Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models

TL;DR

This paper introduces a Chebyshev polynomial-based spectral method for simulating quantum spin models, enabling efficient and accurate analysis of thermodynamics, phase transitions, and dynamics in complex two-dimensional systems.

Contribution

The authors develop a unified Chebyshev spectral framework for quantum spin models, demonstrating its effectiveness on honeycomb lattice models and providing new insights into phase transitions and dynamical signatures.

Findings

Accurate computation of phase transitions in Kitaev-Heisenberg model

Finite temperature spin correlations over three decades in temperature

Identification of novel dynamical signatures in quantum phase transitions

Abstract

The proliferation of quantum fluctuations and long-range entanglement presents an outstanding challenge for the numerical simulation of interacting spin systems with exotic ground states. Here, we present a toolset of Chebyshev polynomial-based iterative methods that provides a unified framework to study the thermodynamical properties, critical behavior and dynamics of frustrated quantum spin models with controlled accuracy. Similar to previous applications of the Chebyshev spectral methods to condensed matter systems, the algorithmic complexity scales linearly with the Hilbert space dimension and the Chebyshev truncation order. Using this approach, we study two paradigmatic quantum spin models on the honeycomb lattice: the Kitaev-Heisenberg (K-H) and the Kitaev-Ising (K-I) models. We start by applying the Chebyshev toolset to compute nearest-neighbor spin correlations, specific heat and entropy of the K-H model on a 24-spin cluster. Our results are benchmarked against exact diagonalization and a popular iterative method based on thermal pure quantum states. The transitions between a variety of magnetic phases, namely ferromagnetic, N\'eel, zigzag and stripy antiferromagnetic and quantum spin liquid phases are obtained accurately and efficiently. We also accurately obtain the temperature dependence of the spin correlations, over more than three decades in temperature, by means of a finite temperature Chebyshev polynomial method introduced here. Finally, we report novel dynamical signatures of the quantum phase transitions in the K-I model. Our findings suggest that the efficiency, versatility and low-temperature stability of the Chebyshev framework developed here could pave the way for previously unattainable studies of quantum spin models in two dimensions.