Scientific Series

An ongoing program of work in statistical physics and quantum dynamics is concerned with understanding the character of systems which follow an unconventional approach towards thermal equilibrium. In this talk, I will add to this story by introducing examples of simple 1D systems---both classical and quantum---which thermalize in very unusual ways. These examples have dynamics which is strictly local and translation-invariant, but in spite of this, they: a) can have very long thermalization times, with expectation values of local operators relaxing only over times exponential in the system size; and b) can thermalize only when they are placed in extremely large baths, with the required bath size growing exponentially (or even faster) in system size. Proofs of these results will be given using techniques from geometric group theory, a beautiful area of mathematics concerned with the complexity and geometry of infinite discrete groups. This talk will be based on a paper in preparation with Shankar Balasubramanian, Sarang Golaparakrishnan, and Alexey Khudorozhkov.

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Zoom link: https://pitp.zoom.us/j/99430001465?pwd=NENlS1M5UGc5UWM1ekQvRWFrZGYyUT09

In 2013, Cachazo, He and Yuan discovered a remarkable framework for scattering amplitudes in Quantum Field Theory (QFT) which mixes the real, complex and tropical geometry associated to the moduli space of n points on the projective line, $M_{0,n}$. By duality, this moduli space has a twin moduli space of $n$ generic points in $P^{n-3}$, leading to dual realization of scattering amplitudes, using a generalization of the CHY formalism introduced in 2019 by Cachazo, Early, Guevara and Mizera (CEGM). Any duality begs for an explanation! And, what physical phenomena lie between the twin moduli spaces? CEGM developed a framework to answer the question for moduli spaces of $n$ points in any $P^{k-1}$, leading to the discovery of rich, recursive structures and novel behaviors which portend an extension of QFT. We discuss recent joint works with Cachazo and Zhang, and with Geiger, Panizzut, Sturmfels, Yun, in which we dig deeper into some of the many mysteries which arise.

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Zoom link: https://pitp.zoom.us/j/95706337178?pwd=cnBka3lFWDBoRlFZV1VadXdGZ1JnZz09

Quantum Hall phases are the most exotic experimentally established quantum phases of matter.Recently they have been discovered at zero external magnetic field in two dimensional moire materials. I will describe recent work (with Xue-Yang Song and Ya-Hui Zhang) on their proximate phases and associated phase transitions that is motivated by the high tunability of thede moire systems. These phase transitions (and some of the proximate phases) are exotic as well, and realize novel ‘beyond Landau’ criticality that have been explored theoretically for many years. I will show that these moiré platforms provide a great experimental opportunity to study these unconventional phase transitions and related unconventional phases, thereby opening a new direction for research in quantum matter.

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Zoom link : https://pitp.zoom.us/j/97483204701?pwd=S2x4ck9tNHFjM0RiTDNWNFhaMk9SUT09

 I will present a galaxy formation model within the Lambda Cold Dark Matter (LCDM) framework that is calibrated on the results of galaxy formation simulations and some of the empirical properties of nearby dwarf galaxies. I will then use the model to interpret a number of ostensible challenges to the LCDM framework, such as the "too-big-too-fail problem", "central density problem" and the "planes of satellites" problem and will argue that none of these pose a serious challenge to LCDM, as the corresponding observations can be largely understood within the current galaxy formation modeling. I will also show that the same galaxy formation model can explain the abundance of UV-bright galaxies at z>5 measured by the Hubble Space Telescope and James Webb Space Telescope recently, if the expected increase of burstiness of star formation in galaxies towards early epochs is taken into account.

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Zoom link https://pitp.zoom.us/j/91798519705?pwd=Nk9rM0tFSXcrWDhLdXFhVmJWbGgvUT09

With the main purpose of identifying the existence of gravitational radiation at infinity (scri), a novel approach to the asymptotic structure of spacetime is presented, focusing mainly in cases with non-negative cosmological constant. The basic idea is to consider the strength of tidal forces experienced by scri. To that end I will introduce the asymptotic (radiant) super-momentum, a causal vector defined at scri with remarkable properties that, in particular, provides an innovative characterization of gravitational radiation valid for the general case with Λ ≥ 0 (and which has been proven to be equivalent when Λ = 0 to the standard one based on the News tensor). This analysis is also shown to be supported by the initial- (or final-) value Cauchy-type problem defined at scri. The implications are discussed in some detail. The geometric structure of scri, and of its cuts, is clarified. The question of whether or not a News tensor can be defined in the presence of a positive cosmological constant is addressed. Several definitions of asymptotic symmetries are presented. Conserved charges that may detect gravitational radiation are exhibited. Balance laws that might be useful as diagnostic tools to test the accuracy of model waveforms discussed. An interpretation of the Geroch `rho' tensor is found. The whole thing will be complemented with a series of illustrative examples based on exact solutions. In particular we will see that exact solutions with black holes will be radiative if, and only if, they are accelerated.

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Zoom link https://pitp.zoom.us/j/96816406686?pwd=eGZINlo2R0d1YkZMRGhackRNMzBVUT09

Two major approaches are used when numerically solving the Einstein field equations. The first one is to use spatial Cauchy slices and treat the system as a standard Cauchy initial value problem. Cauchy-characteristic evolution (CCE) serves as the second approach, which evolves spacetime based on null hypersurfaces. The Cauchy formulation is suitable for the strong field region but is computationally expensive to extend to the wave zone, whereas the Characteristic approach is fast in the wave zone but fails near the binary system where the null surfaces are ill-defined. By combining those two techniques — simulating the inner region with Cauchy evolution and the outer region with CCE, Cauchy-Characteristic matching (CCM) enables us to take advantage of both methods. In this talk, I present our recent implementation of CCM based on a numerical relativity code SpECTRE. I also discuss how CCM improves the accuracy of Cauchy boundary conditions — a benefit that allows us to evolve less of the wave zone in the Cauchy code without losing precision.

