Computing excited states with isometric tensor networks in two-dimensions

TL;DR

This paper introduces a novel tensor network method, block-isoPEPS, for efficiently computing low-energy excited states in two-dimensional quantum many-body systems, extending PEPS techniques from 1D to 2D.

Contribution

The paper develops a new block-isoPEPS ansatz and subspace iteration method for 2D systems, enabling scalable excited state calculations with improved features over existing PEPS approaches.

Findings

Successfully computed excitations of 2D Ising and Heisenberg models.

Demonstrated scalability and advantages of block-isoPEPS over traditional PEPS.

Validated results against existing methods, showing improved efficiency.

Abstract

We present a new subspace iteration method for computing low-lying eigenpairs (excited states) of high-dimensional quantum many-body Hamiltonians with nearest neighbor interactions on two-dimensional lattices. The method is based on a new block isometric projected entangled pair state (block-isoPEPS) ansatz that generalizes the block matrix product state (MPS) framework, widely used for Hamiltonians defined on one-dimensional chains, to two-dimensions. The proposed block-isoPEPS ansatz offers several attractive features for PEPS-based algorithms, including exact block orthogonalization, controlled local truncation via singular value decompositions, and efficient evaluation of observables. We demonstrate the proposed inexact subspace iteration for block-isoPEPS by computing excitations of the two-dimensional transverse-field Ising and Heisenberg models and compare our results with existing PEPS methods. Our results demonstrate that block isometric tensor networks provide a scalable framework for studying excitations in quantum many-body systems beyond one dimension.