Zero-point energy of tensor fluctuations on the MPS manifold

TL;DR

This paper introduces a novel method combining tensor fluctuations and the MPS manifold to improve low-energy physics modeling in highly correlated magnetic systems, especially near AKLT states.

Contribution

It adapts the spin-wave approach to the MPS framework, enabling better fluctuation analysis for complex entangled states like the AKLT model.

Findings

Improved energy approximations for the bilinear-biquadratic Heisenberg model.

Demonstrated the effectiveness of tensor fluctuation analysis on the MPS manifold.

Highlighted the potential for new low-energy effective theories in correlated materials.

Abstract

This work presents a method for studying low-energy physics in highly correlated magnetic systems using the matrix product state (MPS) manifold. We adapt the spin-wave approach, which has been very successful in modeling certain low-entanglement magnetic materials, to systems where the ground state is better represented by an MPS, such as the S = 1 Affleck-Kennedy-Lieb-Tasaki (AKLT) model. We argue that the quasi-local action of tensor fluctuations and the natural K\"ahler structure of the MPS manifold facilitate a description in terms of bosonic modes. We apply this approach to compute fluctuation corrections to the bilinear-biquadratic Heisenberg model, whose ground state we expect to be close to the exact bond dimension 2 AKLT state in a certain parameter range. Our results show significant improvements in energy approximations, highlighting both the qualitative and quantitative potential of this paradigm for studying complex entangled systems. This approach paves the way for new insights into the low-energy physics of correlated materials and the development of effective field theories beyond traditional semiclassical methods.