Excitation spectrum and staggering transformations in lattice quantum models

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory
• Statistical Mechanics

Background:

• Investigating excitation spectra in diverse lattice Hamiltonian systems is crucial for understanding fundamental physical phenomena.
• Lattice Hamiltonians model systems ranging from quantum field theories to classical spin systems.

Purpose of the Study:

• To analyze the energy-momentum excitation spectrum of various lattice Hamiltonian operators.
• To determine the conditions for the existence of bound states in relation to the two-particle band.

Main Methods:

• Utilized a lattice version of the Bethe-Salpeter equation to determine the two-particle spectrum.
• Employed a nonrelativistic single-particle lattice Schrödinger Hamiltonian with a delta potential for analysis.
• Applied a staggering transformation to relate attractive and repulsive interaction cases.

Main Results:

• The low-lying spectrum consistently features a one-particle state and a two-particle band.
• Bound states can appear below (attractive interaction) or above (repulsive interaction) the two-particle band.
• The existence of these bound states is linked to the lattice dimension and interaction character.

Conclusions:

• The study provides a unified framework for understanding bound state formation in diverse lattice systems.
• The findings offer insights into the behavior of quantum and classical systems on a lattice.
• The connection to single-particle Schrödinger Hamiltonians simplifies the interpretation of complex many-body phenomena.