Papers › Numerical evidence for many-body localization in two and three dimensions
Numerical evidence for many-body localization in two and three dimensions
Eli Chertkov, Benjamin Villalonga, Bryan K. Clark
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Disorder and interactions can lead to the breakdown of statistical mechanics in certain quantum systems, a phenomenon known as many-body localization (MBL). Much of the phenomenology of MBL emerges from the existence of ℓ-bits, a set of conserved quantities that are quasilocal and binary (i.e., possess only ±1 eigenvalues). While MBL and ℓ-bits are known to exist in one-dimensional systems, their existence in dimensions greater than one is a key open question. To tackle this question, we develop an algorithm that can find approximate binary ℓ-bits in arbitrary dimensions by adaptively generating a basis of operators in which to represent the ℓ-bit. We use the algorithm to study four models: the one-, two-, and three-dimensional disordered Heisenberg models and the two-dimensional disordered hard-core Bose-Hubbard model. For all four of the models studied, our algorithm finds high-quality ℓ-bits at large disorder strength and rapid qualitative changes in the distributions of ℓ-bits in particular ranges of disorder strengths, suggesting the existence of MBL transitions. These transitions in the one-dimensional Heisenberg model and two-dimensional Bose-Hubbard model coincide well with past estimates of the critical disorder strengths in these models which further validates the evidence of MBL phenomenology in the other two and three-dimensional models we examine. In addition to finding MBL behavior in higher dimensions, our algorithm can be used to probe MBL in various geometries and dimensionality.
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