Entanglement entropy in generalised quantum Lifshitz models

Abstract

We compute universal finite corrections to entanglement entropy for generalised quantum Lifshitz models in arbitrary odd spacetime dimensions. These are generalised free field theories with Lifshitz scaling symmetry, where the dynamical critical exponent z equals the number of spatial dimensions d, and which generalise the 2+1-dimensional quantum Lifshitz model to higher dimensions. We analyse two cases: one where the spatial manifold is a d-dimensional sphere and the entanglement entropy is evaluated for a hemisphere, and another where a d-dimensional flat torus is divided into two cylinders. In both examples the finite universal terms in the entanglement entropy are scale invariant and depend on the compactification radius of the scalar field.

Entanglement entropy with Lifshitz fermions

“…This also follows from equation ( 39): since |k| < 1, we have ω k → 0 as z → ∞. Furthermore, we study the temperature corrections to the area law as a function of z in the high and low temperature regime as suggested in equations ( 25) to (27) by numerically computing the EE as a function of temperature in both regimes and making fits for each value of z. The results are given in figures 3 and 4a.…”

“…Entanglement entropy for Lifshitz bosons also have been studied, such as in the quantum Lifshitz model with z = 2 in 2+1 dimensions (see e.g. [18][19][20][21][22][23][24][25] for a partial list of references), and more generally for z = d + 1 in [26][27][28]. More recently studies for generic z were carried out in in e.g.…”

Entanglement of skeletal regions

“…, where κ is a dimensionless parameter. The corresponding groundstate wavefunctional, of Rokhsar-Kivelson-type, is given in terms of the partition function of a d-dimensional free Euclidean scalar field, a CFT [35,36]. In d = 2, the celebrated Fradkin-Moore formula [37] gives the bipartite (Rényi) EE for the Lifshitz groundstate, S = − log(Z A Z B /Z), up to nonuniversal terms, where Z X is the lower-dimensional CFT 2 partition function on X with Dirichlet boundary conditions, and Z is that on the entire system A ∪ B.…”

“…In d = 2, the celebrated Fradkin-Moore formula [37] gives the bipartite (Rényi) EE for the Lifshitz groundstate, S = − log(Z A Z B /Z), up to nonuniversal terms, where Z X is the lower-dimensional CFT 2 partition function on X with Dirichlet boundary conditions, and Z is that on the entire system A ∪ B. In flat space, this formula generalizes to all dimensions and positive even z (see [36,38]), and can be straightforwardly applied to skeletal regions.…”

Spinformation

“…Entanglement entropy for Lifshitz bosons also have been studied, such as in the quantum Lifshitz model with z = 2 in 2+1 dimensions (see e.g. [194][195][196][197][198][199][200][201] for a partial list of references), and more generally for z = d + 1 in [202][203][204]. More recently studies for generic z were carried out in in e.g.…”