Automatic differentiation applied to excitations with projected entangled pair states

Abstract

The excitation ansatz for tensor networks is a powerful tool for simulating the low-lying quasiparticle excitations above ground states of strongly correlated quantum many-body systems. Recently, the two-dimensional tensor network class of infinite projected entangled-pair states gained new ground state optimization methods based on automatic differentiation, which are at the same time highly accurate and simple to implement. Naturally, the question arises whether these new ideas can also be used to optimize the excitation ansatz, which has recently been implemented in two dimensions as well. In this paper, we describe a straightforward way to reimplement the framework for excitations using automatic differentiation, and demonstrate its performance for the Hubbard model at half filling.

Spin excitation spectra of the spin-$1/2$ triangular Heisenberg antiferromagnets from tensor networks

“…The tensor-network renormalization group methods [30,31,[35][36][37] are used to calculate dynamical response functions of the anisotropic Heisenberg model, defined in Eq. ( 1), with J = 1.67 meV and ∆ = 0.95.…”

“…A translation invariant PEPS on an infinite lattice is used to represent the ground state with 120 • antiferromagnetic order. An ansatz based on the single-mode approximation [31,[35][36][37] is used to construct the wave functions of excitation states. The local tensors for both the ground state and the excitation states are optimized by minimizing the corresponding energies with the aid of automatic differentiation [30,31].…”

“…In particular, it is unknown how the spectral weights are transferred to or from low-energy magnon excitations, damped longitudinal Higgs modes and high-energy continuum. The aim of this work is to resolve these problems through a thorough investigation on the spin-1/2 triangular Heisenberg model using a state-of-the-art tensor-network renormalization group method [28,29] in combination with the technique of automatic differentiation [30,31].…”

“…[30]. Recently, this approach was extended to the calculation of excitation states in the single-mode approximation of PEPS [31].…”

“…S1 of the Supplementary Material (SM)) and Ref. [31]), and can be directly applied to an infinite-lattice system without being bothered by the finite size effect.…”