The sequence of ground-state energy density at finite size, ${e}_{L}$ , provides much more information than usually believed. Having at our disposal ${e}_{L}$ for short lattice sizes, we show how to reconstruct an approximate quasiparticle dispersion for any interacting model. The accuracy of this method relies on the best possible quasifree approximation to the model, consistent with the observed values of the energy ${e}_{L}$ . We also provide a simple criterion to assess whether such a quasifree approximation is valid. As a side effect, our method is able to assess whether the nature of the quasiparticles is fermionic or bosonic together with the effective boundary conditions of the model. When applied to the spin-1$/ $2 Heisenberg model, the method produces a band of Fermi quasiparticles very close to the exact one of des Cloizeaux and Pearson. The method is further tested on a spin-1$ /$2 Heisenberg model with explicit dimerization and on a spin-1 chain with single-ion anisotropy. A connection with the Riemann hypothesis is also pointed out.The sequence of ground-state energy density at finite size, ${e}_{L}$, provides much more information than usually believed. Having at our disposal ${e}_{L}$ for short lattice sizes, we show how to reconstruct an approximate quasiparticle dispersion for any interacting model. The accuracy of this method relies on the best possible quasifree approximation to the model, consistent with the observed values of the energy ${e}_{L}$. We also provide a simple criterion to assess whether such a quasifree approximation is valid. As a side effect, our method is able to assess whether the nature of the quasiparticles is fermionic or bosonic together with the effective boundary conditions of the model. When applied to the spin-1$/$2 Heisenberg model, the method produces a band of Fermi quasiparticles very close to the exact one of des Cloizeaux and Pearson. The method is further tested on a spin-1$/$2 Heisenberg model with explicit dimerization and on a spin-1 chain with single-ion anisotropy. A connection with the Riemann hypothesis is also pointed out.

arXiv:1101.2163Physical Review BJul 14, 20110 citations

Exact analysis of one-dimensional quantum spin models

康広藤井

Jan 1, 20010 citations

Dynamical properties of the one-dimensional Holstein model

Chunli Zhang, Eric Jeckelmann, Steven R. White

The spectral weight functions and the optical conductivity of the Holstein model are studied on a one-dimensional six-site lattice with periodic boundary conditions for three different electron concentrations: a single electron, two electrons of opposite spins, and half filling. A density matrix approach is used to obtain an optimal phonon basis and to truncate the phonon Hilbert space without significant loss of accuracy. This approach allows us to calculate spectral functions for electrons dressed locally by the optimal phonons as well as for bare electrons. We obtain evidence for a smooth crossover from quasifree electrons to a heavy itinerant small polaron (single-electron case) or bipolaron (two-electron case) as the electron-phonon coupling strength increases. At half filling, we observe a crossover from a quasifree-electron ground state to a quasidegenerate Peierls charge-density-wave ground state for a finite electron-phonon coupling. This crossover is marked by an abrupt drop of the Drude weight, which is vanishingly small in the Peierls phase.The spectral weight functions and the optical conductivity of the Holstein model are studied on a one-dimensional six-site lattice with periodic boundary conditions for three different electron concentrations: a single electron, two electrons of opposite spins, and half filling. A density matrix approach is used to obtain an optimal phonon basis and to truncate the phonon Hilbert space without significant loss of accuracy. This approach allows us to calculate spectral functions for electrons dressed locally by the optimal phonons as well as for bare electrons. We obtain evidence for a smooth crossover from quasifree electrons to a heavy itinerant small polaron (single-electron case) or bipolaron (two-electron case) as the electron-phonon coupling strength increases. At half filling, we observe a crossover from a quasifree-electron ground state to a quasidegenerate Peierls charge-density-wave ground state for a finite electron-phonon coupling. This crossover is marked by an abrupt drop of the Drude weight, which is vanishingly small in the Peierls phase.

arXiv:cond-mat/9812353Physical review. B, Condensed matterNov 15, 199976 citations

Remarks on duality of 1 dimensional quantum spin models

Taku Matsui

Communications in Mathematical PhysicsNov 1, 19920 citations

The sequence of ground-state energy density at finite size,

{e}_{L}

, provides much more information than usually believed. Having at our disposal

{e}_{L}

for short lattice sizes, we show how to reconstruct an approximate quasiparticle dispersion for any interacting model. The accuracy of this method relies on the best possible quasifree approximation to the model, consistent with the observed values of the energy

{e}_{L}

. We also provide a simple criterion to assess whether such a quasifree approximation is valid. As a side effect, our method is able to assess whether the nature of the quasiparticles is fermionic or bosonic together with the effective boundary conditions of the model. When applied to the spin-1$/

2 Heisenberg model, the method produces a band of Fermi quasiparticles very close to the exact one of des Cloizeaux and Pearson. The method is further tested on a spin-1

/$2 Heisenberg model with explicit dimerization and on a spin-1 chain with single-ion anisotropy. A connection with the Riemann hypothesis is also pointed out.