Scientific Series

Topological phases of matter offer a promising platform for quantum computation and quantum error correction. Nevertheless, unlike its counterpart in pure states, descriptions of topological order in mixed states remain relatively under-explored. We will give various definitions for replica topological order in mixed states. Similar to the replica trick, our definitions also involve n copies of density matrix of the mixed state. Within this framework, we categorize topological orders in mixed states as either quantum, classical, or trivial, depending on the type of information they encode.

For the case of the toric code model in the presence of decoherence, we associate for each phase a quantum channel and describes the structure of the code space. We show that in the quantum-topological phase, there exists a postselection-based error correction protocol that recovers the quantum information, while in the classical-topological phase, the quantum information has decohere and cannot be fully recovered. We accomplish this by describing the mixed state as a projected entangled pairs state (PEPS) and identifying the symmetry-protected topological order of its boundary state to the bulk topology.

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Hilbert spaces are incomprehensibly vast and rich. Model Hamiltonians are space ships. They could take us to new worlds, such as cold \textit{spin liquid oasis} in hot regions in Hilbert space deserts. Exact decomposition of isotropic Heisenberg Hamiltonian on a Honeycomb lattice into a sum of 3 non-commuting (permuted) Kitaev Hamiltonians, helps us build a degenerate \textit{manifold of metastable flux free Kitaev spin liquid vacua} and vector Fermionic (Goldstone like) collective modes. Our method, \textit{symmetric decomposition of Hamiltonians}, will help design exotic metastable quantum scars and exotic quasi particles, in nonexotic real systems.
G. Baskaran, arXiv:2309.07119

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Present-day galaxies still contain a multitude of clues about their formation histories. But which properties should we best look at and what do they actually reveal about the past? Using cosmological simulations, I will show what insights about a galaxy's formation and merger history can be gained from a diverse set of measurements. For this, I will show how the overall galaxy shapes and tidal features in the outskirts are related to the inner kinematics. These results give us indications about the correlation with the recent merger histories of the galaxies. Finally, I will discuss how early gas-rich mergers can be revealed through the ages of globular cluster populations.

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The axion is one of the most compelling new physics candidates, deriving many of its important properties from an approximate shift symmetry. In this talk, we will consider the general form of the axion coupling to photons in the presence of such a broken shift symmetry. We will show that the axion-photon in general becomes a non-linear monodromic function of the axion. The non-linearity is correlated with the axion mass and singularities in the axion-photon coupling are associated with cusps in the axion potential. We derive the general form of the axion-photon coupling for several examples including the QCD axion and show that there is a uniform general form for this monodromic function. The full non-linear profile of this coupling is phenomenologically relevant to the dynamics induced on axion domain walls/strings and other extended objects involving the axion.

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A Planck scale inflationary era—in a quantum gravity theory predicting discreteness of quantum geometry at the fundamental scale—produces the scale invariant spectrum of inhomogeneities with very small tensor-to-scalar ratio of perturbations and a hot big bang leading to a natural dark matter genesis scenario. In this talk I evoke the possibility that some of the major puzzles in cosmology could have an explanation rooted in quantum gravity.

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A 2-group is a categorical generalization of a group: it's a category with a multiplication operation which satisfies the usual group axioms only up to coherent isomorphisms. The isomorphism classes of its objects form an ordinary group, G. Given a 2-group G with underlying group G, we can similarly define a categorical generalization of the notion of principal bundles over a manifold (or stack) X, and obtain a bicategory Bun_G(X), living over the category Bun_G(X) of ordinary G-bundles on X. For G finite and X a Riemann surface, we prove that this gives a categorification of the Freed--Quinn line bundle, a mapping-class group equivariant line bundle on Bun_G(X) which plays an important role in Dijkgraaf--Witten theory (i.e. Chern--Simons theory for the finite group G). This talk is based on joint work with Daniel Berwick-Evans, Laura Murray, Apurva Nakade, and Emma Phillips.

I will not assume previous knowledge of 2-groups: I will provide a quick overview in the main talk, as well as a more detailed discussion during a pre-talk on Tuesday. 

