Scientific Series

The main feature of tensor models is their melonic large N limit, leading to applications ranging from random geometry and quantum gravity to  many-body quantum mechanics and conformal field theories. However, this melonic limit is lacking for tensor models with ordinary representations of O(N) or Sp(N). We demonstrate that random tensors with sextic interaction transforming under rank-5 irreducible representations of O(N) have a melonic large N limit. This extends the recent proof obtained for rank-3 models with quartic interaction. After giving an introduction to random tensors, I will present the main ideas of our proof relying on recursive bounds derived from a detailed combinatorial analysis of the Feynman graphs.

Zoom Link: https://pitp.zoom.us/j/94691275506?pwd=RGFaN0NZR0FScFdOTXFzeFVXaXUvUT09

Accurate waveform models are crucial for gravitational-wave (GW) data analysis, and since numerical-relativity waveforms are computationally expensive, it is important to improve the analytical approximations for the binary dynamics. The post-Newtonian (PN) approximation is most suited for describing the inspiral of comparable-mass binaries, which are the main sources for ground-based GW detectors. In this talk, I discuss a method for deriving PN results valid for arbitrary mass ratios from first-order self-force results, by exploiting the simple mass dependence of the scattering angle in the post-Minkowskian expansion. I present results for the spin-orbit dynamics up to the fourth-subleading PN order (5.5PN) and the spin-spin dynamics up to the third-subleading PN order (5PN). I also discuss implications for the first law of binary mechanics.

Zoom Link: https://pitp.zoom.us/j/92861625861?pwd=cHpXUlM1d01pc09mNGhhQVZxRHBiQT09

This talk focuses on the semiclassical behavior of the spinfoam quantum gravity in 4 dimensions. There has been long-standing confusion, known as the flatness problem, about whether the curved geometry exists in the semiclassical regime of the spinfoam amplitude. The confusion is resolved by the present work. By numerical computations, we explicitly find curved Regge geometries from the large-j Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam amplitudes on triangulations. These curved geometries are with small deficit angles and relate to the complex critical points of the amplitude. The dominant contribution from the curved geometry to the spinfoam amplitude is proportional to e^{i I}, where I is the Regge action of the geometry plus corrections of higher order in curvature. As a result, the spinfoam amplitude reduces to an integral over Regge geometries weighted by e^{i I} in the semiclassical regime.  As a byproduct, our result also provides a mechanism to relax the cosine problem in the spinfoam model. Our results provide important evidence supporting the semiclassical consistency of the spinfoam quantum gravity.

Zoom Link: https://pitp.zoom.us/j/93699343757?pwd=RnpFeitaTU5qTktzNjlXQW45K1gvQT09

Currently, no general theory exists that explains what life is. While many definitions for life do exist, these are primarily descriptive, not predictive, and they have so far proved insufficient to explain the origins of life, or to provide rigorous constraints on what properties we might expect all examples of life to share (e.g., in our search for life in alien environments). In this talk I discuss new approaches to understanding what universal principles might explain the nature of life and elucidate the mechanisms of its origins, focusing on recent work in our group elucidating regularities and law-like behavior of biochemical networks on Earth from the scale of individual organisms to the planetary scale.

Zoom Link: https://pitp.zoom.us/j/91944267625?pwd=QzBmTzRKK0k3YXhXWnQ3WjNBSDR2UT09

Suppressing noise in physical systems is of fundamental importance. As quantum computers mature, quantum error correcting codes (QECs) will be adopted in order to suppress errors to any desired level. However in the noisy, intermediate-scale quantum (NISQ) era, the complexity and scale required to adopt even the smallest QEC is prohibitive: a single logical qubit needs to be encoded into many thousands of physical qubits. Here we show that, for the crucial case of estimating expectation values of observables (key to almost all NISQ algorithms) one can indeed achieve an effective exponential suppression. We take n independently prepared circuit outputs to create a state whose symmetries prevent errors from contributing bias to the expected value. The approach is very well suited for current and near-term quantum devices as it is modular in the main computation and requires only a shallow circuit that bridges the n copies immediately prior to measurement. Using no more than four circuit copies, we confirm error suppression below 10−6 for circuits consisting of several hundred noisy gates (2-qubit gate error 0.5%) in numerical simulations validating our approach. This talk is based on [B. Koczor, Phys. Rev. X 11, 031057] and [B. Koczor, New J. Phys. (accepted), arXiv:2104.00608].

