[Paper Review] Quantum Simulation of an Extended Fermi-Hubbard Model Using a 2D Lattice of Dopant-based Quantum Dots

Xiqiao Wang, Ehsan Khatami+7 more|arXiv (Cornell University)|Oct 18, 2021

Quantum and electron transport phenomena50 references4 citations

TL;DR

This study demonstrates the first analog quantum simulation of a 2D extended Fermi-Hubbard model using a 3×3 array of STM-fabricated dopant-based quantum dots in silicon. By achieving sub-nanometer control over lattice constants and in-plane gate tuning, the authors observe finite-size transitions from Mott insulating to metallic behavior and validate results via numerical simulations, enabling precise control of hopping amplitudes and long-range interactions.

ABSTRACT

The Hubbard model is one of the primary models for understanding the essential many-body physics in condensed matter systems such as Mott insulators and cuprate high-Tc superconductors. Recent advances in atomically precise fabrication in silicon using scanning tunneling microscopy (STM) have made possible atom-by-atom fabrication of single and few-dopant quantum dots and atomic-scale control of tunneling in dopant-based devices. However, the complex fabrication requirements of multi-component devices have meant that emulating two-dimensional (2D) Fermi-Hubbard physics using these systems has not been demonstrated. Here, we overcome these challenges by integrating the latest developments in atomic fabrication and demonstrate the analog quantum simulation of a 2D extended Fermi-Hubbard Hamiltonian using STM-fabricated 3x3 arrays of single/few-dopant quantum dots. We demonstrate low-temperature quantum transport and tuning of the electron ensemble using in-plane gates as efficient probes to characterize the many-body properties, such as charge addition, tunnel coupling, and the impact of disorder within the array. By controlling the array lattice constants with sub-nm precision, we demonstrate tuning of the hopping amplitude and long-range interactions and observe the finite-size analogue of a transition from Mott insulating to metallic behavior in the array. By increasing the measurement temperature, we simulate the effect of thermally activated hopping and Hubbard band formation in transport spectroscopy. We compare the analog quantum simulations with numerically simulated results to help understand the energy spectrum and resonant tunneling within the array. The results demonstrated in this study serve as a launching point for a new class of engineered artificial lattices to simulate the extended Fermi-Hubbard model of strongly correlated materials.

Motivation & Objective

• To realize a scalable, atomically precise 2D lattice of quantum dots for simulating strongly correlated electron systems.
• To overcome fabrication challenges in multi-component dopant-based devices to enable quantum simulation of the extended Fermi-Hubbard model.
• To demonstrate low-temperature quantum transport and in-plane gate tuning as probes for many-body properties such as charge addition, tunnel coupling, and disorder effects.
• To achieve sub-nanometer control over lattice constants to tune hopping amplitudes and long-range interactions.
• To compare analog quantum simulation results with numerically simulated energy spectra and resonant tunneling behavior.

Proposed method

• Utilized scanning tunneling microscopy (STM) for atom-by-atom fabrication of single- and few-dopant quantum dots in silicon.
• Engineered a 3×3 two-dimensional array of quantum dots with sub-nanometer precision in lattice constant control.
• Employed in-plane gates to tune electron ensemble properties and probe many-body effects such as charge addition and tunnel coupling.
• Conducted low-temperature quantum transport measurements to characterize the system's response and simulate thermally activated hopping.
• Performed analog quantum simulation of the extended Fermi-Hubbard Hamiltonian, including on-site repulsion and long-range interactions.
• Compared experimental transport spectra with numerically simulated energy spectra and resonant tunneling features to validate the model.

Experimental results

Research questions

• RQ1 Can a 2D array of atomically precise dopant-based quantum dots simulate the extended Fermi-Hubbard model with tunable interactions and hopping?
• RQ2 How does sub-nanometer control of lattice constants affect the tuning of hopping amplitudes and long-range interactions in the array?
• RQ3 What is the finite-size behavior of the transition from Mott insulating to metallic phases in a 3×3 quantum dot array?
• RQ4 How do disorder and electron correlation manifest in the transport spectra of the fabricated array?
• RQ5 To what extent do experimentally observed transport features match numerically simulated energy spectra and resonant tunneling behavior?

Key findings

• The 3×3 array of dopant-based quantum dots successfully demonstrated analog quantum simulation of the extended Fermi-Hubbard Hamiltonian with tunable on-site and long-range interactions.
• Sub-nanometer control of lattice constants enabled precise tuning of the hopping amplitude and long-range interactions in the system.
• Finite-size effects were observed in the transition from Mott insulating to metallic behavior, with clear signatures in low-temperature transport measurements.
• In-plane gate tuning allowed effective probing of charge addition, tunnel coupling, and disorder effects within the array.
• Thermal activation effects were simulated by increasing measurement temperature, revealing Hubbard band formation in transport spectroscopy.
• Good qualitative agreement was found between experimental transport spectra and numerically simulated energy spectra, supporting the validity of the analog quantum simulation.