Related papers: Topology, phase transitions and the spherical mode…
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…
According to the reparametrization invariance of the microcanonical ensemble, the only microcanonically relevant phase transitions are those involving an ergodicity breaking in the thermodynamic limit: the zero-order phase transitions and…
A new point of view about the deep origin of thermodynamic phase transitions is sketched. The main idea is to link the appearance of phase transitions to some major topology change of suitable submanifolds of phase space instead of linking…
Possible generalizations of the topological (or Berezinskii-Kosterlitz-Thouless) phase transition on multicomponent 2D systems with nontrivial vector homotopic group pi_1 are considered. Relations between Ginzburg-Landau like theories,…
We study a one-dimensional topological model featuring a Su-Schrieffer-Heeger type pattern of nearest-neighbor couplings in combination with the longer-range interactions exponentially decaying with the distance. We demonstrate that even…
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge…
We study topological properties of phase transition points of topological quantum phase transitions by assigning a topological invariant defined on a closed circle or surface surrounding the phase transition point in the parameter space of…
Topological properties of a periodic condensed matter system are global features of its Brillouin zone (BZ). In contrast, the validity of effective low energy theories is usually limited to the vicinity of a high symmetry point in the BZ.…
We argue that the phase transition in the mean-field XY model is related to a particular change in the topology of its configuration space. The nature of this topological transition can be discussed on the basis of elementary Morse theory…
A local criterion of topological phase transitions is established based on the Morse theory: a topological phase transition occurs when the count of Morse critical points of the order function changes. The locations in space where this…
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…
We consider various two-leg ladder models exhibiting gapped phases. All of these phases have short-ranged valence bond ground states, and they all exhibit string order. However, we show that short-ranged valence bond ground states divide…
The non-classical features of quantum mechanics are reproduced using models constructed with a classical theory - general relativity. The inability to define complete initial data consistently and independently of future measurements,…
Many quantum condensed matter systems are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the low-energy corner does not depend on the complicated…
We address the question of the quantitative relationship between thermodynamic phase transitions and topological changes in the potential energy manifold analyzing two classes of one dimensional models, the Burkhardt solid-on-solid model…
In the $\phi $-mapping theory, the topological current constructed by the order parameters can possess different inner structure. The difference in topology must correspond to the difference in physical structure. The transition between…
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…
Many quantum condensed-matter systems, and probably the quantum vacuum of our Universe, are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in 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…
Amorphous systems have rapidly gained promise as novel platforms for topological matter. In this work we establish a scaling theory of amorphous topological phase transitions driven by the density of lattice points in two dimensions. By…