Related papers: Topology and Phase Transitions I. Preliminary Resu…
In this work, we explore how the geometry and topology of the underlying manifold shape the synchronization phase transition of a system. To do so, we extend the Kuramoto-Sakaguchi model from spheres to compact, connected, orientable, and…
In the framework of a recently proposed topological approach to phase transitions, some sufficient conditions ensuring the presence of the spontaneous breaking of a Z_2 symmetry and of a symmetry-breaking phase transition are introduced and…
Topologically ordered quantum systems have robust physical properties, such as quasiparticle statistics and ground-state degeneracy, which do not depend on the microscopic details of the Hamiltonian. We consider topological phase…
We describe a first-order phase transition of a simple system in a process where the volume is kept constant. We show that, unlike what happens when the pressure is constant, (i) the transformation extends over a finite temperature (and…
The microscopic model in which nodes interacting with each other are statistical systems is introduced. The nodes conditions are connected with a string of distinct microscopic configurations and depend on external parameters (pressure and…
Topological states of matter are characterized by global topological invariants which change their value across a topological quantum phase transition. It is commonly assumed that the transition between topologically distinct noninteracting…
It is discussed how phase transitions of first order (with phase separation and surface tension), continuous transitions and (multi)-critical points can be defined and classified for finite systems from the topology of the energy surface…
Topological phase transition is accompanied with a change of topological numbers. It has been believed that the gap closing and the breakdown of the adiabaticity at the transition point is necessary in general. However, the gap closing is…
We study the coupling of two topologcal subsystems in distinct topological states, and show that it leads to a precursor behavior of the topological phase transition in the overall system. This behavior is solely determined by the symmetry…
Topology forms a cornerstone in modern condensed matter and statistical physics, offering a new framework to classify the phases and phase transitions beyond the traditional Landau paradigm. However, it is widely believed that topological…
In this paper, we investigate signatures of topological phase transitions in interacting systems. We show that the key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the…
The stationary points of the potential energy function V are studied for the \phi^4 model on a two-dimensional square lattice with nearest-neighbor interactions. On the basis of analytical and numerical results, we explore the relation of…
Interacting fermionic ladders are important platforms to study quantum phases of matter, such as different types of Mott insulators. In particular, the D-Mott and S-Mott states hold pre-formed fermion pairs and become paired-fermion liquids…
We study a model for dynamical localization of topology using ideas from non-commutative geometry and topology in quantum mechanics. We consider a collection $X$ of $N$ one-dimensional manifolds and the corresponding set of boundary…
The dynamics at the critical-point of a general first-order quantum phase transition in a finite system is examined, from an algebraic perspective. Suitable Hamiltonians are constructed whose spectra exhibit coexistence of states…
We study topological transitions in one dimensional superconductors that can harbor multiple edge Majorana bound states protected by chiral symmetry. The chiral symmetry arises due to the structure of the internal spin degrees of freedom of…
In a field-theoretical context, we consider the Euclidean $(\phi^4+\phi^6)_D$ model compactified in one of the spatial dimensions. We are able to determine the dependence of the transition temperature ($T_{c}$)for a system described by this…
Despite great successes in the study of gapped phases, a comprehensive understanding of the gapless phases and their transitions is still under developments. In this paper, we study a general phenomenon in the space of (1+1)$d$ critical…
Spontaneous onset of a low temperature topologically ordered phase in a 2-dimensional (2D) lattice model of uniaxial liquid crystal (LC) was debated extensively pointing to a suspected underlying mechanism affecting the RG flow near the…
Topological magnetic textures are particle-like spin configurations stabilized by competing interactions. Their formation is commonly attributed to fluctuation-driven, first-order nucleation processes requiring activation over a topological…