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Exploring the many-body localization transition in two dimensions
Jae-yoon Choi, Sebastian Hild, Johannes Zeiher, Peter Schauß, Antonio Rubio-Abadal, Tarik Yefsah, Vedika Khemani, David A. Huse, Immanuel Bloch, Christian Gross
TL;DR
The paper examines a localization transition in a disordered two-dimensional optical lattice using prepared density patterns, single-site-resolved detection, disorder characterization, and numerical simulations. It reports a measured disorder correlation length of ζ = 0.6(0.1) a_lat and no visible finite-size shift in the critical disorder extracted from imbalance measurements.
Problem
The paper examines how localization-transition measurements depend on the spatial properties of disorder and on system size in a two-dimensional optical lattice.
Method
The experiment prepares a density domain wall, evolves atoms in a characterized disordered lattice, detects parity-projected densities site by site, and compares results with non-interacting exact-diagonalization simulations.
Results
ζ = 0.6(0.1) a_lat for the measured disorder correlation length, agreeing with the simulated value ζ_NA = 0.64 a_lat; the smaller system yielded Δ_c,I = 5.4(6), consistent with Δ_c,I = 5.5(4) J for the larger system.
Takeaways & Limitations
The measured disorder correlations agree with simulations, and the extracted critical disorder shows no visible change under the tested reduction in system size.
Abstract
from arXiv · showhide
One fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalize under their own dynamics. Recently, the emergence of many-body localized systems has questioned this concept, challenging our understanding of the connection between statistical physics and quantum mechanics. Here we report on the observation of a many-body localization transition between thermal and localized phases for bosons in a two-dimensional disordered optical lattice. With our single site resolved measurements we track the relaxation dynamics of an initially prepared out-of-equilibrium density pattern and find strong evidence for a diverging length scale when approaching the localization transition. Our experiments mark the first demonstration and in-depth characterization of many-body localization in a regime not accessible with state-of-the-art simulations on classical computers.
I. INITIAL STATE PREPARATION AND DETECTION OF THE ATOMS
The experiment prepared a sharp density domain wall from a two-dimensional Mott insulator and detected its evolution using single-site-resolved fluorescence imaging.
- A two-dimensional Mott insulator was prepared with approximately 0.90(5) parity-projected central density at lattice depth 40 Er.
- The preparation used state-selective light shifts, microwave transfer, resonant removal, and subsequent transfer into the disorder-potential state.
- After evolution, the lattice was rapidly deepened to 40 Er and the parity-projected density was measured with single-site-resolved fluorescence imaging.Multiply occupied sites are lost under parity projection; their estimated fractions were 2% without disorder and 9% at ∆=17 J.
II. DISORDER POTENTIAL
The experiment generated and spectroscopically characterized a spatially correlated two-dimensional disorder potential, while testing its uniformity and associated heating-related controls.
- A digital micro-mirror device generated a 31 × 31 random disorder pattern projected onto the atoms through a high-resolution objective.Approximately 7 × 7 mirrors were focused onto each lattice site to create grayscale control.
- Microwave spectroscopy measured the local light-shift potential at each lattice site, enabling calculation of its autocorrelation function.
- The imaging point-spread function produced a finite disorder correlation length of ζ = 0.6(0.1) alat, consistent with the simulated ζNA = 0.64 alat.
- The measured correlation profiles decayed exponentially with distance, and the figure compares averaged horizontal and vertical cuts with the full autocorrelation and finite-resolution expectation.
- The overall disorder-light uniformity was better than 5%, with additional tests finding symmetric or indistinguishable steady-state distributions under the stated controls.
III. HEATING DYNAMICS OF MOTT INSULATOR
Heating was quantified in an approximately unity-filled Mott insulator to assess energy growth during the experimental evolution times.
- Temperature and energy density increased approximately linearly up to 2 s at 12 Er lattice depth.
- The fitted heating rates were ˙T = 0.11(2) U/s for temperature and ˙E/N = 0.09(3) U/s for energy density.Here U = h × 601 Hz at 12 Er lattice depth.
- The heating estimate used an atomic-limit decoupling assumption that may slightly overestimate temperature because of particle-hole fluctuations.
- Because the rate was measured near the superfluid–Mott insulator transition, it was expected to provide an upper bound for external-noise coupling in the disordered system.
IV. SYSTEM SIZE EFFECT
Reducing the system size did not visibly shift the localization transition inferred from imbalance measurements.
- Reducing the atom number by 60% shrank the initial Mott-insulator radius from 9 to 7 sites while keeping E0/N constant.
- The smaller system gave ∆c,I = 5.4(6), consistent with ∆c,I = 5.5(4) J for the larger system.
- The imbalance measurements showed no visible change in the critical disorder after the system-size reduction.
V. NUMERICS FOR NON-INTERACTING ATOMS
The paper uses exact diagonalization to model non-interacting atoms under experimentally matched disorder and lattice conditions, averaging observables across disorder realizations. These simulations assess trapping effects and the robustness of the disorder model.
- Exact diagonalization simulates non-interacting atoms on a 31×31 square lattice matching the experiment’s disorder-pattern size.The simulations optionally include the experiment’s harmonic confinement.
- The simulated imbalance is compared between systems with and without harmonic confinement across disorder strengths.The two configurations agree well at strong disorder, while the trap produces slight differences at lower disorder.
- 100 disorder realizations are simulated and averaged, with observables depending only slightly on the precise disorder-distribution shape when spatial correlations are fixed.A measured distribution and a symmetric Gaussian distribution with the same full width at half maximum yield little difference.