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Register a new userOptical phonons for Peierls chains with long-range Coulomb interactions
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We consider a chain of atoms that are bound together by a harmonic force. Spin-1/2 electrons that move between neighboring chain sites (Huckel model) induce a lattice dimerization at half band filling (Peierls effect). We supplement the Huckel model with a local Hubbard interaction and a long-range Ohno potential, and calculate the average bond-length, dimerization, and optical phonon frequencies for finite straight and zig-zag chains using the density-matrix renormalization group (DMRG) method. We check our numerical approach against analytic results for the Huckel model. The Hubbard interaction mildly affects the average bond length but substantially enhances the dimerization and increases the optical phonon frequencies whereas, for moderate Coulomb parameters, the long-range Ohno interaction plays no role.
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We propose and analyze a generalization of the Kitaev chain for fermions with long-range $p$-wave pairing, which decays with distance as a power-law with exponent $alpha$. Using the integrability of the model, we demonstrate the existence of two types of gapped regimes, where correlation functions decay exponentially at short range and algebraically at long range ($alpha > 1$) or purely algebraically ($alpha < 1$). Most interestingly, along the critical lines, long-range pairing is found to break conformal symmetry for sufficiently small $alpha$. This is accompanied by a violation of the area law for the entanglement entropy in large parts of the phase diagram in the presence of a gap, and can be detected via the dynamics of entanglement following a quench. Some of these features may be relevant for current experiments with cold atomic ions.
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We study the thermodynamics and critical behavior of su($m|n$) supersymmetric spin chains of Haldane-Shastry type with a chemical potential term. We obtain a closed-form expression for the partition function and deduce a description of the spectrum in terms of the supersymmetric version of Haldanes motifs, which we apply to obtain an analytic expression for the free energy per site in the thermodynamic limit. By studying the low-temperature behavior of the free energy, we characterize the critical behavior of the chains with $1le m,nle2$, determining the critical regions and the corresponding central charge. We also show that in the su($2|1$), su($1|2$) and su($2|2$) chains the bosonic or fermionic densities can undergo first-order (discontinuous) phase transitions at $T=0$, in contrast with the previously studied su(2) case.
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