Related papers: Classical criticality establishes quantum topologi…
The correspondence between classical spin models and quantum states has attracted much attention in recent years. However, it remains an open problem as to which specific spin model a given (well-known) quantum state maps to. In this…
In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely…
The discovery of topological phases in condensed matter systems has changed the modern conception of phases of matter. The global nature of topological ordering makes these phases robust and hence promising for applications. However, the…
Using the mapping of the Fokker-Planck description of classical stochastic dynamics onto a quantum Hamiltonian, we argue that a dynamical glass transition in the former must have a precise definition in terms of a quantum phase transition…
Topological phase transitions challenge conventional paradigms in many-body physics by separating phases that are locally indistinguishable yet globally distinct. Using a quantum simulator of interacting erbium atoms in an optical lattice,…
We discuss a certain class of two-dimensional quantum systems which exhibit conventional order and topological order, as well as two-dimensional quantum critical points separating these phases. All of the ground-state equal-time correlators…
The investigation and characterization of topological quantum phase transition between gapless phases is one of the recent interest of research in topological states of matter. We consider transverse field Ising model with three spin…
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…
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 studied quantum phase transitions in the antiferromagnetic dimerized spin-1/2 XY chain andvtwo-leg ladders. From analysis of several spin models we present our main result: the framework to deal with topological orders and hidden…
In topological insulators and topological superconductors, the discrete jump of the topological invariant upon tuning a certain system parameter defines a topological phase transition. A unified framework is employed to address the quantum…
Critical phase transitions contain a variety of deep and universal physics, and are intimately tied to thermodynamic quantities through scaling relations. Yet, these notions are challenged in the context of non-Hermiticity, where spatial or…
We propose a topological approach suitable to establish a connection between thermodynamics and topology in the microcanonical ensemble. Indeed, we report on results that point to the possibility of describing {\it interacting classical…
The ability to manipulate single atoms has opened up the door to constructing interesting and useful quantum structures from the ground up. On the one hand, nanoscale arrangements of magnetic atoms are at the heart of future quantum…
Ordered phases of matter have close connections to computation. Two prominent examples are spin glass order, with wide-ranging applications in machine learning and optimization, and topological order, closely related to quantum error…
We discuss the behavior of quantum and classical pairwise correlations in critical systems, with the quantumness of the correlations measured by the quantum discord. We analytically derive these correlations for general real density…
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…
In quantum spin-1 chains, there is a nonlocal unitary transformation known as the Kennedy-Tasaki transformation $U_{\text{KT}}$, which defines a duality between the Haldane phase and the $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry-breaking…
We face the problem of detecting and featuring footprints of quantum criticality in the finite-temperature behavior of quantum many-body systems. Our strategy is that of comparing the phase diagram of a system displaying a T=0 quantum phase…
We study the quantum correlations in a 2D system that possesses a topological quantum phase transition. The quantumness of two-body correlations is measured by quantum discord. We calculate both the correlation of two local spins and that…