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Physica B Condensed Matter

Critical parameters of the CDW—luttinger liquid transition based on the bond entropy

Rafael A. Molina, Peter Schmitteckert

Published Oct 25, 2007• 1 citation
Publisher
DOI
10.1016/j.physb.2007.10.129

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Using a model of spinless fermions in a lattice with nearest-neighbor and next-nearest-neighbor interactions, we show that the entropy of the reduced two-site density matrix (the bond entropy) can be used as an extremely accurate and easy to calculate numerical indicator for the critical parameters of the quantum phase transition when the basic ordering pattern has a two-site periodicity. The actual behavior of the bond entropy depends on the particular characteristics of the transition under study. For the Kosterlitz-Thouless-type phase transition from a Luttinger liquid phase to a charge-density wave state, the bond entropy has a local maximum, while in the transition from the Luttinger liquid to the phase separated state, the derivative of the bond entropy has a divergence due to the cancellation of the third eigenvalue of the two-site reduced density matrix.
An interacting spinless fermion wire coupled to a three-dimensional (3D) semiconducting substrate is approximated by a narrow ladder model (NLM) with varying number of legs. We compute density distributions, gaps, charge density wave (CDW) order parameters, correlation functions, and the central charge using the density-matrix renormalization group method. Three ground-state phases are observed: a one-component Luttinger liquid, a quasi-one-dimensional (1D) CDW insulator, and a band insulator. We investigated the convergence of the NLM properties with increasing number of legs systematically and confirm that the NLM is a good approximation for the quasi-1D phases (Luttinger liquid and CDW) of the 3D wire-substrate model. The quantum phase transitions between these phases are investigated as function of the coupling between wire and substrate. The critical nearest-neighbor interaction increases with increasing coupling between wire and substrate and thus the substrate stabilizes the Luttinger liquid in the wire. Our study confirms that a Luttinger liquid or CDW insulator phase could occur in the low-energy properties of atomic wires deposited on semiconducting substrates.
We determine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U (V) and nearest-neighbor hopping t using the density-matrix renormalization group technique. Based on the results of the excitation gaps, Luttinger-liquid exponents, and bond-order-wave (BOW) order parameter, we confirm that the BOW phase appears in a substantial region between the charge-density-wave (CDW) and spin-density-wave phases. Each phase boundary is determined by multiple means and it allows us to make a cross-check on the validity of our estimations. We also find that the BOW-CDW transition changes from continuous to first order at the tricritical point (U(t),V(t)) approximately (5.89 t,3.10 t) and the BOW phase shrinks to zero at the critical end point (U(c),V(c)) approximately (9.25 t,4.76 t).