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I will describe an infinite set of exotic gauge theories that have recently and simultaneously emerged in several a priori unrelated areas of condensed matter physics such as self-correcting quantum memory, topological order in 3+1 dimensions, spin liquids and quantum elasticity. In these theories the gauge field is a symmetric tensor (not to be confused with higher form, which is an anti-symmetric tensor), or in more exotic situations, the gauge fields do not have a well-defined transformation properties under rotations. I will discuss a few exotic features of these theories such as (i) corresponding Gauss law constraints (ii) failure of the gauge invariance in curved space, (iii) the nature of the gauge group, etc. I will also discuss the what kind of matter such theories can couple to. It turns out that the corresponding matter must conserve electric charge and various multipole moments of the electric charge (or number) density. The conservation laws of multipole moments lead to dramatic consequences for the dynamics. I will also discuss how such theories can be obtained by gauging a global symmetry. Finally, I will discuss non-local operators in this type of theories. Remarkably, in addition to more-or-less expected Wilson line and surface operators, such theories exhibit (at least upon discretization on a lattice) non-local operators supported on a space of fractional dimension (in between line and surfaces).

Two topics have been gaining momentum in different fields of physics: At the intersection of condensed matter and high-energy physics lies the out-of-time-ordered correlator (OTOC). The OTOC reflects quantum many-body equilibration; chaos; and scrambling, the spread of quantum information through many-body entanglement. In quantum optics and quantum foundations, quasiprobabilities resemble probabilities but can become negative and nonreal. Such nonclassical values can signal nonclassical physics, such as the capacity for superclassical computation. I unite these two topics, showing that the OTOC equals an average over a quasiprobability distribution. The distribution, a set of numbers, contains more information than the OTOC, one number that follows from coarse-graining over the distribution. Aside from providing insight into the OTOC’s fundamental nature, the OTOC quasiprobability has several applications: Theoretically, the quasiprobability interrelates scrambling with uncertainty relations, nonequilibrium statistical mechanics, and chaos. Experimentally, the quasiprobability points to a scheme for measuring the OTOC (via weak measurements, which refrain from disturbing the measured system much). The quasiprobability also signals false positives in attempts to measure scrambling of open systems. Finally, the quasiprobability underlies a quantum advantage in metrology. References • NYH, Phys. Rev. A 95, 012120 (2017). https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.012120 • NYH, Swingle, and Dressel, Phys. Rev. A 97, 042105 (2018). https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.042105 • NYH, Bartolotta, and Pollack, accepted by Comms. Phys. (in press). https://arxiv.org/abs/1806.04147 • Gonzàlez Alonso, NYH, and Dressel, Phys. Rev. Lett. 122, 040404 (2019). https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.040404 • Swingle and NYH, Phys. Rev. A 97, 062113 (2018). https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.062113 • Dressel, Gonzàlez Alonso, Waegell, and NYH, Phys. Rev. A 98, 012132 (2018). https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.012132 • Arvidsson-Shukur, NYH, Lepage, Lasek, Barnes, and Lloyd, arXiv:1903.02563 (2019). https://arxiv.org/abs/1903.02563

The fine grained energy spectrum of quantum chaotic systems, which are widely believed to be characterized by random matrix statistics. A basic scale in these systems is the energy range over which this behavior persists. We defined the corresponding time scale by the time at which the linearly growing ramp region in the spectral form factor begins. We dubbed this ramp time. It is also referred to as the ergodic or Thouless time in the condensed matter physics community. The purpose of my talk is to understand this scale in many-body quantum systems that display strong chaos (such as SYK and spin chain), sometimes referred to as scrambling systems. Using numerical results and analytic estimates for random quantum circuits, I will provide summary of results on scaling of ramp time with system size in the presence/absence of conservation laws.

