Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations

Abstract

The quantum-critical properties of the transverse-field Ising model with algebraically decaying interactions are investigated by means of stochastic series expansion quantum Monte Carlo, on both the one-dimensional linear chain and the two-dimensional square lattice. We extract the critical exponents $\nu$ and $\beta$ as a function of the decay exponent of the long-range interactions. For ferromagnetic Ising interactions, we resolve the limiting regimes known from field theory, ranging from the nearest-neighbor Ising to the long-range Gaussian universality classes, as well as the intermediate regime with continuously varying critical exponents. In the long-range Gaussian regime, we treat the effect of dangerous irrelevant variables on finite-size scaling forms. For antiferromagnetic and therefore competing Ising interactions, the stochastic series expansion algorithm displays growing auto-correlation times leading to a reduced performance. Nevertheless, our results are consistent with the nearest-neighbor Ising universality for all investigated interaction ranges both on the linear chain and the square lattice.

11 pages, 4 figures

References in corpus (9)

• Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas
• Entanglement entropy for the long range Ising chain
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions
• Fidelity Susceptibility Study of Quantum Long-Range Antiferromagnetic Ising Chain
• Finite-size scaling above the upper critical dimension in Ising models with long-range interactions
• Fisher's scaling relation above the upper critical dimension
• A new critical exponent koppa and its logarithmic counterpart koppa-hat
• Thermal Kosterlitz-Thouless transitions in the $1/r^2$ long-range ferromagnetic quantum Ising chain revisited

Cited by in corpus (26)

• Finite-temperature critical behavior of long-range quantum Ising models
• Scaling at quantum phase transitions above the upper critical dimension
• Many-body enhancement in a spin-chain quantum heat engine
• Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model
• Dynamical properties of quantum many-body systems with long range interactions
• Monte Carlo based techniques for quantum magnets with long-range interactions
• Emus live on the Gross-Neveu-Yukawa archipelago
• Study of the long-range transverse field Ising model with fermionic Gaussian states
• Systematic Analysis of Crystalline Phases in Bosonic Lattice Models with Algebraically Decaying Density-Density Interactions
• Exact solution for quantum strong long-range models via a generalized Hubbard-Stratonovich transformation
• Unconventional Scalings of Quantum Entropies in Long-Range Heisenberg Chains
• Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices
• Transformer Wave Function for Quantum Long-Range models
• Effective-Dimension Theory of Critical Phenomena above Upper Critical Dimensions
• Transverse-field $XY$ spin chain with the competing long-range interactions: Multi-criticality around the $XX$-symmetric point
• First- and second-order quantum phase transitions in the long-range unfrustrated antiferromagnetic Ising chain
• Quantum robustness of the toric code in a parallel field on the honeycomb and triangular lattice
• Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations
• Quantum phase diagrams of Dicke-Ising models by a wormhole algorithm
• Neural-network quantum state study of the long-range antiferromagnetic Ising chain
• Clock Factorized Quantum Monte Carlo Method for Long-range Interacting Systems
• Continuously varying critical exponents in an exactly solvable long-range cluster XY mode
• Singular transport in non-equilibrium strongly internal-coupled 1D tilted field spin-1/2 chain
• Stochastic parameter optimization analysis of dynamical quantum critical phenomena in long-range transverse-field Ising chain
• Spatiotemporal Quenches in Long-Range Hamiltonians
• Temporal Entanglement Transitions in the Periodically Driven Ising Chain