Quantumliquid regimes for spin chains coupled to phonons: Phonon density wave versus magnetic order
Abstract
We consider a chain of localized spins, coupled to phonons. Recently this problem has been solved exactly for a ``basic model,'' a family of spinphonon Hamiltonians H_{BM} characterized by one parameter (coupling constant K), and a zeroT firstorder phase transition from the magnetic (ferro or antiferro) state at low couplings to the nonmagnetic state with a phonon density wave at high couplings was found. Here we probe the general case, constructing an effective Hamiltonian H for lowenergy degrees of freedom by means of regular expansion in deviations δH=HH_{BM} of the general Hamiltonian H from that of the basic model. In linear approximation in δH the problem appears to be exactly 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 magnetic state is dramatically reconstructed: Here the ground state is a gapless magnetic quantum liquid, consisting of mobile singlet spinphonon complexes and unbound spins. The fraction of singlets increases gradually upon approaching K_{c}, and the magnetic order parameter gradually vanishes. Thus we have here a partial screening of spins by phonons without formation of a phonon density wave. The latter appears only at K=K_{c} in the firstorder phase transition. Corrections, quadratic in δH, destroy the integrability of the system, but outside a narrow 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 continuous magnetic phase transition at K=K_{c} becomes a firstorder one, but close to second order. The relevance of our results for threedimensional systems and possible applications to compounds with anomalously weak magnetism are briefly discussed.
 Publication:

Physical Review B
 Pub Date:
 June 1996
 DOI:
 10.1103/PhysRevB.53.15231
 Bibcode:
 1996PhRvB..5315231I
 Keywords:

 75.30.Mb;
 63.20.Kr;
 75.30.Kz;
 Valence fluctuation Kondo lattice and heavyfermion phenomena;
 Phononelectron and phononphonon interactions;
 Magnetic phase boundaries