Multi-boundary generalization of thermofield double states and their realization in critical quantum spin chains

Abstract

We propose a multi-boundary generalization of thermofield double states (TFD) of a twodimensional conformal field theory (CFT) and show, through a conformal map to the complex plane, that they are closely related to multi-point correlation functions. We then also describe how to approximately realize these multi-boundary TFD states numerically on the lattice, starting from a critical quantum spin chain Hamiltonian. In addition, finite size corrections on the lattice are seen to be significantly reduced by the use of smoothers -numerically optimized unitary transformations that locally re-arrange the quantum spin degrees of freedom. One merit of the spin chain realization is that it allows us to probe the properties of the proposed multi-boundary TFD states through numerical experiments, including the characterization of their entanglement structure. As an illustration, we explicitly construct generalized TFD states with three and four boundaries for the Ising CFT and compute entanglement quantities using novel free fermion techniques. We find ranges of parameters where their multipartite entanglement is significant or negligible.

Multipartitioning topological phases by vertex states and quantum entanglement

“…For example, in (1+1)d CFT, the reflected entropy has been studied for the ground state [26], and for time-dependent states after quantum quench [57][58][59]. The reflected entropy was also computed for multi-sided thermofield double states in (non-chiral) (1+1)d CFT (which has some similarly to vertex states that we will introduce later) [60]. The reflected entropy is a more sensitive probe of multipartite entanglement than the von Neumann entropy [61,62].…”