This series consists of talks in the area of Quantum Matter.
Many model quantum spin systems have been proposed to realize critical points or phases described by 2+1 dimensional conformal gauge theories. On a torus of size L and modular parameter τ, the energy levels of such gauge theories equal (1/L) times universal functions of τ. We compute the universal spectrum of QED3, a U(1) gauge theory with Nf two-component massless Dirac fermions, in the large-Nf limit.
A fundamental assumption of quantum statistical mechanics is that closed isolated systems always thermalize under their own dynamics. Progress on the topic of many-body localization has challenged this vital assumption, describing a phase where thermalization, and with it, equilibrium thermodynamics, breaks down.
We classify quantum states proximate to the semiclassical Neel state of the spin S=1/2 square lattice antiferromagnet with two-spin near-neighbor and four-spin ring exchange interactions. Motivated by a number of recent experiments on the cuprates and the iridates, we examine states with Z_2 topological order, an order which is not present in the semiclassical limit. Some of the states break one or more of reflection, time-reversal, and lattice rotation symmetries, and can account for the observations. We discuss implications for the pseudogap phase.
How can we quantify the entanglement between subsystems when we only have access to incomplete information about them and their environment? Existing approaches (such as Rényi entropies) can only detect the short-range entanglement across a boundary between a subsystem and its surroundings, and then only if the whole system is pure. These methods cannot detect the long-range entanglement between two subsystems embedded in a larger system.
Recent studies of highly frustrated antiferromagnets (AFMs) have demonstrated the qualitative impact of virtual, longer-range singlet excitations on the effective RVB tunneling parameters of the low energy sector of the problem [1,2]. Here, I will discuss the current state of affairs on the RVB description of the spin-1/2 kagome AFM, and present new results that settle a number of issues in this problem [3].
[1] I. Rousochatzakis, Y. Wan, O. Tchernyshyov, and F. Mila, PRB 90,
100406(R) (2014)
We consider the problem of certifying entanglement and nonlocality in one-dimensional translation-invariant (TI) infinite systems when just averaged near-neighbor correlators are available. Exploiting the triviality of the marginal problem for 1D TI distributions, we arrive at a practical characterization of the near-neighbor density matrices of multi-separable TI quantum states. This allows us, e.g., to identify a family of separable two-qubit states which only admit entangled TI extensions.
Quantum triangles can work as interferometers. Depending on their geometric size and interactions between paths, “beats” and/or “steps”
A central theme of modern condensed matter physics is the study of topological quantum matter enabled by quantum mechanics, which provides a further "topological" twist to the classical theory of ordered phases.
The quest for quantum spin liquids is an important enterprise in strongly correlated physics, yet candidate materials are still few and far between. Meanwhile, the classical front has had far more success, epitomized by the exceptional agreement between theory and experiment for a class of materials called spin ices. It is therefore natural to introduce quantum fluctuations into this well-established classical spin liquid model, in the hopes of obtaining a fully quantum spin liquid state.
Topological quantum computing requires phases of matter which host fractionalized excitations that are neither bosons nor fermions. I will present a new route toward realizing such fractionalized phases of matter by literally building on existing topological phases. I will first discuss how existing topological phases, when interfaced with other systems, can exhibit a “topological proximity effect” in which nontrivial topology of a different nature is induced in the neighboring system.