On entanglement Hamiltonians of an interval in massless harmonic chains

Abstract

We study the continuum limit of the entanglement hamiltonians of a block of consecutive sites in massless harmonic chains. This block is either in the chain on the infinite line or at the beginning of a chain on the semi-infinite line with Dirichlet boundary conditions imposed at its origin. The entanglement hamiltonians of the interval predicted by Conformal Field Theory for the massless scalar field are obtained in the continuum limit. We also study the corresponding entanglement spectra and the numerical results for the ratios of the gaps are compatible with the operator content of the Boundary Conformal Field Theory of a massless scalar field with Neumann boundary conditions imposed along the boundaries introduced around the entangling points by the regularisation procedure. arXiv:1911.07188v1 [cond-mat.stat-mech]

Operator content of entanglement spectra in the transverse field Ising chain after global quenches

“…The relation between the ES after a quench across the QCP and the features of the dynamical quantum phase transitions also deserves further, more quantitative, analysis. Interesting results about the ES could be obtained also by considering directly the full entanglement Hamiltonian [73,85,[97][98][99][100][101][102][103][104][105], even for spatially inhomogeneous lattice systems [88]. Extending all these analyses to higher dimensions is also very important.…”

Complexity of mixed Gaussian states from Fisher information geometry

“…The entanglement hamiltonians associated to some particular reduced density matrices have been largely studied for simple models, both in quantum field theories [50,[107][108][109][110][111][112][113][114] and on the lattice [52,95,[115][116][117][118][119][120][121]. The spectrum of the entanglement hamiltonian, that is usually called entanglement spectrum [122], is rich in information.…”

“…The spectrum of the entanglement hamiltonian, that is usually called entanglement spectrum [122], is rich in information. For instance, in conformal field theories the entanglement spectrum provides both the central charge [123] and the conformal spectrum of the underlying model [110,113,114,120,121,[124][125][126].…”

“…We denote H as the entanglement hamiltonian matrix. It can be written in terms of the corresponding covariance matrix γ as follows [50,95,[115][116][117]121]…”

“…This formula cannot be applied for pure states, which have D = 1 2 1. The symplectic matrices W and W , introduced in (2.20) and (6.6) respectively, are related as follows [117,121] W ≡ J t W J = W −t .…”