Recently we pointed out that the black hole interior operators can be reconstructed by using the Hayden-Preskill recovery protocols. Building on this observation, we propose a resolution of the firewall problem by presenting a state-independent reconstruction of interior operators. Our construction avoids the non-locality problem which plagued the "A=RB" or "ER=EPR" proposals. We show that the gravitational backreaction by the infalling observer, who simply falls into a black hole, disentangles the outgoing mode from the early radiation. The infalling observer crosses the horizon smoothly and sees quantum entanglement between the outgoing mode and the interior mode which is distinct from the originally entangled qubit. Namely, any quantum operation on the early radiation cannot influence the experience of the infalling observer as description of the interior mode does not involve the early radiation at all. We also argue that verification of entanglement by the outside observer does not create a firewall. Instead it will perform the Hayden-Preskill recovery which saves an infalling observer from crossing the horizon.

In this talk, I will discuss a newly proposed (pseudo-)critical phenomena governed by complex fixed points. I will start with the idea of complex fixed point at complex physical couplings and then introduce the recent conjectured complex conformal field theory with complex conformal data (e.g. central charge and scaling dimensions) which is suggested to describe these complex fixed points. These new concepts are putatively related to many interesting topics, such as the deconfined criticality, walking behavior in the gauge theories, weakly first order phase transitions and so on. Particularly, I will focus on a concrete example of the weakly first order phase transition, the Q>4 Potts model, where we did our numerics and found approximate conformality at intermediate length scale. Our results also give supportive evidence for the complex conformal data proposed based on the conjecture of complex CFT.

I will present a study of the single-particle properties of hot, lukewarm and cold electrons that coexist in the two-dimensional antiferromagnetic quantum critical metal within a unified theory. I will show how to generalize the theory that describes the interaction of critical spin-density wave fluctuations and electrons near the hot spots on the Fermi surface (hot electrons) by including electrons far away from the hot spots (lukewarm and cold electrons). Through an analytically tractable functional renormalization group scheme it will be shown that low-energy electrons are characterized by a universal momentum-dependent quasi-particle weight that decays to zero as the hot spots are approached along the Fermi surface, owing to the coexistence of quasiparticle and non-quasiparticle excitations within the same metallic state. This approach allows to characterize how the global shape of the Fermi surface is renormalized due to the strong interaction between the electrons and the critical spin fluctuations. I will finalize by commenting on the scope of this approach to study properties that are sensitive to the entirety of the Fermi surface, paying special attention to some preliminary results on the superconducting instability of this metallic state.

The interplay of symmetry and topology has been at the forefront of recent progress in quantum matter. In this talk I will discuss an unexpected connection between band topology and competing orders in a quantum magnet. The key player is the two-dimensional Dirac spin liquid (DSL), which at low energies is described by an emergent Quantum Electrodynamics (QED) with massless Dirac fermions (a.k.a. spinons) coupled to a U(1) gauge field. A long-standing open question concerns the symmetry properties of the magnetic monopoles, an important class of critical degrees of freedom. I will show that the monopole properties can be determined from the topology of the underlying spinon band structure. In particular, the lattice momentum and angular momentum of monopoles can be determined from the charge (or Wannier) centers of the corresponding spinon insulators. I will then discuss the consequences of the monopole properties, such as the stability of the DSL on different lattices, universal (experimental and numerical) signatures of DSL, and competing symmetry-breaking phases near the DSL state.

I will discuss several examples of novel continuous phase transitions, primarily in 3+1-D, that are beyond the standard Landau paradigm of order parameter fluctuations. These provide non-trivial examples of deconfined quantum critical points.

In the study of three-dimensional gapped models, two-dimensional gapped states can be considered as a free resource. This is the basic idea underlying our proposal of the notion of `foliated fracton order'. Using this idea, we have found that many of the known type-I fracton models, like the X-cube model and the checkerboard model, have the same foliated fracton order. In this talk, I will present three-dimensional fracton models with a different kind of foliated fracton order. The previously known foliated fracton order corresponds to the gauge theory of a simple paramagnet with subsystem planar symmetry. The new order corresponds to a twisted version of the gauge theory where the system before gauging has nontrivial order protected by the subsystem planar symmetries. I will discuss a way to identify the nontrivial order by compactifying the system in the z direction and analyzing the resulting two dimensional order.