Based on the relationship between reduced and thermal density matrices in conformal field theory (CFT), we show that the entanglement spectrum of a conformal critical chain with exponentially decaying terms consists of conformal towers of the associated chiral CFT, with only weak finite-size effects. Through free-fermion and interacting examples, we show that these entanglement spectra present a reliable method to extract detailed CFT spectra from single wave functions without access to the parent Hamiltonian. We complement our method with a Wilsonian numerical renormalisation group algorithm for solving interacting, exponentially decaying chain Hamiltonians.Based on the relationship between reduced and thermal density matrices in conformal field theory (CFT), we show that the entanglement spectrum of a conformal critical chain with exponentially decaying terms consists of conformal towers of the associated chiral CFT, with only weak finite-size effects. Through free-fermion and interacting examples, we show that these entanglement spectra present a reliable method to extract detailed CFT spectra from single wave functions without access to the parent Hamiltonian. We complement our method with a Wilsonian numerical renormalisation group algorithm for solving interacting, exponentially decaying chain Hamiltonians.

arXiv:2412.09685SciPost PhysicsSep 26, 20252 citations

Entanglement entropy of large- N Wilson-Fisher conformal field theory

Seth Whitsitt, William Witczak‐Krempa, Subir Sachdev A

We compute the entanglement entropy of the Wilson-Fisher conformal field theory (CFT) in 2+1 dimensions with $\mathrm{O}(N)$ symmetry in the limit of large $N$ for general entanglement geometries. We show that the leading large- $N$ result can be obtained from the entanglement entropy of $N$ Gaussian scalar fields with their mass determined by the geometry. For a few geometries, the universal part of the entanglement entropy of the Wilson-Fisher CFT equals that of a CFT of $N$ massless scalar fields. However, in most cases, these CFTs have a distinct universal entanglement entropy even at $N=\ensuremath{\infty}$. Notably, for a semi-infinite cylindrical region it scales as ${N}^{0}$ in the Wilson-Fisher theory, in stark contrast to the $N$ -linear result of the Gaussian fixed point.We compute the entanglement entropy of the Wilson-Fisher conformal field theory (CFT) in 2+1 dimensions with $\mathrm{O}(N)$ symmetry in the limit of large $N$ for general entanglement geometries. We show that the leading large-$N$ result can be obtained from the entanglement entropy of $N$ Gaussian scalar fields with their mass determined by the geometry. For a few geometries, the universal part of the entanglement entropy of the Wilson-Fisher CFT equals that of a CFT of $N$ massless scalar fields. However, in most cases, these CFTs have a distinct universal entanglement entropy even at $N=\ensuremath{\infty}$. Notably, for a semi-infinite cylindrical region it scales as ${N}^{0}$ in the Wilson-Fisher theory, in stark contrast to the $N$-linear result of the Gaussian fixed point.

arXiv:1610.06568Physical review. B./Physical review. BJan 30, 201751 citations

Aspects of higher-spin conformal field theories and their renormalization group flows

Kenan S. Diab

Aug 26, 20170 citations

Conformal Field Theories and Quantum Phase Transitions

Horaƫiu Năstase

Cambridge University Press eBooksSep 21, 20170 citations

Spectrum of the Wilson-Fisher conformal field theory on the torus

Seth Whitsitt, Michael Schuler, Louis-Paul Henry +2 more

The authors study the finite-size energy spectrum of the O( $N$ ) symmetric Wilson-Fisher conformal field theory (CFT) on the spatial torus. They first perform an analytic calculation of the spectrum using the $ϵ$ expansion with a careful treatment of the zero-momentum modes. The authors also perform exact diagonalization on several lattice Hamiltonians whose critical points are known to be described by the Wilson-Fisher CFT. Comparison of the analytic and numerical data demonstrates that the energy spectrum is a useful diagnostic for determining the universality class of a critical point. These results have applications in determining the critical behavior of more complicated many-body systems.The authors study the finite-size energy spectrum of the O($N$) symmetric Wilson-Fisher conformal field theory (CFT) on the spatial torus. They first perform an analytic calculation of the spectrum using the $ϵ$ expansion with a careful treatment of the zero-momentum modes. The authors also perform exact diagonalization on several lattice Hamiltonians whose critical points are known to be described by the Wilson-Fisher CFT. Comparison of the analytic and numerical data demonstrates that the energy spectrum is a useful diagnostic for determining the universality class of a critical point. These results have applications in determining the critical behavior of more complicated many-body systems.

arXiv:1701.03111Physical review. B./Physical review. BJul 24, 201724 citations

We compute the entanglement entropy of the Wilson-Fisher conformal field theory (CFT) in 2+1 dimensions with

\mathrm{O}(N)

symmetry in the limit of large

N

for general entanglement geometries. We show that the leading large-

N

result can be obtained from the entanglement entropy of

N

Gaussian scalar fields with their mass determined by the geometry. For a few geometries, the universal part of the entanglement entropy of the Wilson-Fisher CFT equals that of a CFT of

N

massless scalar fields. However, in most cases, these CFTs have a distinct universal entanglement entropy even at $N=\ensuremath{\infty}$. Notably, for a semi-infinite cylindrical region it scales as

{N}^{0}

in the Wilson-Fisher theory, in stark contrast to the

N

-linear result of the Gaussian fixed point.

The authors study the finite-size energy spectrum of the O(

N

) symmetric Wilson-Fisher conformal field theory (CFT) on the spatial torus. They first perform an analytic calculation of the spectrum using the

ϵ

expansion with a careful treatment of the zero-momentum modes. The authors also perform exact diagonalization on several lattice Hamiltonians whose critical points are known to be described by the Wilson-Fisher CFT. Comparison of the analytic and numerical data demonstrates that the energy spectrum is a useful diagnostic for determining the universality class of a critical point. These results have applications in determining the critical behavior of more complicated many-body systems.