Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model

Abstract

The Mermin-Wagner theorem states that spontaneous continuous symmetry breaking is prohibited in systems with short-range interactions at spatial dimension $D\le 2$. For long-range interactions with a power-law form ($1/r^{\alpha }$), the theorem further forbids ferromagnetic or antiferromagnetic order at finite temperature when $\alpha \ge 2D$. However, the situation for $\alpha \in (2,4)$ at $D=2$ is not covered by the theorem. To address this, we conduct large-scale quantum Monte Carlo simulations and field theoretical analysis. Our findings show spontaneous breaking of $SU(2)$ symmetry in the ferromagnetic Heisenberg model with $1/r^{\alpha }$-form long-range interactions at $D=2$. We determine critical exponents through finite-size analysis for $\alpha <3$ (above the upper critical dimension with Gaussian fixed point) and $3\le \alpha <4$ (below the upper critical dimension with non-Gaussian fixed point). These results reveal new critical behaviors in 2D long-range Heisenberg models, encouraging further experimental studies of quantum materials with long-range interactions beyond the Mermin-Wagner theorem's scope.

References in corpus (40)

• Cold atoms in cavity-generated dynamical optical potentials
• Graphene Bilayers with a Twist
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Strongly Correlated Chern Insulators in Magic-Angle Twisted Bilayer Graphene
• Numerical studies of confined states in rotated bilayers of graphene
• Long-range interacting quantum systems
• MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
• Flavour Hund's Coupling, Correlated Chern Gaps, and Diffusivity in Moiré Flat Bands
• Entropic evidence for a Pomeranchuk effect in magic angle graphene
• Quantum phases of Rydberg atoms on a kagome lattice
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Competing zero-field Chern insulators in Superconducting Twisted Bilayer Graphene
• Spin-orbit driven ferromagnetism at half moiré filling in magic-angle twisted bilayer graphene
• Anomalous Behavior of Spin Systems with Dipolar Interactions
• Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions
• Breaking through the Mermin-Wagner limit in 2D van der Waals magnets
• Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains
• Momentum space quantum Monte Carlo on twisted bilayer Graphene
• Metastability and discrete spectrum of long-range systems
• Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations
• Skyrmion Superconductivity: DMRG evidence for a topological route to superconductivity
• A Complete Renormalization Group Trajectory Between Two Fixed Points
• Reentrant Correlated Insulators in Twisted Bilayer Graphene at 25T ($2\pi$ Flux)
• Correlated insulators, density wave states, and their nonlinear optical response in magic-angle twisted bilayer graphene
• Emergent glassy behavior in a kagome Rydberg atom array
• Finite-size scaling above the upper critical dimension in Ising models with long-range interactions
• Exciton Proliferation and Fate of the Topological Mott Insulator in a Twisted Bilayer Graphene Lattice Model
• Finite-temperature critical behavior of long-range quantum Ising models
• Fisher's scaling relation above the upper critical dimension
• Superconductivity and bosonic fluid emerging from Moiré flat bands
• Dissipation-Induced Order: The $S=1/2$ Quantum Spin Chain Coupled to an Ohmic Bath
• A new critical exponent koppa and its logarithmic counterpart koppa-hat
• Generalized Higgs mechanism in long-range interacting quantum systems
• Thermodynamic characteristic for correlated flat-band system with quantum anomalous Hall ground state
• Scaling at quantum phase transitions above the upper critical dimension
• Characterizing Topological Excitations of a Long-Range Heisenberg Model with Trapped Ions
• Fermion sign bounds theory in quantum Monte Carlo simulation
• Evolution from quantum anomalous Hall insulator to heavy-fermion semimetal in magic-angle twisted bilayer graphene
• Dynamical properties of quantum many-body systems with long range interactions
• Nematic insulator at charge neutrality in twisted bilayer graphene

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• Monte Carlo based techniques for quantum magnets with long-range interactions
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• Finite-size versus finite-temperature effects in the critical long-range $O(N)$ model
• Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system
• Unconventional Scalings of Quantum Entropies in Long-Range Heisenberg Chains
• Critical phase induced by Berry phase and dissipation in a spin chain
• Dipolar ordering transitions in many-body quantum optics: Analytical diagrammatic approach to equilibrium quantum spins
• The Nonclassical Regime of the Two-dimensional Long-range XY Model: a Comprehensive Monte Carlo Study
• Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions
• High-temperature partition functions and classical simulatability of long-range quantum systems
• Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum