Spectral function of the $J_1-J_2$ Heisenberg model on the triangular lattice

Abstract

Spectral probes, such as neutron scattering, are crucial for characterizing excitations in quantum many-body systems and the properties of quantum materials. Among the most elusive phases of matter are quantum spin liquids, which have no long-range order even at zero temperature and host exotic fractionalized excitations with non-trivial statistics. These phases can occur in frustrated quantum magnets, such as the paradigmatic Heisenberg model with nearest and next-nearest neighbor exchange interactions on the triangular lattice, the so-called $J_1-J_2$ model. In this work, we compute the spectral function using large scale matrix product state simulations across the three different phases of this model's phase diagram, including a quantum spin liquid phase at intermediate $J_2/J_1$. Despite a plethora of theoretical and experimental studies, the exact nature of this phase is still contested, with the dominant candidates being a gapped ${\mathbb{Z}}_2$, a gapless $U(1)$ Dirac, and a spinon Fermi surface quantum spin liquid state. We find a V-shaped spectrum near the center of the Brillouin zone ($\Gamma$ point), a key signature of a spinon Fermi surface, observed in prior neutron scattering experiments. However, we find a small gap near the $\Gamma$ point, ruling out such a phase. Furthermore, we find localized gapless excitations at the corner of the Brillouin zone boundary (K point) and the middle of the edge of the Brillouin zone boundary (M point), ruling out the gapped ${\mathbb{Z}}_2$ spin liquid phase. Our results imply that the intermediate spin liquid phase is a gapless $U(1)$ Dirac spin liquid, and provide clear signatures to detect this phase in future neutron scattering experiments.

18 pages (8 figures)

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• Resistivity and Thermal Conductivity of an Organic Insulator beta'-EtMe3Sb[Pd(dmit)2]2

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• Empowering deep neural quantum states through efficient optimization
• Complete field-induced spectral response of the spin-1/2 triangular-lattice antiferromagnet CsYbSe${}_2$
• Evidence of Dirac Quantum Spin Liquid in YbZn2GaO5
• Spectral evidence for Dirac spinons in a kagome lattice antiferromagnet
• Dynamical Signatures of Symmetry Broken and Liquid Phases in an $S=1/2$ Heisenberg Antiferromagnet on the Triangular Lattice
• Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet
• Spin-Peierls instability of the U(1) Dirac spin liquid
• Phase Diagram of the Easy-Axis Triangular-Lattice $J_1-J_2$ Model
• Simulating Spin Dynamics of Supersolid States in a Quantum Ising Magnet
• Evidence of quantum spin liquid state in a Cu${}^{2+}$-based $S=1/2$ triangular lattice antiferromagnet
• Superconductivity in doped triangular Mott insulators: the roles of parent spin backgrounds and charge kinetic energy
• Emergent photons and fractionalized excitations in a quantum spin liquid
• Spin dynamics in the Dirac $U(1)$ spin liquid YbZn${}_2$GaO${}_5$
• Classical dynamics of the antiferromagnetic Heisenberg $S=1/2$ spin ladder
• Observation of the spiral spin liquid in a triangular-lattice material
• Exciton interacting with a moiré lattice: Polarons, strings, and optical probing of spin correlations
• Modified large-$N$ approach to gapless spin liquids, magnetic orders, and dynamics: Application to triangular lattice antiferromagnets
• Collective spin oscillations in a magnetized graphene sheet
• Emergent Quantum Phenomena of Noncentrosymmetric Charge-Density Wave in 1T-Transition Metal Dichalcogenides
• Prospects for NMR Spectral Prediction on Fault-Tolerant Quantum Computers
• Topical review: the nature of the ground state and possibility of a quantum spin liquid in 1T metal dichalcogenides
• Keldysh pseudo-fermion functional renormalization group for quantum magnetism
• Scalable hybrid quantum Monte Carlo simulation of U(1) gauge field coupled to fermions on GPU
• Gapped magnetic ground state in the spin-liquid candidate $\kappa$-(BEDT-TTF)${}_2$Ag${}_2$(CN)${}_3$ suggested by magnetic spectroscopy
• Stability of algebraic spin liquids coupled to quantum phonons
• 5d-mediated indirect exchange and effective spin Hamiltonians in Ce triangular-lattice delafossites
• Competing states in the $S=1/2$ triangular-lattice $J_1$-$J_2$ Heisenberg model: a dynamical density-matrix renormalization group study
• Fate of Bosonic Topological Edge Modes in the Presence of Many-Body Interactions
• Unconventional Spin Dynamics and Supersolid Excitations in the Triangular-Lattice XXZ Model
• Quantum spin liquid ground state with the evidence of roton-like excitations at elevated temperatures in the triangular-lattice delafossite YbCuSe${}_2$