**Alvaro Alhambra**, Perimeter Institute

*Dynamics of two-point correlation functions in quantum systems*

We give rigorous analytical results on the temporal behavior of two-point correlation functions (also known as dynamical response functions or Green’s functions) in quantum many body systems undergoing unitary dynamics. Using recent results from large deviation theory, we show that in a large class of models the correlation functions factorize at late times <A(t)B> -> <A><B>, thus proving that dissipation emerges out of the unitary dynamics of the system. We also show that the fluctuations around this late-time value are bounded by the purity of the thermal ensemble, which generally decays exponentially with system size. This conclusion connects the behavior of correlation functions to that of the late-time fluctuations of quenched systems out of equilibrium.

For auto-correlation functions such as <A(t)A> (as well as the symmetrized and anti-symmetrized versions) we provide an upper bound on the timescale at which they reach that factorized late time value. Remarkably, this bound is a function of local expectation values only, and does not increase with system size. As such it constraints, for instance, the behavior of current auto-correlation functions that appear in quantum transport. We give numerical examples that show that this bound is a good estimate in chaotic models, and argue that the timescale that appears can be understood in terms of an emergent fluctuation-dissipation theorem. Our study extends to further classes of two point functions such as the Kubo function of linear response theory, for which we give an analogous result.

Joint work with Luis Pedro Garcia-Pintos and Jonathon Riddell

**Ehud Altman**, University of California, Berkeley

*Theory of entanglement phase transitions and natural error correction in quantum circuits with measurement*

**Xie Chen**, California Institute of Technology

*Twisted foliated fracton order*

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.

**Meng Cheng**, Yale University

*From translation symmetry-enriched topological order to fracton phases*

**Matthew Fisher**, University of California, Santa Barbara

*Taming Quantum Entanglement*

Non-local quantum entanglement is the key feature that distinguishes quantum from classical systems. In this talk I will discuss a mechanism to tame entanglement - by \looking repeatedly" at the system (i.e. making projective measurements) - a many-body quantum Zeno e ect. I will explore a novel hybrid quantum circuit model consisting of both unitary gates and projective measurements, presenting evidence for a new quantum dynamical phase transition between a weak measurement phase and a quantum Zeno phase. Detailed critical properties of this novel quantum entanglement transition will be described.

**Hrant Gharibyan**, Stanford University

*Onset of Random Matrix Statistics in Scrambling Systems*

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.

**Andrey Gromov**, University of Chicago

*Multipole gauge theories and fractons*

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).

**Yingfei Gu**, Harvard University

*On the relation between the magnitude and exponent of OTOCs*

**Yin-Chen He**, Perimeter Institute

*Phase transition of fractional Chern insulators: QED3 and beyond*

Recent experiments in graphene heterostructures have observed Chern insulators - integer and fractional Quantum Hall states made possible by a periodic substrate potential. Here we study theoretically that the competition between different Chern insulators, which can be tuned by the amplitude of the periodic potential, leads to a new family of quantum critical points described by QED3-Chern-Simons theory. At these critical points, Nf flavors of Dirac fermions interact through an emergent U(1) gauge theory at Chern-Simons level K, and remarkably, the entire family (with any Nf or K) can be realized at special values of the external magnetic field. I will talk about the physical properties and microscopic realization of those critical points. We propose experiments on Chern insulators that could resolve open questions in the study of 2+1 dimensional conformal field theories and test recent duality inspired conjectures.

**Timothy Hsieh**, Perimeter Institute

*Shortcuts in Real and Imaginary Time*

In the first half, I will demonstrate an efficient and general approach for realizing non-trivial quantum states, such as quantum critical and topologically ordered states, in quantum simulators. In the second half, I will present a related variational ansatz for many-body quantum systems that is remarkably efficient. In particular, representing the critical point of the one-dimensional transverse field Ising model only requires a number of variational parameters scaling logarithmically with system size. Though optimizing the ansatz generally requires Monte Carlo sampling, our ansatz potentially enables a partial mitigation of the sign problem at the expense of having to optimize a few parameters.

