Dynamical properties of quantum many-body systems with long range interactions

TL;DR

This paper uses large-scale quantum Monte Carlo simulations to analyze how long-range interactions in 2D quantum magnets affect their energy spectra, revealing new dynamical behaviors and challenging existing low-energy theories.

Contribution

It provides the first unbiased dynamical data for long-range quantum many-body systems, showing how long-range interactions modify magnon dispersions and introduce anomalous exponents.

Findings

Identified the explicit range of interaction exponents for different spectral types.

Revealed how long-range interactions alter magnon dispersions in 2D quantum magnets.

Discovered cases with gapped excitations despite extensive Hamiltonians.

Abstract

Employing large-scale quantum Monte Carlo simulations, we systematically compute the energy spectra of the 2D spin-1/2 Heisenberg model with long-range interactions. With the $1/r^{\alpha}$ ferromagnetic and staggered antiferromagnetic interactions, we find the explicit range in $\alpha$ for {\color{black} the short-range Goldstone-type (gapless), anomalous Goldstone-type (gapless) and Higgs-type (gapped) spectra. Accompanied by the spin wave analysis, our numerical results vividly reveal how the long-range interactions alter the usual linear and quadratic magnon dispersions in 2D quantum magnets and give rise to anomalous dynamical exponents. Moreover, we find explicit case where the gapped excitation exists even when the Hamiltonian is extensive. This work provides the first set of unbiased dynamical data} of long-range quantum many-body systems and suggests that many universally accepted low-energy customs for short-range systems need to be substantially modified for long-range ones which are of immediate relevance to the ongoing experimental efforts from quantum simulators to 2D quantum moir\'e materials.