QUANTUM-LIQUID REGIMES FOR SPIN CHAINS COUPLED TO PHONONS - PHONON DENSITY WAVE VERSUS MAGNETIC ORDER

We consider a chain of localized spins, coupled to phonons. Recently t his problem has been solved exactly for a ''basic model,'' a family of spin-phonon Hamiltonians H-BM characterized by one parameter (couplin g constant K), and a zero-ir first-order phase transition from the mag netic (ferro or antiferro) state at low couplings to the nonmagnetic s tate with a phonon density wave at high couplings was found. Here we p robe the general case, constructing an effective Hamiltonian H for low -energy degrees of freedom by means of regular expansion in deviations delta H=H-H-BM of the general Hamiltonian H from that of the basic mo del. In linear approximation in delta H the problem appears to be exac tly solvable as well, due to an infinite number of conservation laws. If K is far enough from the critical value K-c, then the character of the basic model solution is not altered. In the vicinity of K-c the ma gnetic state is dramatically reconstructed: Here the ground state is a gapless magnetic quantum liquid, consisting of mobile singlet spin-ph onon complexes and unbound spins. The fraction of singlets increases g radually upon approaching K-c, and the magnetic order parameter gradua lly vanishes. Thus we have here a partial screening of spins by phonon s without formation of a phonon density wave. The latter appears only at K=K-c in the first-order phase transition. Corrections, quadratic i n delta H, destroy the integrability of the system, but outside a narr ow critical region around K-c they only lead to an opening of a small gap in the spectrum of the quantum liquid. The behavior of the system within the critical region is an open question. Most likely the contin uous magnetic phase transition at K=K-c becomes a first-order one, but close to second order. The relevance of our results for three-dimensi onal systems and possible applications to compounds with anomalously w eak magnetism are briefly discussed.