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

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 moiré materials.

5 pages,3 figures

References in corpus (20)

• Cold atoms in cavity-generated dynamical optical potentials
• Continuum Model of the Twisted Bilayer
• Entanglement entropy for the long range Ising chain
• Quantum phases of Rydberg atoms on a kagome lattice
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Anomalous Behavior of Spin Systems with Dipolar Interactions
• Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions
• On the Hohenberg-Mermin-Wagner theorem and its limitations
• Momentum space quantum Monte Carlo on twisted bilayer Graphene
• Emergent ${\mathbb{Z}}_2$ gauge theories and topological excitations in Rydberg atom arrays
• Universal threshold for the dynamical behavior of lattice systems with long-range interactions
• Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
• Emergent glassy behavior in a kagome Rydberg atom array
• Spectrum of short-wavelength magnons in two-dimensional quantum Heisenberg antiferromagnet on a square lattice: third order expansion in 1/S
• Thermodynamic characteristic for correlated flat-band system with quantum anomalous Hall ground state
• Quantum Monte Carlo sign bounds, topological Mott insulator and thermodynamic transitions in twisted bilayer graphene model
• Trions in Twisted Bilayer Graphene
• Fully packed quantum loop model on the square lattice: phase diagram and application for Rydberg atoms
• Evolution of Dynamical Signature in the X-cube Fracton Topological Order
• Validity of SLAC fermions for the (1 + 1)-dimensional helical Luttinger liquid

Cited by in corpus (13)

• Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model
• Magnetism in the two-dimensional dipolar XY model
• Monte Carlo based techniques for quantum magnets with long-range interactions
• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
• Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system
• Caution on Gross-Neveu criticality with a single Dirac cone: Violation of locality and its consequence of unexpected finite-temperature transition
• Unconventional Scalings of Quantum Entropies in Long-Range Heisenberg Chains
• Floquet-engineered Emergent Massive Nambu-Goldstone Modes
• Accessing Excitation of Many-body Systems via Single-Mode Approximation within Quantum Monte Carlo Simulations
• Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum
• Stability of current-carrying states in hard-core bosons with long-range hopping on a square lattice
• Higgs and Nambu-Goldstone modes in a spin-1 $XY$ model with long-range interactions