# Determination of ground states of one-dimensional quantum systems using the cluster iTEBD method

## TL;DR

This paper introduces a cluster iTEBD method that improves the accuracy of ground state calculations in one-dimensional quantum systems by incorporating multiple degrees of freedom, enhancing entanglement representation without increasing computational complexity.

## Contribution

The authors develop a cluster version of the iTEBD algorithm that better captures quantum correlations in 1D systems, addressing accuracy issues in strongly correlated physics.

## Key findings

- Enhanced accuracy in ground-state energy and entanglement entropy.
- Successful application to spin chains with complex phase transitions.
- Maintains computational efficiency comparable to standard methods.

## Abstract

Within the framework of imaginary-time evolution for matrix product states, we introduce a cluster version of the infinite time-evolving block decimation algorithm for simulating quantum many-body systems, addressing the computational accuracy challenges in strongly correlated physics. By redefining the wave-function ansatz to incorporate multiple physical degrees of freedom, we enhance the representation of entanglement, thereby improving the accuracy of the ground states. Utilizing the Trotter-Suzuki decomposition and optimized truncation schemes, our method maintains roughly the same computational complexity while capturing more quantum correlations. We apply this approach to three nontrivial cases: the gapless spin-1/2 Heisenberg chain, the spin-1 anisotropic XXZD chain with a higher-order Gaussian-type phase transition, and a spin-1/2 twisted triangular prism hosting a magnetic plateau phase. Improved accuracy in physical quantities, such as magnetization, ground-state energy, and entanglement entropy, has been demonstrated. This method provides a scalable framework for studying complex quantum systems with high precision, making it suitable for situations where a pure increase in bond dimension alone cannot guarantee satisfactory results.