We consider the Schrödinger-like operatorH in which the role of a potential is played by the lattice sum of rank 1 operators $$|\left. {v_n } \right\rangle \left\langle {v_n |} \right.$$ multiplied by g tan π[(α,n)+ω],g>0, α∈ℝ d ,n∈ℤ d , ω∈[0, 1]. We show that if the vector α satisfies the Diophantine condition and the Fourier transform support of the functionsv n (x)=v(x-n),x∈ℝ d ,n∈ℤ d , is small then the spectrum ofH consists of a dense point component coinciding withℝ and an absolutely continuous component coinciding with [ϱ, ∞), where ϱ is the radius of the mentioned support. Besides, we find the integrated density of statesN(λ) (it has a jump at λ=ϱ) and zero temperature a.c. conductivityσ λ (v), that also has a jump at λ=ϱ and vanishes faster than any power of the external field frequency ν as ν→0 and λ≠ϱ.