**Yong-Baek Kim**, University of Toronto

*Topological phases in Kitaev Materials*

We discuss recent progress in theory and experiment on emergent topological phases in Kitaev materials. Here the competition between different anisotropic spin-exchange interactions may lead to a number of exotic phases of matter. We investigate possible emergence of quantum spin liquid, topological magnons, and topological superconductivity in two and three dimensional systems. We make connections to existing and future experiments.

**Stefan Kuhn**, Perimeter Institute

*Application of Tensor Network States to Lattice Field Theories*

The conventional Euclidean time Monte Carlo approach to Lattice Field Theories faces a major obstacle in the sign problem in certain parameter regimes, such as the presence of a nonzero chemical potential or a topological theta-term. Tensor Network States, a family of ansatzes for the efficient description of quantum many-body states, offer a promising alternative for addressing Lattice Field Theories in the Hamiltonian formulation. In particular, numerical methods based on Tensor Network states do not suffer from the sign problem which makes it possible to study scenarios which are not accessible with standard Monte Carlo methods. In this talk I will present some recent work demonstrating this capability using two (1+1)-dimensional models as a test bed. Studying the O(3) nonlinear sigma model at nonzero chemical potential and the Schwinger model with topological theta-term, I will show how Tensor Networks States accurately describe the low-energy spectrum and that numerical errors can be controlled well enough to make contact with continuum predictions.

**Andreas Lauchli**, Leopold-Franzens Universität Innsbruck

*Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions*

It is an open question how well tensor network states in the form of an infinite projected entangled-pair states (iPEPS) tensor network can approximate gapless quantum states of matter. In this talk we address this issue for two different physical scenarios: (i) a conformally invariant (2+1)d quantum critical point in the incarnation of the transverse-field Ising model on the square lattice and (ii) spontaneously broken continuous symmetries with gapless Goldstone modes exemplified by the S=1/2 antiferromagnetic Heisenberg and XY models on the square lattice. We find that the energetically best wave functions display finite correlation lengths and we introduce a powerful finite correlation length scaling framework for the analysis of such finite bond dimension (finite-D) iPEPS states. The framework is important (i) to understand the mild limitations of the finite-D iPEPS manifold in representing Lorentz-invariant, gapless many-body quantum states and (ii) to put forward a practical scheme in which the finite correlation length ξ(D) combined with field theory inspired formulas can be used to extrapolate the data to infinite correlation length, i.e., to the thermodynamic limit. The finite correlation length scaling framework opens the way for further exploration of quantum matter with an (expected) Lorentz-invariant, massless low-energy description, with many applications ranging from condensed matter to high-energy physics.

**Yuan-Ming Lu**, Ohio State University

*Spontaneous symmetry breaking from anyon condensation*

In the context of quantum spin liquids, it is long known that the condensation of fractionalized excitations will inevitably break certain physical symmetries sometimes. For example, condensing spinons will usually break spin rotation and time reversal symmetries. We generalize these phenomena to generic continuous quantum phase transitions between symmetry enriched topological orders driven by anyon condensation. We provide a generic rule to determine whether a symmetry is enforced to break across an anyon condensation transition. Using a dimensional reduction scheme, we establish a mapping between these symmetry-breaking anyon-condensation transitions in two spatial dimensions, and deconfined quantum criticality in one spatial dimension.

**Han Ma**, University of Colorado Boulder

*Shadow of complex fixed point: Approxmiate conformality of Q>4 Potts model*

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.

**Ashley Milsted**, Perimeter Institute &

**Yijian Zou**, Perimeter Institute

*Extracting conformal and superconformal data from critical quantum spin chains*

Key to characterizing universality in critical systems is the identification of the RG fixed point, which is very often a conformal field theory (CFT). We show how to use lattice operators that mimic the Virasoro generators of conformal symmetry to systematically extract, from a generic critical quantum spin chain, a complete set of the conformal data (central charge, scaling dimensions of primary fields, OPE coefficients) specifying a 2D CFT. We further show that, in the case of an extended superconformal symmetry, one can construct lattice operators that mimic the generators of the superconformal algebra, which allows us to identify superconformal primary states.

