Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations

Abstract

We develop a nonequilibrium increment method in quantum Monte Carlo simulations to obtain the Rényi entanglement entropy of various quantum many-body systems with high efficiency and precision. To demonstrate its power, we show the results on a few important yet difficult $(2+1)d$ quantum lattice models, ranging from the Heisenberg quantum antiferromagnet with spontaneous symmetry breaking, the quantum critical point with O(3) conformal field theory (CFT) to the toric code ${\mathbb{Z}}_2$ topological ordered state and the Kagome ${\mathbb{Z}}_2$ quantum spin liquid model with frustration and multi-spin interactions. In all these cases, our method either reveals the precise CFT data from the logarithmic correction or extracts the quantum dimension in topological order, from the dominant area law in finite-size scaling, with very large system sizes, controlled errorbars and minimal computational costs. Our method therefore establishes a controlled and practical computation paradigm to obtain the difficult yet important universal properties in highly entangled quantum matter.

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Cited by in corpus (43)

• Many-body magic via Pauli-Markov chains -- from criticality to gauge theories
• Experimental signatures of quantum and topological states in frustrated magnetism
• Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
• Critical behaviors of non-stabilizerness in quantum spin chains
• Topological Disorder Parameter
• Universal features of entanglement entropy in the honeycomb Hubbard model
• Investigating Topological Order using Recurrent Neural Networks
• Unlocking the general relationship between energy and entanglement spectra via the wormhole effect
• Stable computation of entanglement entropy for 2D interacting fermion systems
• Diagnosing $SO(5)$ Symmetry and First-Order Transition in the $J-Q_3$ Model via Entanglement Entropy
• Extracting subleading corrections in entanglement entropy at quantum phase transitions
• Evolution of entanglement entropy at SU($N$) deconfined quantum critical points
• Incremental SWAP Operator for Entanglement Entropy: Application for Exponential Observables in Quantum Monte Carlo Simulation
• An integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulation
• Improved scaling of the entanglement entropy of quantum antiferromagnetic Heisenberg systems
• Non-equilibrium quantum Monte Carlo algorithm for stabilizer Renyi entropy in spin systems
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Evolution of Dynamical Signature in the X-cube Fracton Topological Order
• Classical model emerges in quantum entanglement: Quantum Monte Carlo study for an Ising-Heisenberg bilayer
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Demonstrating the wormhole mechanism of the entanglement spectrum via a perturbed boundary
• Tracking the variation of entanglement Rényi negativity: a quantum Monte Carlo study
• Reweight-annealing method for evaluating the partition function via quantum Monte Carlo calculations
• Accurate neural quantum states for interacting lattice bosons
• An analog of topological entanglement entropy for mixed states
• 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
• Perspective on Physical Interpretations of Rényi Entropy in Statistical Mechanics
• Predicting Topological Entanglement Entropy in a Rydberg analog simulator
• Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation
• Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects
• Extracting Universal Corner Entanglement Entropy during the Quantum Monte Carlo Simulation
• Rényi entanglement entropy of spin chain with Generative Neural Networks
• Topologically protected negative entanglement
• Rényi entropy of quantum anharmonic chain at non-zero temperature
• Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits
• Universal term of Entanglement Entropy in the $\pi$-flux Hubbard model
• Pseudocriticality in antiferromagnetic spin chains
• Symmetrizing the Constraints -- Density Matrix Renormalization Group for Constrained Lattice Models
• Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum
• Rényi complexity in mean-field disordered systems
• Bell sampling in Quantum Monte Carlo simulations
• Entanglement entropy dynamics of non-Gaussian states in free boson systems: Random sampling approach