Related papers: The Quantum Torus Chain
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
Quantum criticality often lies beyond the scope of the conventional Landau paradigm, and a unifying framework has yet to emerge, due in part to the wide variety of quantum orders. We propose a geometric approach to quantum phase transitions…
Symmetry-breaking quantum phase transitions play a key role in several condensed matter, cosmology and nuclear physics theoretical models. Its observation in real systems is often hampered by finite temperatures and limited control of the…
Topological quantum phase transitions are characterised by changes in global topological invariants. These invariants classify many body systems beyond the conventional paradigm of local order parameters describing spontaneous symmetry…
We consider a prototypical two-parameter family of invertible maps of $\mathbb{Z}^2$, representing rotations with decreasing rotation number. These maps describe the dynamics inside the island chains of a piecewise affine discrete twist map…
On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal,…
The large spacing phase of the infinite random matrix chain, which represents the strongly coupled two-dimensional O(2) model on a random planar lattice, is explored. A class of solutions valid for large lattice spacings is constructed. It…
We construct a one-parameter family of lattice models starting from a two-dimensional rational conformal field theory on a torus with a regular lattice of holes, each of which is equipped with a conformal boundary condition. The lattice…
The model which is the generalization of the one-dimensional XY-spin chain for the case of the two-dimensional square lattice is considered. The subspace of the ``string'' states is studied. The solution to the eigenvalue problem is…
Motivated by the goal to give the simplest possible microscopic foundation for a broad class of topological phases, we study quantum mechanical lattice models where the topology of the lattice is one of the dynamical variables. However, a…
Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B)…
We investigate the persistence of spectral gaps of one-dimensional frustration free quantum lattice systems under weak perturbations and with open boundary conditions. Assuming the interactions of the system satisfy a form of local…
Quantum computers promise to perform computations beyond the reach of modern computers with profound implications for scientific research. Due to remarkable technological advances, small scale devices are now becoming available for use. One…
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the symmetry of the emergent topological…
We analyze the free energy and construct the Gibbs-KMS states for a class of quantum lattice systems, at low temperatures and when the interactions are almost diagonal in a suitable basis. We study systems with continuous symmetry, but our…
We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as…
We present a theory characterizing the phases emerging as a consequence of continuous symmetry-breaking in quantum and classical systems. In symmetry-breaking phases, dynamics is restricted due to the existence of a set of conserved charges…
We study a model of strongly correlated electrons on the square lattice which exhibits charge frustration and quantum critical behavior. The potential is tuned to make the interactions supersymmetric. We establish a rigorous mathematical…
Phase transitions are commonly held to occur only in the thermodynamical limit of large number of system components. Here we exemplify at the hand of the exactly solvable Jaynes-Cummings (JC) model and its generalization to finite…
Despite the fact that a complete theoretical description of critical phenomena in connection with phase transitions has been well-established through the renormalization group theory, the microscopic nature of the phase transitions remains…