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Reports on Mathematical Physics

Double-chain Ising model with interchain multispin interactions as a soluble problem of many Fermions

Zbigniew Strycharski, Jerzy Ciso̵, Jerzy Janicki

Published Oct 1, 1989• 1 citation
Publisher
DOI
10.1016/0034-4877(89)90040-2

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A new family of free fermionic quantum spin chains with multispin interactions was recently introduced. Here we show that it is possible to build standard quantum Ising chains---but with inhomogeneous couplings---which have the same spectra as the novel spin chains with multispin interactions. The Ising models are obtained by associating an antisymmetric tridiagonal matrix to the polynomials that characterize the quasienergies of the system via a modified Euclidean algorithm. For the simplest nontrivial case, corresponding to the Fendley model, the phase diagram of the inhomogeneous Ising model is investigated numerically. It is characterized by gapped phases separated by critical lines with order-disorder transitions depending on the parity of the total number of energy density operators in the Hamiltonian.
The coherence of transport between two one-dimensional interacting Fermi liquids, coupled by single-particle hopping and interchain interaction, is examined in the context of two exactly soluble models. It is found that the coherence of the interchain hopping depends on the interplay between interchain hopping and interchain interaction terms, and not simply on the ground state spectral properties of an isolated chain. Specifically, the splitting of levels associated with interchain hopping in a g(4) soluble model is found to be enhanced by the introduction of interchain interaction. It is also shown that, for an exactly solvable model with both g(2) and g(4) interactions, coherent interchain hopping coexists with anomalous scaling and non-Fermi liquid behavior in the chain direction.