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Stochastic parameter optimization analysis of dynamical quantum critical phenomena in the long-range transverse-field
1The University of Tokyo, Department of Physics, Tokyo 113-0033, Japan.
Physical Review. E
|February 7, 2025
Summary
This study explores quantum phase transitions in a 1D Ising model using quantum Monte Carlo simulations. Researchers identified a universality boundary at σ=7/4, distinguishing between different critical behaviors.
Area of Science:
- Condensed Matter Physics
- Quantum Many-Body Systems
- Statistical Mechanics
Background:
- Understanding quantum phase transitions is crucial for characterizing exotic states of matter.
- The one-dimensional long-range transverse-field Ising model presents a complex theoretical challenge.
- Previous studies often require prior knowledge of critical points and universality classes.
Purpose of the Study:
- To investigate the quantum phase transition in the 1D long-range transverse-field Ising model.
- To explore the dependence of critical exponents on the decay exponent (σ) of the long-range interaction.
- To identify universality boundaries and critical behaviors without prior assumptions.
Main Methods:
- Combined quantum Monte Carlo (QMC) simulations with stochastic parameter optimization.
- Achieved isotropic space and imaginary time by tuning correlation ratios.
- Automatically determined sampling parameters and eliminated finite-size corrections by comparing systems of different sizes.
Main Results:
- Successfully simulated the model without prior knowledge of critical parameters or universality class.
- Investigated the σ dependence of the dynamical and other critical exponents across different regimes.
- Provided numerical evidence for σ=7/4 as the universality boundary between mean-field and 2D classical Ising universality.
Conclusions:
- The study demonstrates a robust QMC approach for analyzing quantum phase transitions.
- The identified universality boundary at σ=7/4 offers new insights into critical phenomena in long-range interacting systems.
- The findings contribute to a deeper understanding of critical exponents and universality in diverse physical regimes.
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