Talks

I will discuss the question of thermal stability of a passive quantum memory, or finite-temperature topological order, in two or three spatial dimensions. We will analyze the criteria for thermal stability. We will present new results on Majorana fermion codes and a new extension of the 2D surface code to three dimensions.

Anyons are a special kind of excitations which are allowed in two dimensional systems, along with fermions and bosons. The topological nature of braiding of non-abelian anyons may allow a realization of quantum computing gates which is immune to noise. While the insensitivity of the such systems to a localized noise source is a built-in feature, an issue of great importance is more subtle: the robustness to slight deformations of the amiltonian describing the phase by perturbations which are locally tiny but are spread over through the entire system. Such will always arise if the realization of the Hamiltonian in a particular system is not quite perfect. The subject of the talk will be a proof of such stability, and the cluster expansion representation of deformed topological states.

Adiabatic evolutions connect two gapped quantum states in the same phase. We argue that the adiabatic evolutions are closely related to local unitary transformations which define a equivalence relation. So the equivalence classes of the local unitary transformations are the universality classes that define the different phases of quantum system. Since local unitary transformations can remove local entanglements, the above equivalence/universality classes correspond to pattern of long range entanglement, which is the essence of topological order. The local unitary transformation also allows us to define wave function renormalization, where a wave function can flow to a simpler one within the same equivalence/universality class. Using such a setup, we find conditions on the possible fixed-point wave functions where the local unitary transformations have finite dimensions. The solutions of the conditions allow us to classify this type of topological orders, which include all the string-net states.

Many crystalline materials predicted by band theory to be metals are insulators due to strong electron interactions. Both experiment and theory suggest that such Mott-insulators can exhibit exotic gapless spin-liquid ground states, having no magnetic or any other order. Such “critical spin liquids” will possess power law spin correlations which oscillate at various wavevectors. In a sub-class dubbed “Spin Bose-Metals” the singularities reside along surfaces in momentum space, analogous to a Fermi surface but without long-lived quasiparticle excitations. I will describe recent theoretical progress in accessing such states via controlled numerical and analytical studies on quasi-1d model systems.

I discuss a class of systems with a very special property: exact results for physical quantities can be found in the many-body limit in terms of the original (bare) parameters in the Hamiltonian. A classic result of this type is Onsager and Yang's formula for the magnetization in the Ising model. I show how analogous results occur in a fermion chain with strong interactions, closely related to the XXZ spin chain. This is done by exploiting a supersymmetry, and noting that certain quantites are independent of finite-size effects. I also discuss how these ideas are related to an interacting generalization of the Kitaev honeycomb model.

In the Ho2Ti2O7 and Dy2Ti2O7 magnetic pyrochlore oxides, the Ho and Dy Ising magnetic moments interact via geometrically frustrated effective ferromagnetic coupling. These systems possess and extensive zero entropy related to the extensive entropy of ice water -- hence the name spin ice. The classical ground states of spin ice obey a constraint on each individual tetrahedron of interacting spins -- the so-called "ice rules". At large distance, the ice-rules can be described by an effective divergent-free field and, therefore, by an emergent classical gauge theory. In contrast, while it would appear at first sight to relate to the spin ices, the Tb2Ti2O7 material displays properties that much differ from spin ices and the behaviour of that system has largely remained unexplained for over ten years. In this talk, I will review the key features of the (Ho,Dy)2Ti2O7 spin ice materials, discuss the recent experimental results that support the emergent gauge theory description of spin ices and discuss how Tb2Ti2O7 is perhaps a ''quantum melted'' spin ice.

Many one dimensional random quantum systems exhibit infinite randomness phases, such as the random singlet phase of the spin-1/2 Heisenberg model. These phases are typically the result of destabilizing systems described by a conformal field theory with disorder. Interestingly, entanglement entropy in 1d infinite randomness phases also exhibits a universal log scaling with length. In my talk I will touch upon calculating the entanglement entropy for inifinite-randomness phases, as well as describe the exotic infinite randomness phases realized in chains of non-abelian anyon chains. It was speculated that the entanglement entropy of an infinite-randomness phase is associated with the direction of RG flow, just as the c-theorem dictates the direction of RG flows for CFT's. I will also show that the entanglement entropy in disordered non-abelian chains provide the only known counter example.

The quantum states postulated to occur in situations of the "Schroedinger's Cat" type are essentially N-particle GHZ states with N very large compared to 1,and their observation would thus be particularly compelling evidence for the ubiquity of the phenomenon of entanglement. However, in the traditional quantum measurement literature considerable scepticism has been expressed about the observability of this kind of "macroscopically entangled" state, primarily because of the putatively disastrous effect on it of decoherence. In this talk I first examine why much of the literature has grossly overestimated the effects of decoherence,and then review the current experimental situation with respect to such states, as they (may) occur in fullerene diffraction, magnetic biomolecules, quantum-optical systems and Josephson devices; I also consider the prospects for their observation in nanomechanical systems. I conclude by reviewing and the theoretical implications of the experiments of the last decade in this area.

Many one dimensional random quantum systems exhibit infinite randomness phases, such as the random singlet phase of the spin-1/2 Heisenberg model. These phases are typically the result of destabilizing systems described by a conformal field theory with disorder. Interestingly, entanglement entropy in 1d infinite randomness phases also exhibits a universal log scaling with length. In my talk I will touch upon calculating the entanglement entropy for inifinite-randomness phases, as well as describe the exotic infinite randomness phases realized in chains of non-abelian anyon chains. It was speculated that the entanglement entropy of an infinite-randomness phase is associated with the direction of RG flow, just as the c-theorem dictates the direction of RG flows for CFT's. I will also show that the entanglement entropy in disordered non-abelian chains provide the only known counter example.

Condensed matter theorists have recently begun exploiting the properties of entanglement as a resource for studying quantum materials. At the forefront of current efforts is the question of how the entanglement of two subregions in a quantum many-body groundstate scales with the subregion size. The general belief is that typical groundstates obey the so-called "area law", with entanglement entropy scaling as the boundary between regions. This has lead theorists to propose that sub-leading corrections to the area law provide new universal quantities at quantum critical points and in exotic quantum phases (i.e. topological Mott insulators). However, away from one dimension, entanglement entropy is difficult or impossible to calculate exactly, leaving the community in the dark about scaling in all but the simplest non-interacting systems. In this talk, I will discuss recent breakthroughs in calculating entanglement entropy in two dimensions and higher using advanced quantum Monte Carlo simulation techniques. We show, for the first time, evidence of leading-order area law scaling in a prototypical model of strongly-interacting quantum spins. This paves the way for future work in calculating new universal quantities derived from entanglement, in the plethora of real condensed matter systems amenable to numerical simulation.