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We define a map from an arbitrary quantum circuit to a local Hamiltonian whose ground state encodes the quantum computation. All previous maps relied on the Feynman-Kitaev construction, which introduces an ancillary ‘clock register’ to track the computational steps. Our construction, on the other hand, relies on injective tensor networks with associated parent Hamiltonians, avoiding the introduction of a clock register. This comes at the cost of the ground state containing only a noisy version of the quantum computation, with independent stochastic noise. We can remedy this - making our construction robust - by using quantum fault tolerance. In addition to the stochastic noise, we show that any state with energy density exponentially small in the circuit depth encodes a noisy version of the quantum computation with adversarial noise. We also show that any ‘combinatorial state’ with energy density polynomially small in depth encodes the quantum computation with adversarial noise. This serves as evidence that any state with energy density polynomially small in depth has a similar property. As an application, we give a new proof of the QMA-completeness of the local Hamiltonian problem (with logarithmic locality) and show that contracting injective tensor networks to additive error is BQP- hard. We also discuss the implication of our construction to the quantum PCP conjecture, combining with an observation that QMA verification can be done in logarithmic depth. Based on joint work with Anurag Anshu and Nikolas P. Breuckmann. (https://arxiv.org/abs/2309.16475)

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It is well known that the study and observation of core collapse Supernovae (SN) provide powerful tools to probe possible scenarios of physics beyond the Standard Model (SM). After reviewing the basics beyond the mechanism of a SN explosion and how these observations can constraint models of new physics, I will focus on two novel ideas to exploit the already available data from past SN and the observation of a future, long due, galactic one. Firstly. I will discuss constraints, from the cooling on the SN, on the interactions of SM particles with an hypothetical dark sector, leading to bounds on the mediators of such interactions competitive with collider ones. Then, I will turn on the constrains on the emission of axion-like particles (ALPs) that can convert into photons in an external magnetic field, leading to a gamma-ray signal. I will discuss the possibility that ALPs can convert to gamma-rays in the stellar magnetic fields of the progenitor stars. Applying this concept to gamma-ray data from SN1987A leads to the strongest constraints on axion-like particles for masses within a few orders of magnitude of 10^-5 eV. The implications for a future galactic blue supergiant supernova will be discussed.

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In this talk, I will present a novel framework for modeling the weak lensing source galaxy redshift distribution and galaxy intrinsic alignment via a shared luminosity function. In the context of LSST Year 1 and Year 10 cosmic shear analysis, I demonstrate the significant impact of the luminosity function on source galaxy redshift distributions and intrinsic alignment contamination. I establish the influence of Schechter luminosity function parameters on the redshift distribution of a magnitude-limited sample and show the effects of marginalizing over these parameters in intrinsic alignment modeling. I forecast how this joint modeling approach affects cosmological parameter constraints, finding that it yields constraints comparable to standard analyses while mitigating potential biases from incorrectly fixed luminosity function parameters. I highlight the specific impact of the luminosity function shape on the cosmic shear data vector and discuss the method's potential for modeling generic selection functions and extending to a 3x2pt analysis with galaxy bias incorporation. While focused on LSST cosmic shear, this framework is broadly applicable to weak lensing surveys.

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Presented as part of the SciComm Collider 2 workshop.
All PI Residents are invited. 

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A colloquium featuring 2 perspectives on science communication.

Tatiana Erukhimova - Making Physics Fun and Approachable
Matthew Strassler - The Challenge of Communicating Physics Accessibly, Clearly and Accurately

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The correlation functions of large-scale fluctuations are crucial observables in modern cosmology. These boundary correlators contain rich information about the bulk dynamics and can be used to probe physics at the inflation scale. There have been considerable efforts in the analytical study of inflation correlators in recent years. In this talk, I will introduce the basic structure of inflation correlators and several analytical methods we have developed for their computation. In particular, I will introduce the method of partial Mellin-Barnes (PMB) representation. With this method, we can largely solve the massive tree correlators analytically. At the loop level, we use PMB to prove a factorization theorem for the nonanalytical part of inflation correlators, which produces a characteristic nonlocal signal. Finally, we can recover the full correlator starting from this nonanalytical part using a dispersion integral.

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