Spin crossovers and superdiffusion in the one-dimensional Hubbard model

Fava, Michele; Ware, Brayden; Gopalakrishnan, Sarang; Vasseur, Romain; Parameswaran, S. A.

doi:10.1103/physrevb.102.115121

Spin crossovers and superdiffusion in the one-dimensional Hubbard model

Journal Article · Thu Sep 10 00:00:00 EDT 2020 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.102.115121· OSTI ID:1663368

^[1]; Ware, Brayden ^[2]; Gopalakrishnan, Sarang ^[3]; Vasseur, Romain ^[2]; ^[4]

Clarendon Laboratory, Oxford (United Kingdom); UMass Amherst
University of Massachusetts, Amherst, MA (United States)
CUNY College of Staten Island, NY (United States); CUNY, New York, NY (United States)
Clarendon Laboratory, Oxford (United Kingdom)

We use tools from integrability and generalized hydrodynamics to study finite-temperature dynamics in the one-dimensional Hubbard model. First, we examine charge, spin, and energy transport away from half-filling and zero magnetization, focusing on the strong coupling regime where we identify a rich interplay of temperature and energy scales, with crossovers between distinct dynamical regimes. We identify an intermediate-temperature regime analogous to the spin-incoherent Luttinger liquid, where spin degrees of freedom are hot but charge degrees of freedom are at low temperature. We demonstrate that the spin Drude weight exhibits sharp features at the crossover between this regime and the low-temperature Luttinger liquid regime, which are absent in the charge and energy response, and rationalize this behavior in terms of the properties of Bethe ansatz quasiparticles.We then turn to the dynamics along special lines in the phase diagram corresponding to half-filling and/or zero magnetization where on general grounds we anticipate that the transport is subballistic but superdiffusive. We provide analytical and numerical evidence for Kardar-Parisi-Zhang (KPZ) dynamical scaling (with length and time scales related via x ~ t^2/3) along both lines and at the SO(4)-symmetric point where they intersect. Furthermore, our results suggest that both spin-coherence crossovers and KPZ scaling may be accessed in near-term experiments with optical lattice Hubbard emulators.

View Accepted Manuscript (DOE)

Research Organization:: University of Massachusetts, Amherst, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; NSF

Grant/Contract Number:: SC0019168

OSTI ID:: 1663368

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 11 Vol. 102; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Introducing iFluid: a numerical framework for solving hydrodynamical equations in integrable models Møller, Frederik Skovbo; Schmiedmayer, Jörg SciPost Physics, Vol. 8, Issue 3 https://doi.org/10.21468/SciPostPhys.8.3.041	journal	January 2020

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