This series consists of talks in the area of Condensed Matter.
In recent years, entanglement has become a new frontier with applications across several fields in physics. Nevertheless, simple conceptual pictures and practical ways to quantify entanglement in many-body systems have remained elusive even for the simplest models. In this talk, I will consider entanglement and Renyi entropies as well as quantum (mutual, tripartite, etc.) information in a quantum field theory.
Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under non-equilibrium dynamics.
Recent experiments show that charge-density wave correlations are prevalent in underdoped cuprate superconductors. The correlations are short-ranged at weak magnetic fields but their intensity and spatial extent increase rapidly at low temperatures beyond a crossover field. Here we consider the possibility of long-range charge-density wave order in a model of a layered system where such order competes with superconductivity. We show that in the clean limit, low-temperature long-range order is stabilized by arbitrarily weak magnetic fields.
The iron chalcogenide FeSe has attracted much recent interest due to a high superconducting transition in monolayer samples. In bulk samples, nematic order is seen without the presence of magnetic order, hinting at the importance of nematic order in determining the monolayer properties. More generally, there has been growing evidence of the importance of nematic fluctuations in a variety of strongly correlated high-temperature superconductors.
The concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. I will demonstrate that the existence of symmetry breaking is a consequence of the geometric structure of the convex set of reduced density matrices of all possible many body wavefunctions. The surfaces of these convex bodies exhibit certain features, which signal the emergence of symmetry breaking and of an associated order parameter.
Concepts of information theory are increasingly used to characterize collective phenomena in condensed matter systems, such as the use of entanglement entropies to identify emergent topological order in interacting quantum many-body systems. Here we employ classical variants of these concepts, in particular Renyi entropies and their associated mutual information, to identify topological order in classical systems.
Solitons in a ferromagnet have interesting dynamics because atomic magnetic moments behave like little gyroscopes. A domain wall in a magnetic wire can be modeled as a bead on a string: it has two soft modes, position and orientation. This "bead" rotates when it is pushed and moves when twisted.
While entanglement entropy of ground states usually follows the area law, violations do exist, and it is important to understand their origin. In 1D they are found to be associated with quantum criticality. Until recently the only established examples of such violation in higher dimensions are free fermion ground states with Fermi surfaces, where it is found that the area law is enhanced by a logarithmic factor. In Ref. [1], we use multi-dimensional bosonization to provide a simple derivation of this result, and show that the logarithimic factor has a 1D origin.
The evolution of many kinetic processes in 1+1 dimensions results in 2D directed percolative landscapes. The active phases of those models possess numerous hidden geometric orders characterized by distinct percolative patterns.
The condensation of bosons can induce transitions between topological quantum field theories (TQFTs). This as been previously investigated through the formalism of Frobenius algebras and with the use of Vertex lifting coefficients. I will discuss an alternative, algebraic approach to boson condensation in TQFTs that is physically motivated and computationally efficient.