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

TL;DR

This paper introduces a multi-boundary generalization of thermofield double states in 2D CFTs, demonstrates their realization in critical quantum spin chains, and explores their entanglement properties through numerical methods.

Contribution

It proposes a new multi-boundary TFD framework, provides a lattice realization method, and analyzes multipartite entanglement in these states.

Findings

Multi-boundary TFD states relate to multi-point correlation functions.

Finite size corrections are reduced using optimized local unitaries.

Multipartite entanglement varies with parameters, showing significant or negligible entanglement.

Abstract

We propose a multi-boundary generalization of thermofield double states (TFD) of a two-dimensional 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 \textit{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.