Ground state and excitation of an asymmetric spin ladder model

Abstract

We perform a systematic investigation on an asymmetric zig-zag spin ladder with inter-leg exchange J1 and different exchange integrals J2 ± δ on both legs. In the weak frustration limit, the spin model can be mapped to a revised double frequency sine-Gorden model by using bosonization. Renormalization group analysis shows that the Heisenberg critical point flows to an intermediatecoupling fixed point with gapless excitations and a vanishing spin velocity. When the frustration is large, a spin gap opens and a dimer ground state is realized. Fixing J2 = J1/2, we find, as a function of δ, a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model. While the ground state is independent of the alternating next-nearest-neighbor exchange δ, the gap size of excitations is found to decrease with increasing δ. We also extend our study to a two-dimensional double layer model with an exactly known ground state.

Exact ground state and elementary excitations of the spin tetrahedron chain

“…In fact, utilizing the Raleigh-Ritz variational principle 11,19,20,21 , we can exactly prove the state given by Eq. (4) is the ground state of Hamiltonian (2) as long as J ⊥ ≥ 2J.…”

“…Because there exists no intrinsic mechanics responsible for binding the dimer and monomer together to form a bound state in a spontaneously trimerized system, it is reasonable to assume that the dimer and monomer are well separated and they could be treated separately. Similar schemes have been used to evaluate the excitation spectrum in the spin-sawtooth system 19,20 . Under such an approximation, the excitation spectrum can be represented as a sum of monomer part and dimer part, i.e.,…”

“…For a mixed spin △ chain with size of 8 + 8, we get its ground state energy given by E g 1/2,1 (8, 8) /16 = −0.646773. We note that the ground state of a spin △ chain or a spin sawtooth model with S i = 1/2 is exactly known 19,20,27 .…”

Laserless trapped-ion quantum simulations without spontaneous scattering using microtrap arrays

“…For some of these mappings, linear lattices with hopping particles map to interacting spins on ladders with different interaction strengths on the rungs and legs of the ladder [41] including configurations with asymmetric ladders [42]. This can be implemented in this architecture in one of three ways: (i) by fixing the direction of the quantizing magnetic field that pins the ion moments such that it points not directly along the square array diagonal but along a direction whose x and y components are in proportion to the desired ladder-rung strength ratio (in cases with uniform lattice vectors throughout the array); (ii) by tailoring the geometry of the trap during fabrication such that the microtrap spacings in the ladder and rung direction are different, leading to different interaction strengths in those directions; or (iii) by modifying individual ion trap frequencies, possibly in combination with methods (i) or (ii), to locally modify the interaction [see Eq.…”

Phase transitions and thermal entanglement of the distorted Ising–Heisenberg spin chain: topology of multiple-spin exchange interactions in spin ladders

“…Equivalent to the diamond chains [20][21][22][23][24], magnetic spin ladders [25,26] are a class of low-dimensional materials with structural and physical properties between those of one-dimensional chains and two-dimensional planes [27]. Meanwhile, exact solvable one-dimensional lattices sawtooth chain with Ising-Heisenberg model and also Hubbard model have investigated from theoretical [28][29][30] and experimental [31,32] point of view.…”