Phase Transitions in Quantum Systems

Pedro D Sacramento

Jincheng Zhang

This paper introduces the concept of Quantum State Boundary Phase Transition (QSBT), a novel theoretical framework proposing that phase transitions can occur not only at fixed points of Hamiltonian systems, but also at boundaries within the Hilbert space of a quantum system. Specifically, we hypothesize that the partial derivative of the wavefunction, [∂ψ], at a boundary represents a critical point where a phase transition can initiate or be amplified. The core of this theory rests on the observation that quantum systems, particularly in topologically complex environments, exhibit emergent behaviors that defy traditional phase transition models. We explore the potential of QSBT within topological quantum systems, suggesting it could lead to the discovery of entirely new quantum phases. This work lays the foundation for a paradigm shift in our understanding of phase transitions, with the potential to unlock significant advancements in quantum materials research and fundamental physics. The presented model offers a mechanism for understanding transitions driven by boundary conditions, offering a pathway to predict and control novel quantum phenomena. ---

Thomas Vojta

These lecture notes give a pedagogical introduction to phase transitions in disordered quantum systems and to the exotic Griffiths phases induced in their vicinity. We first review some fundamental concepts in the physics of phase transitions. We then derive criteria governing under what conditions spatial disorder or randomness can change the properties of a phase transition. After introducing the strong-disorder renormalization group method, we discuss in detail some of the exotic phenomena arising at phase transitions in disordered quantum systems. These include infinite-randomness criticality, rare regions and quantum Griffiths singularities, as well as the smearing of phase transitions. We also present a number of experimental examples.

Chon‐Fai Kam, Wei-Min Zhang, D.H. Feng

Simone Montangero

Tai Kai Ng

We provide an overview of some modern developments in the theory of phases and phase transitions in classical and quantum systems. We show the link between non-ergodicity and fidelity in quantum systems and discuss topological phase transitions. We show that the quantum phase transitions are associated with qualitative changes in some properties of the quantum wavefunctions across the phase transition. We discuss the topological phase transition associated with p-wave superconductor since it is a topic of wide interest because of the possible observation of Majorana fermions.