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Full Counting Statistics for Interacting Fermions with Determinantal Quantum Monte Carlo Simulations
Stephan Humeniuk1, Hans Peter Büchler1
1Institute for Theoretical Physics III and Center for Integrated Quantum Science and Technology, University of Stuttgart, 70550 Stuttgart, Germany.
Physical Review Letters
|December 30, 2017
Summary
We developed a new method to calculate full counting statistics for the Fermi-Hubbard model using quantum Monte Carlo. This approach reveals insights into preformed pairs and matches experimental results for magnetic properties.
Area of Science:
- Condensed Matter Physics
- Quantum Simulation
- Cold Atom Experiments
Background:
- The Fermi-Hubbard model is crucial for understanding strongly correlated electron systems.
- Determinantal quantum Monte Carlo (DQMC) is a powerful numerical technique, but calculating full probability distributions is challenging.
- Cold atom experiments offer unique platforms for simulating quantum models with high precision.
Purpose of the Study:
- To develop and present a novel method for computing the full probability distribution function (PDF) of quadratic observables in the Fermi-Hubbard model.
- To utilize determinantal quantum Monte Carlo (DQMC) calculations for obtaining this full counting statistics.
- To demonstrate the utility of full counting statistics in characterizing quantum systems, particularly in the context of cold atom experiments.
Main Methods:
- Implementation of a method to compute the full probability distribution function of quadratic observables (e.g., particle number, magnetization) within DQMC.
- Application of the method to analyze the Fermi-Hubbard model, focusing on systems with single-site resolution achievable in cold atom experiments.
- Calculation of the full counting statistics for staggered magnetization in the repulsive Hubbard model at half filling.
Main Results:
- The developed method successfully computes the full probability distribution function for quadratic observables in the Fermi-Hubbard model.
- Full counting statistics provide valuable information regarding the size of preformed pairs in the system.
- Calculated full counting statistics for staggered magnetization show excellent agreement with recent experimental findings.
- The study confirms that current cold atom experiments can distinguish between the Hubbard model and the limiting Heisenberg model.
Conclusions:
- The presented DQMC method enables the computation of full counting statistics for quadratic observables, offering deeper insights into quantum many-body systems.
- Full counting statistics are a sensitive probe for understanding pairing phenomena and distinguishing between different quantum models.
- Experimental techniques in cold atom systems are sufficiently advanced to validate theoretical predictions and explore fundamental quantum physics.
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