Accurate computation of the energy variance and $\langle\langle \mathcal{L}^\dagger \mathcal{L} \rangle\rangle$ using iPEPS

TL;DR

This paper presents a highly accurate method for computing the energy variance in iPEPS tensor networks, enabling better ground-state energy extrapolations and analysis of quantum phase transitions in complex models.

Contribution

The authors introduce a novel approach using CTRG to compute the energy variance in iPEPS, significantly improving accuracy over previous methods.

Findings

Enhanced accuracy in energy variance computation

Successful variance extrapolation for multiple models

Application to steady-state and phase transition analysis

Abstract

Infinite projected entangled-pair states (iPEPS) provide a powerful tensor network ansatz for two-dimensional quantum many-body systems in the thermodynamic limit. In this paper we introduce an approach to accurately compute the energy variance of an iPEPS, enabling systematic extrapolations of the ground-state energy to the exact zero-variance limit. It is based on the contraction of a large cell of tensors using the corner transfer matrix renormalization group (CTRMG) method, to evaluate the correlator between pairs of local Hamiltonian terms. We show that the accuracy of this approach is substantially higher than that of previous methods, and we demonstrate the usefulness of variance extrapolation for the Heisenberg model, for a free fermionic model, and for the Shastry-Sutherland model. Finally, we apply the approach to compute $\langle \langle \mathcal{L}^\dagger \mathcal{L} \rangle \rangle$ for an open quantum system described by the Liouvillian $\mathcal{L}$, in order to assess the quality of the steady-state solution and to locate first-order phase transitions, using the dissipative quantum Ising model as an example.