Scientific Series

Understanding entanglement in QFTs is a challenging topic that involves many aspects. One important probe for this is the modular (or entanglement) Hamiltonian, which is closely related to the Unruh effect. We determine this operator for the chiral fermion at finite temperature on the circle using complex analysis, and show that it exhibits surprising new features. This simple system illustrates how a modular flow can transition from complete locality to complete non-locality as a function of temperature, thus bridging the gap between previously known limits. We also derive the first exact results for the entanglement and relative entropies of this system for the different spin sectors. Based on [1905.05768,1906.02207].

In this talk I will report on recent progress in building QFT models on causal sets. The framework I'm using is that of perturbative algebraic quantum field theory (pAQFT). It was developed for rigorous study of perturbative QFT in the continuum, but can also be applied in the situation where spacetime is replaced by a discrete structure. Causality plays a key role in pAQFT, so it is natural to apply it to causets. Construction of models in this framework is purely algebraic and one does not need to specify a state or a Hilbert space representation until the final step, in which correlation functions are computed.

 In the 90s Turaev, Viro, Barrett and Westbury constructed a (2+1)D state sum TQFT associated to any fusion category. The associated phases of matter were popularized by Kiteav, Levin and Wen and are now central  examples in condensed matter physics and quantum information theory.

Despite the importance of these phases, many of the computational techniques for working with fusion categories have not percolated into condensed matter physics. Many of these techniques are "folk theorems"
and have not appeared in the literature in a digestible form.

Jacob Bridgeman and myself have spent the last two years extracting these computational techniques from Corey Jones, and have been using them to understand defects in Levin-Wen phases. Our papers 1806.01279,
1810.09469, 1901.08069, 1907.06692 document the development of our understanding, and demonstrate how to do physically relevant fusion category computations.

We present a paradigm for effective descriptions of quantum magnets. Typically, a magnet has many classical ground states — configurations of spins (as classical vectors) that have the least energy. The set of all such ground states forms an abstract space. Remarkably, the low energy physics of the quantum magnet maps to that of a single particle moving in this space.

This presents an elegant route to simulate simple quantum mechanical models using molecular magnets. For instance, a dimer coupled by an XY bond maps to a particle moving on a ring. An XY triangular magnet maps to a particle moving on two disjoint rings. We can even simulate Berry phases; when the spin has half-integer values, the particle sees a pi-flux  threaded through the rings.

A particularly interesting example is the XY tetrahedral magnet. Here, the ground state space is a 'non-manifold' due to singularities. These singularities behave like strong impurities to create bound states. The entire low energy physics of the magnet is dominated by these bound states. We call this phenomenon 'order by singularity’. This leads to a preference for certain classical ground states purely due to topology, rather than due to thermal or quantum fluctuations. Unlike order-by-disorder, this effect persists even in the classical limit.

Randomness is a valuable resource in both classical and quantum networks and we wish to generate desired probability distributions as cheaply as possible. If we are allowed to slightly change the distribution under some tolerance level, we can sometimes greatly reduce the cardinality of the randomness or the dimension of the entanglement. By studying statistical inequalities, we show how to upper bound of the amount of randomness required for any given classical network and tolerance level. We also present a problem we encounter when compressing the randomness in a quantum network.

We study remarkable RG flows in 4d QFT where supersymmetry enhances from N=1 to N=2 in the IR. This is triggered by the N=1 preserving deformation of 4d N=2 SCFTs with non-Abelian flavor symmetry by adding a chiral multiplet in the adjoint representation of the flavor symmetry and giving a nilpotent vev to the chiral multiplet. When the original N=2 SCFT and choice of the vev satisfy certain conditions, the resulting RG flows give N=2 Argyres-Douglas theories in the IR. These flows thus enable us to compute partition functions of Argyres-Douglas theories via localization. We also consider the more general and systematic deformation procedure which is applicable to any N=1 SCFTs and thus includes the above nilpotent one. Starting from N=1 SCFTs we allow all possible relevant deformations and/or coupling to a free chiral sector. We apply this to simple N=1 SCFTs and discuss the landscape of the IR fixed points, focusing on the enhancement of supersymmetry.

The Wilson formulation of lattice gauge theories provides a first-principles study of many properties of strongly interacting theories, such as quantum chromodynamics (QCD). Certain other properties, such as real-time dynamics, pose insurmountable challenges in this paradigm. Quantum Link Models are generalized lattice gauge theories, which not only offer novel approaches to study dynamics of gauge theories with quantum simulators, but also connect to
gauge theory descriptions of certain condensed matter systems (such as frustrated magnetism). In this talk, we explore some novel properties of gauge theories using quantum link models on classical computers, and explain how to realize them on quantum simulators.  

The out-of-time-ordered correlator (OTOC) and entanglement are two physically motivated and widely used probes of the ``scrambling'' of quantum information, which has drawn great interest recently in quantum gravity and many-body physics. By proving upper and lower bounds for OTOC saturation on graphs with bounded degree and a lower bound for entanglement on general graphs, we show that the time scales of scrambling as given by the growth of OTOC and entanglement entropy can be asymptotically separated in a random quantum circuit model defined on graphs with a tight bottleneck. Our result counters the intuition that a random quantum circuit mixes in time proportional to the diameter of the underlying graph of interactions.  It also serves as a more rigorous justification for an argument of [Shor, 1807.04363], that black holes may be very slow scramblers in terms of entanglement generation. Such observations may be of fundamental importance in the understanding of the black hole information problem. The bound we obtained for OTOC is interesting in its own right in that it generalized previous studies of OTOC on lattices to the geometries on graphs and proved it rigorously.   Based on [Harrow-Kong-Liu-Mehraban-Shor, 1906.02219]

In this talk, I will focus on topological aspects and edge states of a spin system on a Kagome lattice. with the anisotropic XXZ and Dzyaloshinskii-Moriya interaction (DMI). I will begin with the rich phase diagram in the classical limit arising as a result of the interplay of the two interaction strengths, followed by a spin-wave analysis in some of these phases. These spin-waves (or magnons) are studied using the Holstein-Primakoff transformations.   In the  ferromagnetic phase in which all the spins point along the +z or -z direction the bulk bands are separated from each other by finite energy gaps. Finding the Chern numbers here one finds that, there are four topologically distinct phases sharing the same ground state spin-configuration.  Hence an infinite strip of the system hosts robust edge states which are directly related to the Chern number of the bands. The other phases also are found to have edge modes. However, these are not topologically protected because of the gapless nature of the energy dispersion. 

We uncover a rich phenomenology of the self-organized honeycomb network superstructure of one-dimensional metals in a nearly-commensurate charge-density wave 1T-TaS${}_2$, which may play a significant role in understanding global topology of phase diagrams and superconductivity. The key observation is that the emergent honeycomb network magically supports a cascade of flat bands, whose unusual stability we thoroughly investigate. Furthermore, by combining the weak-coupling mean-field and strong-coupling approaches, we argue that the superconductivity will be strongly enhanced in the network. This provides a natural cooperative mechanism of the charge order and superconductivity, which coexist side-by-side in the 1T-TaS${}_2$. Not only explaining the superconductivity, we show that abundant topological band structures including several symmetry-protected band crossings and corner states, which are closely related to that of the higher-order topology, appear. The results reported here can be generically applicable to various other systems with similar network superstructures.

It has been recently pointed out that variable weak gravitational lensing effects on the motion of background stars can be used to probe nonluminous structures inside the Milky Way halo. I will describe one possible detection strategy targeting collapsed dark matter structures in the mass range from million to billion solar masses. The data analysis technique will be discussed in detail with an application to the second data release of Gaia.