, 2026•0 citations

Universal logarithmic terms in the entanglement entropy of 2d, 3d and 4d random transverse-field Ising models

István A. Kovács, Ferenc Iglói

The entanglement entropy of the random transverse-field Ising model is calculated by a numerical implementation of the asymptotically exact strong disorder renormalization group method in 2 d , 3 d and 4 d hypercubic lattices for different shapes of the subregion. We find that the area law is always satisfied, but there are analytic corrections due to E -dimensional edges (1⩽ E ⩽ d − 2). More interesting is the contribution arising from corners, which is logarithmically divergent at the critical point and its prefactor in a given dimension is universal, i.e. , independent of the form of disorder.

arXiv:1108.3942•Europhysics Letters (EPL)•Mar 1, 2012•43 citations
Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the "Shannon entropy" of a 1D spin chain with open boundary conditions. The Shannon entropy of the XXZ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient ±0.25. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on the replica or Rényi index resulting from flows to different boundary conditions at the entanglement cut.
We study the bipartite entanglement entropy of the 2D transverse-field Ising model in the thermodynamic limit. Series expansions are developed for the Renyi entropy around both the small-field and large-field limits, allowing the separate calculation of the entanglement associated with lines and corners at the boundary between subsystems. Series extrapolations are used to extract power laws and logarithmic singularities as the quantum critical point is approached, giving access to new universal quantities. In 1D, we find excellent agreement with exact results as well as quantum Monte Carlo simulations. In 2D, we find compelling evidence that the entanglement at a corner is significantly different from a free boson field theory. These results demonstrate the power of the series expansion method for calculating entanglement entropy in interacting systems, a fact that will be particularly useful in searches for exotic quantum criticality in models with and without the sign problem.
The entanglement entropy of the random transverse-field Ising model is calculated by a numerical implementation of the asymptotically exact strong disorder renormalization group method in 2 d , 3 d and 4 d hypercubic lattices for different shapes of the subregion. We find that the area law is always satisfied, but there are analytic corrections due to E -dimensional edges (1⩽ E ⩽ d − 2). More interesting is the contribution arising from corners, which is logarithmically divergent at the critical point and its prefactor in a given dimension is universal, i.e. , independent of the form of disorder.