Efficient and systematic calculation of arbitrary observables for the matrix product state excitation ansatz

• URL: http://arxiv.org/abs/2408.17117v1
• Date: Fri, 30 Aug 2024 08:59:29 GMT
• Title: Efficient and systematic calculation of arbitrary observables for the matrix product state excitation ansatz
• Authors: Jesse J. Osborne, Ian P. McCulloch,
• Abstract summary: We present a method for calculating expectation values for excitations with a single-particle character in the thermodynamic limit. We demonstrate the versatility of our method by studying the low-lying excitations in the spin-1 Heisenberg chain and the one-dimensional Hubbard model. We hope that this technique will foster further advancements with the excitation ansatz.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Numerical methods based on matrix product states (MPSs) are currently the de facto standard for calculating the ground state properties of (quasi-)one-dimensional quantum many-body systems. While the properties of the low-lying excitations in such systems are often studied in this MPS framework through _dynamics_ by means of time-evolution simulations, we can also look at their _statics_ by directly calculating eigenstates corresponding to these excitations. The so-called MPS excitation ansatz is a powerful method for finding such eigenstates with a single-particle character in the thermodynamic limit. Although this excitation ansatz has been used quite extensively, a general method for calculating expectation values for these states is lacking in the literature: we aim to fill this gap by presenting a recursive algorithm to calculate arbitrary observables expressed as matrix product operators. This method concisely encapsulates existing methods for -- as well as extensions to -- the excitation ansatz, such as excitations with a larger spatial support and multi-particle excitations, and is robust to handle further innovations. We demonstrate the versatility of our method by studying the low-lying excitations in the spin-1 Heisenberg chain and the one-dimensional Hubbard model, looking at how the excitations converge in the former, while in the latter, we present a novel method of targeting single-particle excitations inside of a continuum by minimizing the energy _variance_ rather than the energy itself. We hope that this technique will foster further advancements with the excitation ansatz.

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