Some properties for the low-lying spectrum of the ferromagnetic, quantum XXZ spin system

Abstract

In this thesis we present three results about the ferromagnetic quantum XXZ model: 1) Existence of a spectral gap above all infinite-volume ground states in one dimension for any choice of spin S>1/2 (for S=1/2 this was already known); 2) Characterization of one-dimensional "droplet" states as ground states of the spin-1/2 model with up spin boundary fields; 3) An upper bound for the spectral gap above the spin-1/2 interface ground states in dimension two and higher. The upper bound vanishes as 1/R^2, where R is the linear size of the system. This thesis contains research performed in collboration with other authors: O. Bolina, P. Contucci, T. Koma, B. Nachtergaele.

arXiv comment221 pages, 22 figures, contains one Matlab script and one Mathematica script "in the source"

References in corpus (10)

• Quantum Inverse Scattering Method and Correlation Functions
• Another proof of the alternating sign matrix conjecture
• Finite size and temperature effects in the AF Heisenberg model
• Spin chains and combinatorics
• Super-Instantons and the Reliability of Perturbation Theory in Non-Abelian Models
• Ground states of the infinite q-deformed Heisenberg ferromagnet
• The spectral gap of the ferromagnetic XXZ chain
• Path Integral Representation for Interface States of the Anisotropic Heisenberg Model
• Asymmetric diffusion and the energy gap above the 111 ground state of the quantum XXZ model
• Interface states of quantum spin systems

Cited by in corpus (6)

• Quantum Crystals and Spin Chains
• Droplet states in quantum XXZ spin systems on general graphs
• The large-spin asymptotics of the ferromagnetic XXZ chain
• Entanglement Entropy Bounds in the Higher Spin XXZ Chain
• Path integral representations for the spin-pinned quantum XXZ chain
• Low Temperature Results for the Heisenberg XXZ and XY Models