Superdiffusive transport of energy in one-dimensional metals

Journal Article · 26 May 2020 · Proceedings of the National Academy of Sciences of the United States of America

DOI: https://doi.org/10.1073/pnas.1916213117 · OSTI ID:1630793

Bulchandani, Vir B.  ^[1]; Karrasch, Christoph ^[2]; Moore, Joel E. ^[3]

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1. Department of Physics, University of California, Berkeley, CA 94720,
2. Institut für Mathematische Physik, Technische Universität Braunschweig, 38106 Braunschweig, Germany,
3. Department of Physics, University of California, Berkeley, CA 94720,, Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

Metals in one spatial dimension are described at the lowest energy scales by the Luttinger liquid theory. It is well understood that this free theory, and even interacting integrable models, can support ballistic transport of conserved quantities including energy. In contrast, realistic one-dimensional metals, even without disorder, contain integrability-breaking interactions that are expected to lead to thermalization and conventional diffusive linear response. We argue that the expansion of energy when such a nonintegrable Luttinger liquid is locally heated above its ground state shows superdiffusive behavior (i.e., spreading of energy that is intermediate between diffusion and ballistic propagation), by combining an analytical anomalous diffusion model with numerical matrix-product–state calculations on a specific perturbed spinless fermion chain. Different metals will have different scaling exponents and shapes in their energy spreading, but the superdiffusive behavior is stable and should be visible in time-resolved experiments.

• Sponsoring Organization: USDOE
• Grant/Contract Number: AC02-05-CH1123
• OSTI ID: 1630793
• Journal Information: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Vol. 117 Journal Issue: 23; ISSN 0027-8424
• Publisher: Proceedings of the National Academy of SciencesCopyright Statement
• Country of Publication: United States
• Language: English