# plane_wave_excitation

• full name: tenpy.algorithms.plane_wave_excitation

• parent module: tenpy.algorithms

• type: module

Classes

 MultiSitePlaneWaveExcitationEngine(psi, ...) Engine to compute quasiparticle excitations across multiple sites for uniform MPS. PlaneWaveExcitationEngine(psi, model, ...) Base engine to compute quasiparticle excitations for uniform MPS.

Functions

 append_left_env(As, Bs, L[, Ws]) Contract all tensors in As and Bs to the left environment L. append_right_env(As, Bs, R[, Ws]) Contract all tensors in As and Bs to the right environment R. construct_orthogonal(M[, left]) find (left) orthogonal complement of tensor M

Module description

Plane wave excitations ansatz

The quasiparticle ansatz, utilizing plane wave states, offers a powerful approach for computing low-energy excitations. For finite systems, we could employ DMRG with different charge sectors to find these states. For infinite systems, an efficient algorithm was introduced in . By working directly in the tangent space of a uniform MPS , we can use translational invariance to specify momentum.

The plane wave excitation finds excitation of a UniformMPS. By summing over all states, where one tensor is replaced with an excited tensor B, we get a state with a fixed momentum MomentumMPS. The tensors B are decomposed into -B- = -V-X-, where V is the orthogonal complement of the usual A-tensors of the uniform MPS, and X contains the variational parameters. The algorithm constructs an effective Hamiltonian for X and finds the low-energy states using an iterative eigensolver. Since we don’t sweep as e.g. in DMRG, more Lanczos steps may be required. Increase those until the energy is converged!

Additionally, we can specify X to be in a given charge sector.

The PlaneWaveExcitationEngine optimizes the X for each tensor in the unit cell. The ansatz can be extended to include excitations that span several sites. This is implemented in MultiSitePlaneWaveExcitationEngine. Note that with the current implementation, the numerical costs scale exponentially with the number of exciting sites.