Zoom Link: https://pitp.zoom.us/j/91654758635?pwd=TEtPMmZMNGZya1JOc05KbGt6OUpjdz09

Competition between unitary dynamics that scramble quantum information non-locally and local measurements that probe and collapse the quantum state can result in a measurement-induced entanglement phase transition. We introduce large-N Brownian hybrid circuits acting on clusters of qubits, which provide an analytically tractable model for measurement-induced criticality. The system is initially entangled with an equal sized reference, and the subsequent hybrid system dynamics either partially preserves or destroys this entanglement depending on the measurement rate. Our approach can access a variety of entropic observables, which are represented as a replica path integral with twisted boundary conditions. Saddle-point analysis reveals a second-order phase transition corresponding to replica permutation symmetry breaking below a critical measurement rate. The transition is mean-field-like and we characterize the critical properties near the transition in terms of a simple Ising field theory in 0+1 dimensions. By coupling the large-N clusters on a lattice, we also extend these solvable models to study the effects of power-law long-range couplings on measurement-induced phases. In one dimension, the long-range coupling is relevant for α<3/2, with α being the power-law exponent, leading to a nontrivial dynamical exponent at the measurement-induced phase transition. More interestingly, for α<1 the entanglement pattern receives a sub-volume correction for both area-law and volume-law phases. The volume-law phase for α<1 realizes a novel quantum error correcting code whose code distance scales as L^(2−2α).

References: 
[1] Phys. Rev. B 104, 094304 (2021), ArXiv:2104.07688.
[2] ArXiv:2109.00013.

Despite years of research into dark matter, little has been done to explore models which are heavier than most WIMPs and lighter than most primordial black hole models, "blobs".  This parameter space is particularly difficult to probe, due to low number densities and low masses.  This talk will present a new model-independent mechanism that can be used to probe this difficult to reach region of dark matter parameter space.  Blobs form binaries which spin down and merge at high rates in the present and recent past.  The abundance of mergers can produce observable gravitational wave and electromagnetic signals.  I describe some of these unique signals and show how they already constrain parts of blob parameter space.

Zoom Link: https://pitp.zoom.us/j/98024869740?pwd=eDlPSTB3UzhIcEVYVGNQakRHVUtFQT09

We investigate interactions between branes of various dimensions, both charged and uncharged, in some non-supersymmetric string models. These include the USp(32) and U(32) orientifolds of the type IIB and type 0B strings, as well as the SO(16) x SO(16) projection of the exceptional heterotic string. The resulting ten-dimensional spectra are free of tachyons and the combinations of branes that they contain give rise to rich and varied dynamics. We focus on potentials that describe their mutual interactions, both in the probe regime and in the string-amplitude regime, finding qualitative agreement despite the absence of supersymmetry and confirming the Weak Gravity Conjecture for charged branes.

Spectroscopic surveys are a powerful cosmological probe, encoding information about structure formation and the geometry of the universe in the 3D distribution of galaxies. Upcoming surveys like DESI, which will increase the number of measured galaxy redshifts by an order of magnitude, will test our ability to use this information while providing opportunities to test fundamental physics in unprecedented ways. In this talk I will discuss our recent work on a new method to combine the two main prongs of these surveys--redshift-space distortions and BAO--within the framework of Lagrangian perturbation theory. As an illustrative example, I will discuss the application of this method to data from the BOSS survey, obtaining cosmological constraints that are competitive but consistent with primary CMB and lensing measurements. I will also discuss future prospects for perturbation theory analyses of large-scale structure, for example by jointly analyzing spectroscopic and lensing surveys.

Traditionally, magnetism in solids deals with ordering patterns of the electron magnetic dipole moment, as probed, for instance, via neutron diffraction. However, f-electron heavy fermion systems are well-known candidates for more complex forms of symmetry breaking, involving higher-order magnetic or electric multipoles. In this talk, I will discuss our recent theoretical proposal for Ising octupolar order in d-orbital systems, which appears to explain a wide range of experiments in certain 5d transition metal oxides with spin-orbit coupling. The proposed Ising ferro-octupolar order is shown to be linked to a type of orbital loop-current order. Deviations from cubic symmetry, via strain or surfaces, induces a transverse field on the octupolar order which can lead to surface quantum phase transitions, or transitions in thin films or in strained 3D crystals. We propose further experimental tests of our proposal.
 

We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions as tensor networks built from the tensors of simple codes or states in a modular fashion. Using a set of local moves known as operator pushing, one can derive properties of the more complex codes, such as transversal non-Clifford gates, by tracing the flow of operators in the network. The framework endows a network geometry to any code it builds and is valid for constructing stabilizer codes as well as non-stabilizer codes over qubits and qudits. For a contractible tensor network, the sequence of contractions also constructs a decoding/encoding circuit. To highlight the framework's range of capabilities and to provide a tutorial, we lay out some examples where we glue together simple stabilizer codes to construct non-trivial codes. These examples include the toric code and its variants, a holographic code with transversal non-Clifford operators, a 3d stabilizer code, and other stabilizer codes with interesting properties. Surprisingly, we find that the surface code is equivalent to the 2d Bacon-Shor code after "dualizing" its tensor network encoding map.
 

Tensor network algorithms are numerical tools widely used in physical research. But traditionally they are only applied to lattice systems with specific structure. In this talk, tensor network algorithms to deal with physical systems with arbitrary topology will be discussed. Theoretical framework will firstly be constructed to analyze the difficulty of contracting an arbitrary tensor network. Then both approximate and exact contraction approaches will be involved according to computational tasks of interest. Finally two applications, one in graphical models and the other in quantum circuit simulations, will be introduced to demonstrate the performance and potential of arbitrary tensor network algorithms.