A matrix product state based algorithm for determining dispersion relations of quantum spin chains with periodic boundary conditions

Understand

We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions.

• By means of a momentum eigenstate ansatz generalizing the one of \"Ostlund and Rommer [1], we separate the Hilbert space of the system into subspaces with different momentum.
• This gives rise to a direct sum of effective Hamiltonians, each one corresponding to a different momentum, and we determine their spectrum by solving a generalized eigenvalue equation.
• Surprisingly, many branches of the dispersion relation are approximated to a very good precision.