Efficient MPS methods for extracting spectral information on rings and cylinders

• URL: http://arxiv.org/abs/2102.10982v2
• Date: Wed, 8 Jun 2022 13:04:48 GMT
• Title: Efficient MPS methods for extracting spectral information on rings and cylinders
• Authors: Maarten Van Damme, Robijn Vanhove, Jutho Haegeman, Frank Verstraete and Laurens Vanderstraeten
• Abstract summary: We introduce an ansatz for capturing excited states in finite systems with open boundary conditions. We show that momentum emerges as a good quantum number, and can be exploited for labeling excitations on top of MPS ground states. Finally, we apply the same idea to compute excitation spectra for 2-D quantum systems on infinite cylinders.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Based on the MPS formalism, we introduce an ansatz for capturing excited states in finite systems with open boundary conditions, providing a very efficient method for computing, e.g., the spectral gap of quantum spin chains. This method can be straightforwardly implemented on top of an existing DMRG or MPS ground-state code. Although this approach is built on open-boundary MPS, we also apply it to systems with periodic boundary conditions. Despite the explicit breaking of translation symmetry by the MPS representation, we show that momentum emerges as a good quantum number, and can be exploited for labeling excitations on top of MPS ground states. We apply our method to the critical Ising chain on a ring and the classical Potts model on a cylinder. Finally, we apply the same idea to compute excitation spectra for 2-D quantum systems on infinite cylinders. Again, despite the explicit breaking of translation symmetry in the periodic direction, we recover momentum as a good quantum number for labeling excitations. We apply this method to the 2-D transverse-field Ising model and the half-filled Hubbard model; for the latter, we obtain accurate results for, e.g., the hole dispersion for cylinder circumferences up to eight sites.

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