High-accuracy evaluation of non-thermal magnetic states beyond spin-wave theory: applications to higher-energy states

TL;DR

This paper introduces a selective Hilbert space truncation method for accurately characterizing non-thermal magnetic states beyond traditional spin-wave theory, applicable to complex multi-magnon and higher-energy states.

Contribution

The authors develop an approximation scheme that exactly diagonalizes restricted bosonic Hamiltonians, significantly improving computational efficiency over exact methods and extending analysis to previously inaccessible states.

Findings

Excellent agreement with exact eigenstates and eigenvalues in a test XXZ spin chain model.

Method effectively captures higher-energy and bound states beyond linear spin-wave theory.

Reduces computational time exponentially compared to exact diagonalization.

Abstract

We present an approximation scheme based on selective Hilbert space truncation for characterizing non-thermal states of magnetic systems beyond spin-wave theory. We study applications to states that are inaccessible through linear spin-wave theory, such as multi-magnon states and higher-energy states. Our approach is based on the existence of an exact representation of spin operators in terms of finite-order polynomials of bosonic operators. It can be applied to systems with and without a magnetically ordered ground state. The approximation exactly diagonalizes the bosonic Hamiltonian restricted to particular boson occupation subspaces, improving the conventional linear spin-wave approach and exponentially reducing the computing time relative to exact diagonalization schemes. As a test case, we apply the approach to a prototypical one-dimensional model - an XXZ spin chain with an applied magnetic field and antisymmetric exchange coupling. Here the antisymmetric coupling introduces a continuous parameter to tune the system away from its exactly solvable limit. We find excellent agreement between numerically exact eigenstates and eigenvalues and those found via the approximation scheme. Our approach applies not just to higher lying states but also to boson bound states, which could make them more accessible to theoretical predictions for comparison with experiment.