Quantum Entanglement and Thermal Reduced Density Matrices in Fermion and Spin Systems on Ladders

Understand

Numerical studies of the reduced density matrix of a gapped spin-1/2 Heisenberg antiferromagnet on a two-leg ladder find that it has the same form as the Gibbs density matrix of a gapless spin-1/2 Heisenberg antiferromagnetic chain at a finite temperature determined by the spin gap of the ladder.

• We investigate this interesting result by considering a model of free fermions on a two-leg ladder (gapped by the inter-chain tunneling operator) and in spin systems on a ladder with a gapped ground state using exact solutions and several controlled approximations.
• We calculate the reduced density matrix and the entanglement entropy for a leg of the ladder (i.e.
• cut made between the chains).