Incommensurate order with translationally invariant projected entangled-pair states: Spiral states and quantum spin liquid on the anisotropic triangular lattice

TL;DR

This paper introduces an iPEPS-based method to simulate incommensurate order in strongly correlated systems directly in the thermodynamic limit, successfully capturing spiral states and a quantum spin liquid phase in the anisotropic triangular lattice Heisenberg model.

Contribution

The authors develop a novel iPEPS Ansatz that overcomes finite-size limitations, enabling direct simulation of incommensurate order and quantum spin liquids in the thermodynamic limit.

Findings

Accurately reproduces magnetically ordered phases with arbitrary wavelength.

Reveals a quantum spin liquid phase between Néel and spiral phases.

Method is computationally independent of spiral wavelength.

Abstract

Simulating strongly correlated systems with incommensurate order poses significant challenges for traditional finite-size-based approaches. Confining such a phase to a finite-size geometry can induce spurious frustration, with spin spirals in frustrated magnets being a typical example. Here, we introduce an Ansatz based on infinite projected entangled-pair states (iPEPS) which overcomes these limitations and enables the direct search for the optimal spiral in the thermodynamic limit, with a computational cost that is independent of the spiral's wavelength. Leveraging this method, we simulate the Heisenberg model on the anisotropic triangular lattice, which interpolates between the square and isotropic triangular lattice limits. Besides accurately reproducing the magnetically ordered phases with arbitrary wavelength, the simulations reveal a quantum spin liquid phase emerging between the N\'eel and spin spiral phases.