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arXiv:cond-mat/0404566 · Physical Review Letters

Implementation of Spin Hamiltonians in Optical Lattices

Juan José García‐Ripoll, Miguel Angel Martin-Delgado, J. I. Cirac

Published Dec 15, 2004• 234 citations
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Abstract

We propose an optical lattice setup to investigate spin chains and ladders. Electric and magnetic fields allow us to vary at will the coupling constants, producing a variety of quantum phases including the Haldane phase, critical phases, quantum dimers, etc. Numerical simulations are presented showing how ground states can be prepared adiabatically. We also propose ways to measure a number of observables, like energy gap, staggered magnetization, end-chain spins effects, spin correlations, and the string-order parameter.

DOI
10.1103/physrevlett.93.250405

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We analyze an experimentally realizable model of bosons in a zigzag optical lattice, showing that, by rapidly modulating the magnetic field, one can tune interaction parameters and realize an analog of the Haldane phase. We explain how quantum gas microscopy can be used to detect this phase's nonlocal string order and its topological edge states. We model the detection process. We also find that this model can display supersolid correlations, but argue that they only occur at parameter values which would be challenging to realize in an experiment.
We study a two-leg antiferromagnetic spin-1/2 ladder in the presence of a staggered magnetic field. We consider two parameter regimes: strong (weak) coupling along the legs and weak (strong) coupling along the rungs. In both cases, the staggered field drives the Haldane spin-liquid phase of the ladder towards a Gaussian quantum criticality. In a generalized spin ladder with a non-Haldane, spontaneously dimerized phase, the staggered magnetic field induces an Ising quantum critical regime. In the vicinity of the critical lines, we derive low-energy effective field theories and use these descriptions to determine the dynamical response functions, the staggered spin susceptibility, and the string order parameter.
Dimerized spin-1/2 ladders exhibit a variety of phase structures, which depend on the intra-chain and inter-chain spin exchange energies as well as on the dimerization pattern of the ladder. Using the density matrix renormalization group (DMRG) algorithm, we study critical properties of the bond-alternating two-leg Heisenberg spin ladder with diagonal interaction J ×. Two types of spin systems, staggered dimerized antiferromagnetic ladder and columnar dimerized ferro-antiferromagnetic couplings ladder, are investigated. To clarify the phase transition behaviors, we simultaneously analyze the string order parameter (SOP), the twisted order parameter (TOP), as well as a measurement of the quantum information analysis. Based on measuring this different observables, we establish the phase diagram accurately and give the fitting functions of the phase boundaries. In addition, the phase transition of cross-coupled spin ladder (in the absence of intrinsic dimerization) is also discussed.