**David Mross**, Weizmann Institute of Science

*Bridging partons and coupled-wire approaches to strongly entangled quantum matter*

The Hallmark of strongly entangled quantum phases is an intrinsic impossibility to describe them locally in terms of microscopic degrees of freedom. Two popular methods that have been developed to analytically describe these exotic states are known as (1) ‘parton construction’ and (2) ‘coupled-wire approach’. The former provides a constructive route for determining which non-trivial phases may arise, in principle, for a given set of constituent degrees of freedom and symmetries. This capability comes at the expense of having very little predictive power what phases do arise, in practice, in any particular system. The latter technique, by contrast, yields explicit expressions of ground states, excitations as well as parent Hamiltonians in terms of microscopic degrees of freedom. The price to pay is a lack of flexibility, and each phase needs to be analyzed on a laborious case-by-case basis. I will show how recent understanding of two-dimensional dualities provides a natural link between the two approaches. Specifically, I will show how a wide range of parton mean-field states can be easily translated into explicit coupled-wire models, and how their universal properties can be obtained in a transparent manner.

**Subir Sachdev**, Harvard University

*Theory of a Planckian metal with a remnant Fermi surface*

**Andres Schlief Carvajal,** Perimeter Institute & McMaster University

*From cold to lukewarm to hot electrons*

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.

**Senthil Todadri**, Massachusetts Institute of Technology

*Landau ordering and other phase transitions beyond the Landau paradigm*

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.

Colloquium: *When topology meets strong interactions in quantum matter*

The study of strongly interacting quantum matter has been at the forefront of condensed matter research in the last several decades. An independent development is the discovery of topological band insulators. In this talk I will describe phenomena that occur at the confluence of topology and strong interactions. I will first discuss how insights from the study of the relatively simple topological insulators are revolutionizing our theoretical understanding of more complex quantum many body systems. Next I will describe some experimental situations in which both band topology and strong correlations are present, the resulting novel phenomena, and the theoretical challenges they present.

**Chong Wang**, Perimeter Institute

*QED and quantum magnetism in (2+1)d*

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.

**Beni Yoshida**, Perimeter Institute

*Firewalls vs. Scrambling*

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.

**Nicole Yunger Halpern**, Harvard University

*When quantum-information scrambling met quasiprobabilities*

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

**Michael Zaletel,** University of California, Berkeley

*Isometric Tensor Network States in Two Dimensions*

We introduce an isometric restriction of the tensor-network ansatz that allows for highly efficient contraction of the network. We consider two concrete applications using this ansatz. First, we show that a matrix-product state representation of a 2D quantum state can be iteratively transformed into an isometric 2D tensor network. Second, we introduce a 2D version of the time-evolving block decimation algorithm (TEBD2) for approximating the ground state of a Hamiltonian as an isometric tensor network, which we demonstrate for the 2D transverse field Ising model.

**Liujun Zou**, Massachusetts Institute of Technology

*Field-induced neutral Fermi surfaces and QCD3 quantum criticalities*

We perform both numerical and theoretical studies on the phase diagram of the Kitaev materials in the presence of a magnetic field. We find that a new quantum spin liquid state with neutral Fermi surfaces emerges at intermediate field strengths, between the regimes for the non-Abelian chiral spin liquid state and for the trivial polarized state. We discuss the exotic field-induced quantum phase transitions from this new state with neutral Fermi surfaces to its nearby phases. We also theoretically study the field-induced quantum phase transitions from the non-Abelian chiral spin liquid to the symmetry-broken zigzag phase and to the trivial polarized state. Utilizing the recently developed dualities of gauge theories, we find these transitions can be described by critical bosons or gapless fermions coupled to emergent non-Abelian gauge fields, and the critical theories are of the type of a QCD3-Chern-Simons theory. We propose that all these exotic quantum phase transitions can potentially be direct and continuous in the Kitaev materials, and we present sound evidence for this proposal. Therefore, besides being systems with intriguing quantum magnetism, Kitaev materials may also serve as table-top experimental platforms to study the interesting dynamics of emergent strongly interacting quarks and gluons in 2+1 dimensions. Finally, we address the experimental signatures of these phenomena.