SU(2) gauge theory in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> dimensions on a plaquette chain obeys the eigenstate thermalization hypothesis
Xiaojun Yao
Abstract
We test the eigenstate thermalization hypothesis (ETH) for $2+1$ dimensional SU(2) lattice gauge theory. By considering the theory on a chain of plaquettes and truncating basis states for link variables at $j=1/2$, we can map it onto a quantum spin chain with local interactions and numerically exactly diagonalize the Hamiltonian for reasonably large lattice sizes. We find energy level repulsion in momentum sectors with no remaining discrete symmetry. We study two local observables made up of Wilson loops and calculate their matrix elements in the energy eigenbasis, which are shown consistent with the ETH.
Topics & Concepts
Hamiltonian (control theory)Mathematical physicsGauge theoryPhysicsLattice (music)Eigenvalues and eigenvectorsLattice energyLattice gauge theoryCombinatoricsQuantum mechanicsMathematicsCrystallographyChemistryCrystal structureMathematical optimizationAcousticsQuantum many-body systemsPhysics of Superconductivity and MagnetismQuantum and electron transport phenomena