Simulation of Time-dependent Heisenberg Models in 1D

Abstract

In this paper, we provide a theoretical analysis of strongly interacting quantum systems confined by a time-dependent external potential in one spatial dimension. We show that such systems can be used to simulate spin chains described by Heisenberg Hamiltonians in which the exchange coupling constants can be manipulated by time-dependent driving of the shape of the external confinement. As illustrative examples, we consider a harmonic trapping potential with a variable frequency and an infinite square well potential with a time-dependent barrier in the middle.

Version accepted for publication in PRB

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• Comparing models for the ground state energy of a trapped one-dimensional Fermi gas with a single impurity
• Dynamical fermionization in a one-dimensional Bose-Fermi mixture
• Dynamical realization of magnetic states in a strongly interacting Bose mixture
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• A generalized effective spin-chain formalism for strongly interacting spinor gases in optical lattice
• State transfer in an inhomogeneous spin chain
• Dynamical fermionization in one-dimensional spinor gases at finite temperature
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Dynamical resistivity of a few interacting fermions to the time-dependent potential barrier
• Shortcut to spin dynamics for quantum mixtures
• Generation of spin currents by a temperature gradient in a two-terminal device