In this dissertation, we use the recently developed Entanglement Perturbation Theory (EPT) to solve antiferromagnetic spin chain problems, for both spin 1/2 and spin 1. We firs use EPT-g (EPT algorithm for ground state) to get the ground state properties. We calculated precisely energies, magnetization and spin-spin correlations. The precision of the long range spin-spin correlation functions for spin 1/2 chains is unprecedented. Due to its special structure, we also use EPT-g to calculate the firs excited state properties for spin 1 chains. Hence we plotted the phase diagram for spin 1 xxz chains. Also a generalization of EPT (EPT-e) for elementary excitation in one dimension determined the spin-triplet magnon spectrum for spin 1 chain for the firs time for the entire Brillouin zone, including the Haldane gap at k = π. The spin chains, the 2D&3D Ising models, the 1D&2D Hubbard models and the Bose-Hubbard model whose study by EPT is recently started represent a variety of strongly correlated many body systems with translational symmetry. Namely EPT is a general method for them. On the other hand, the successful application of EPT-e indicates EPT's potential to study the inhomogeneous quantum systems.In this dissertation, we use the recently developed Entanglement Perturbation Theory (EPT) to solve antiferromagnetic spin chain problems, for both spin 1/2 and spin 1. We firs use EPT-g (EPT algorithm for ground state) to get the ground state properties. We calculated precisely energies, magnetization and spin-spin correlations. The precision of the long range spin-spin correlation functions for spin 1/2 chains is unprecedented. Due to its special structure, we also use EPT-g to calculate the firs excited state properties for spin 1 chains. Hence we plotted the phase diagram for spin 1 xxz chains. Also a generalization of EPT (EPT-e) for elementary excitation in one dimension determined the spin-triplet magnon spectrum for spin 1 chain for the firs time for the entire Brillouin zone, including the Haldane gap at k = π. The spin chains, the 2D&3D Ising models, the 1D&2D Hubbard models and the Bose-Hubbard model whose study by EPT is recently started represent a variety of strongly correlated many body systems with translational symmetry. Namely EPT is a general method for them. On the other hand, the successful application of EPT-e indicates EPT's potential to study the inhomogeneous quantum systems.

Jan 1, 20091 citation

Entanglement spectrum in Spin Chains

Ronny Thomale, Daniel P. Arovas, Bogdan Andrei Bernevig

Bulletin of the American Physical SocietyMar 16, 20101 citation

Luttinger liquid in a solvable two-dimensional model

R. Hlubina

We consider spinless electrons in two dimensions with the bare spectrum ${\mathrm{\ensuremath{\epsilon}}}_{\mathbf{p}}$= ${\mathit{v}}_{\mathit{F}}$ (\ensuremath{\Vert} ${\mathit{p}}_{\mathit{x}}$ \ensuremath{\Vert}+\ensuremath{\Vert} ${\mathit{p}}_{\mathit{y}}$ \ensuremath{\Vert}). In momentum space, the interactions among electrons have a finite range ${\mathit{q}}_{0}$ , which is small compared to the Fermi momentum. A golden-rule calculation of the electron lifetime indictes a breakdown of Landau's Fermi-liquid theory in the model. At the one-loop level of perturbation theory, we show that the density wave and the superconducting instabilities cancel each other and there is no symmetry breaking. We solve the model via bosonization; the excitation spectrum is found to consist of gapless bosonic modes as in a one-dimensional Luttinger liquid.We consider spinless electrons in two dimensions with the bare spectrum ${\mathrm{\ensuremath{\epsilon}}}_{\mathbf{p}}$=${\mathit{v}}_{\mathit{F}}$(\ensuremath{\Vert}${\mathit{p}}_{\mathit{x}}$\ensuremath{\Vert}+\ensuremath{\Vert}${\mathit{p}}_{\mathit{y}}$\ensuremath{\Vert}). In momentum space, the interactions among electrons have a finite range ${\mathit{q}}_{0}$, which is small compared to the Fermi momentum. A golden-rule calculation of the electron lifetime indictes a breakdown of Landau's Fermi-liquid theory in the model. At the one-loop level of perturbation theory, we show that the density wave and the superconducting instabilities cancel each other and there is no symmetry breaking. We solve the model via bosonization; the excitation spectrum is found to consist of gapless bosonic modes as in a one-dimensional Luttinger liquid.

arXiv:cond-mat/9312083Physical review. B, Condensed matterSep 15, 199417 citations

We consider spinless electrons in two dimensions with the bare spectrum ${\mathrm{\ensuremath{\epsilon}}}_{\mathbf{p}}$=

{\mathit{v}}_{\mathit{F}}

(\ensuremath{\Vert}

{\mathit{p}}_{\mathit{x}}

\ensuremath{\Vert}+\ensuremath{\Vert}

{\mathit{p}}_{\mathit{y}}

\ensuremath{\Vert}). In momentum space, the interactions among electrons have a finite range

{\mathit{q}}_{0}

, which is small compared to the Fermi momentum. A golden-rule calculation of the electron lifetime indictes a breakdown of Landau's Fermi-liquid theory in the model. At the one-loop level of perturbation theory, we show that the density wave and the superconducting instabilities cancel each other and there is no symmetry breaking. We solve the model via bosonization; the excitation spectrum is found to consist of gapless bosonic modes as in a one-dimensional Luttinger liquid.