Author's School

Graduate School of Arts & Sciences

Author's Department/Program



English (en)

Date of Award

Summer 8-13-2013

Degree Type


Degree Name

Doctor of Philosophy (PhD)

Chair and Committee

Alexander Seidel


This thesis will investigate various aspects of the physics of resonating valence bond spin liquids.

After giving an introduction to the world that lies beyond Landau's priciple of symmetry breaking,

e.g. giving an overview of exotic magnetic phases and how they can be described and: possibly) found, we will study a spin-rotationally invariant model system with a known parent

Hamiltonian, and argue its ground state to lie within a highly sought after exotic phase,

namely the Z$_{2}$ quantum spin liquid phase.

A newly developed numerical procedure --Pfaffian Monte Carlo-- will be introduced

to amass evidence that our model Hamiltonian indeed exhibits a Z$_{2}$ quantum

spin liquid phase.

Subsequently, we will prove a useful mathematical property of the resonating valence bond states:

these states are shown to be linearly independent.

Various lattices are investigated concerning this property, and its applications and usefullness are discussed.

Eventually, we present a simplified model system describing the interplay of the well known

Heisenberg interaction and the Dzyaloshinskii-Moriya: DM) interaction term acting on a sawtooth chain. The effect of the interplay between the two interaction couplings on the phase diagram is investigated.

To do so, we employ modern techniques such as the density matrix renormalization group: DMRG) scheme. We find that for weak DM interaction the system exhibits valence bond order.

However, a strong enough DM coupling destroys this order.


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