Quantum spin chains#

Exact diagonalization of spin-1/2 chains in their symmetry sectors, checked against the classic exact solutions: Bethe’s ansatz for the Heisenberg antiferromagnet, the free-fermion solution of the transverse-field Ising chain, and the Calabrese-Cardy logarithmic entanglement of a critical chain versus the area law of a gapped one.

Bethe’s ansatz for the Heisenberg antiferromagnetic chain

Bethe's ansatz for the Heisenberg antiferromagnetic chain

Calabrese-Cardy: logarithmic entanglement at criticality vs. the area law

Calabrese-Cardy: logarithmic entanglement at criticality vs. the area law

The transverse-field Ising chain as free fermions

The transverse-field Ising chain as free fermions