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1. Generalized effective spin-chain formalism for strongly interacting spinor gases in optical lattices

   https://doi.org/10.1103/PhysRevA.108.063315  

   Basak, Sagarika; Pu, Han (December 2023, Physical Review A)

   A generalized effective spin-chain model is developed for studies of strongly interacting spinor gases in a one-dimensional (1D) optical lattice. The spinor gas is mapped to a system of spinless fermions and a spin chain. A generalized effective spin-chain Hamiltonian that acts on the mapped system is developed to study the static and dynamic properties of the spinor gas. This provides a computationally efficient alternative tool to study strongly interacting spinor gases in 1D lattice systems. This formalism permits the study of spinor gases with arbitrary spin and statistics, providing a generalized approach for 1D strongly interacting gases. By virtue of its simplicity, it provides an easier tool to study and gain deeper insights into the system. In combination with the model defined previously for continuum systems, a unified framework is developed. Studying the mapped system using this formalism recreates the physics of spinor gas in 1D lattice. Additionally, the time evolution of a quenched system is studied. The generalized effective spin-chain formalism has potential applications in the study of a multitude of interesting phenomena arising in lattice systems such as high-Tc superconductivity and the spin-coherent and spin-incoherent Luttinger liquid regimes. 

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2. Engineering dynamical phase diagrams with driven lattices in spinor gases

   https://doi.org/10.1103/PhysRevA.109.043309  

   Austin-Harris, J. O.; Hardesty-Shaw, Z. N.; Guan, Q.; Binegar, C.; Blume, D.; Lewis-Swan, R. J.; Liu, Y. (April 2024, Physical Review A)

   Thomas Pattard; Jan Michael Rost; Franco Dalfovo (Ed.)

   We experimentally demonstrate that well-designed driven lattices are versatile tools to simultaneously tune multiple key parameters (spin-dependent interactions, spinor phase, and quadratic Zeeman energy) for manipulating phase diagrams of spinor gases with negligible heating and atom losses. This opens avenues for studying engineered Hamiltonians and dynamical phase transitions. Modulation-induced harmonics generate progressively narrower separatrices at driving-frequency-determined higher magnetic-field strengths. This technique enables exploration of multiple, previously inaccessible parameter regimes of spinor dynamics (notably high magnetic-field strengths, tunable spinor phase, and individually tunable spin-preserving and spin-changing collisions) and widens the range of cold-atom applications, e.g., in quantum sensing and studies of nonequilibrium dynamics. 

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3. Generalized Bose–Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases

   https://doi.org/10.1088/1751-8121/aca302  

   Yang, Li; Alam, Shah Saad; Pu, Han (November 2022, Journal of Physics A: Mathematical and Theoretical)

   Abstract Quantum many-body systems in one dimension (1D) exhibit some peculiar properties. In this article, we review some of our work on strongly interacting 1D spinor quantum gas. First, we discuss a generalized Bose–Fermi mapping that maps the charge degrees of freedom to a spinless Fermi gas and the spin degrees of freedom to a spin chain model. This also maps the strongly interacting system into a weakly interacting one, which is amenable for perturbative calculations. Next, based on this mapping, we construct an ansatz wavefunction for the strongly interacting system, using which many physical quantities can be conveniently calculated. We showcase the usage of this ansatz wavefunction by considering the collective excitations and quench dynamics of a harmonically trapped system. 

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4. Spin transport in a Mott insulator of ultracold fermions

   https://doi.org/10.1126/science.aat4387  

   Nichols, Matthew A.; Cheuk, Lawrence W.; Okan, Melih; Hartke, Thomas R.; Mendez, Enrique; Senthil, T.; Khatami, Ehsan; Zhang, Hao; Zwierlein, Martin W. (January 2019, Science)

   Strongly correlated materials are expected to feature unconventional transport properties, such that charge, spin, and heat conduction are potentially independent probes of the dynamics. In contrast to charge transport, the measurement of spin transport in such materials is highly challenging. We observed spin conduction and diffusion in a system of ultracold fermionic atoms that realizes the half-filled Fermi-Hubbard model. For strong interactions, spin diffusion is driven by super-exchange and doublon-hole–assisted tunneling, and strongly violates the quantum limit of charge diffusion. The technique developed in this work can be extended to finite doping, which can shed light on the complex interplay between spin and charge in the Hubbard model. 

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5. Nonadiabatic Hydrogen Tunneling Dynamics for Multiple Proton Transfer Processes with Generalized Nuclear-Electronic Orbital Multistate Density Functional Theory

   https://doi.org/10.1021/acs.jctc.4c00737  

   Dickinson, Joseph A; Hammes-Schiffer, Sharon (September 2024, Journal of Chemical Theory and Computation)

   Proton transfer and hydrogen tunneling play key roles in many processes of chemical and biological importance. The generalized nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) method was developed in order to capture hydrogen tunneling effects in systems involving the transfer and tunneling of one or more protons. The generalized NEO-MSDFT method treats the transferring protons quantum mechanically on the same level as the electrons and obtains the delocalized vibronic states associated with hydrogen tunneling by mixing localized NEO-DFT states in a nonorthogonal configuration interaction scheme. Herein, we present the derivation and implementation of analytical gradients for the generalized NEO-MSDFT vibronic state energies and the nonadiabatic coupling vectors between these vibronic states. We use this methodology to perform adiabatic and nonadiabatic dynamics simulations of the double proton transfer reactions in the formic acid dimer and the heterodimer of formamidine and formic acid. The generalized NEO-MSDFT method is shown to capture the strongly coupled synchronous or asynchronous tunneling of the two protons in these processes. Inclusion of vibronically nonadiabatic effects is found to significantly impact the double proton transfer dynamics. This work lays the foundation for a variety of nonadiabatic dynamics simulations of multiple proton transfer systems, such as proton relays and hydrogen-bonding networks. 

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