Hydrodynamic nonlinear response of interacting integrable systems

Journal Article · 06 September 2021 · Proceedings of the National Academy of Sciences of the United States of America

DOI: https://doi.org/10.1073/pnas.2106945118 · OSTI ID:1841465

Fava, Michele  ^[1]; Biswas, Sounak ^[2]; Gopalakrishnan, Sarang  ^[3]; Vasseur, Romain ^[4]; Parameswaran, S. A.  ^[2]

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1. Univ. of Oxford (United Kingdom). Clarendon Lab.; UMass Amherst
2. Univ. of Oxford (United Kingdom). Clarendon Lab.
3. Pennsylvania State Univ., University Park, PA (United States)
4. Univ. of Massachusetts, Amherst, MA (United States)

In this work, we develop a formalism for computing the nonlinear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the Lieb–Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We identify intrinsically nonperturbative regimes of the nonlinear response of integrable systems.

• Research Organization: Univ. of Massachusetts, Amherst, MA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; National Science Foundation (NSF); European Research Council (ERC)
• Grant/Contract Number: SC0019168
• OSTI ID: 1841465
• 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 Journal Issue: 37 Vol. 118; ISSN 0027-8424
• Publisher: National Academy of SciencesCopyright Statement
• Country of Publication: United States
• Language: English