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Zoom link https://pitp.zoom.us/j/98246275227?pwd=QWtmUDNkMlF6bXROLzBoYXVVTGpldz09

In this talk, I will consider the centralizer of the quantum group U_q(sl_2) in the tensor product of three identical spin representations. The case of spin 1/2 (fundamental representation) is understood within the framework of the Schur-Weyl duality for U_q(sl_N), and the centralizer is known to be isomorphic to a Temperley-Lieb algebra. The case of spin 1 has also been studied and corresponds to the Birman-Murakami-Wenzl algebra. For a general spin, I will explain how to describe explicitly the centralizer (by generators and relations) using a combination of the braid group algebra and the Askey-Wilson algebra, which has been introduced in the context of orthogonal polynomials.

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Zoom link: https://pitp.zoom.us/j/98471794356?pwd=NjZFdjRFaDFON05HNkdTZS9hZTUvQT09

Tsirelson’s problem involves two agents, Alice and Bob, who apply measurements on the same quantum system, K. It asks whether commutation, i.e., independence of whether Alice or Bob measures first, is sufficient to conclude that Alice and Bob’s measurements can be factorised so that they act non-trivially only on distinct subsystems of K. In this talk, I will present a “fully quantum generalisation” of this problem, where Alice and Bob’s measurements are replaced by operations on K that may depend on additional quantum inputs and produce quantum outputs. As for Tsirelson’s original problem, it turns out that commutation indeed implies factorisation, provided that all relevant systems are finite-dimensional.

This is joint work with Ramona Wolf; preprint available at arXiv:2308.05792.

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 Zoom link https://pitp.zoom.us/j/99031410183?pwd=MzVoQXpPSll6bFp1b1g3U2J4U21rZz09

Finding ground states of quantum many-body systems is one of the most important---and one of the most notoriously difficult---problems in physics, both in scientific research and in practical applications.  Indeed, we know from a complexity-theoretic perspective that all methods  (quantum or classical) must necessarily fail to find the ground state efficiently in general. The ground state energy problem is already NP-hard even for classical, frustration-free, local Hamiltonians with constant spectral gap. For general quantum Hamiltonians, the problem becomes QMA-hard.

Nonetheless, as ground state problems are of such importance, and classical algorithms are often successful despite the theoretical exponential worst-case complexity, a number of quantum algorithms for the ground state problem have been proposed and studied. From quantum phase estimation-based methods, to adiabatic state preparation, to dissipative state engineering, to the variation quantum eigensolver (VQE), to quantum/probabilistic imaginary-time evolution (QITE/PITE).

Dissipative state engineering was first introduced in 2009 by Verstraete, Cirac and Wolf and by Kraus et al. However, it only works for the restricted class of frustration-free Hamiltonians.

In this talk, I will show how to construct a dissipative state preparation dynamics that provably produces the correct ground state for arbitrary Hamiltonians, including frustrated ones. This leads to a new quantum algorithm for preparing ground states: the Dissipative Quantum Eigensolver (DQE). DQE has a number of interesting advantages over previous ground state preparation algorithms:

• The entire algorithm consists simply of iterating the same set of   simple local measurements repeatedly.
• The expected overlap with the ground state increases monotonically with the length of time this process is allowed to run.
• It converges to the ground state subspace unconditionally, without any assumptions on or prior information about the Hamiltonian (such as spectral gap or ground state energy bound).
• The algorithm does not require any variational optimisation over parameters.
• It is often able to find the ground state in low circuit depth in practice.
• It has a simple implementation on certain types of quantum hardware, in particular photonic quantum computers.
• It is immune to errors in the initial state.
• It is inherently fault-resilient, without incurring any fault-tolerance overhead. I.e.\ not only is it resilient to errors on the quantum state, but also to faulty implementations of the algorithm itself; the overlap of the output with the ground state subspace degrades smoothly with the error rate, independent of the total run-time.

I give a mathematically rigorous analysis of the DQE algorithm and proofs of all the above properties, using non-commutative generalisations of methods from classical probability theory.

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Zoom link https://pitp.zoom.us/j/96022753460?pwd=SWlUVkVta1RyY3dsWUJWckRqOHdNdz09

We study the Petz map, which is a universal recovery channel of a tripartite quantum state upon erasing one party, in quantum many-body systems. The fidelity of the recovered state with the original state quantifies how much information shared by the two parties is not mediated by one of the party, and has a universal lower bound in terms of the conditional mutual information (CMI). I will study this quantity in two different contexts. First, in a CFT ground state, we show that the fidelity is universal, which means it only depends on the central charge and the cross ratio. We compute this universal function numerically and show that it is consistently better than the naive CMI bound. Secondly, we show that for two broad classes of the states, the CMI lower bound is saturated. These include stabilizer states (in any dimensions) and the ground state of 2+1D topological order.

Zoom link: https://pitp.zoom.us/j/92623435839?pwd=N1JIdkUwWHFkZGpqb1p1V3NKYy91QT09

Activation of Bell nonlocality refers to the phenomenon where some entangled mixed states that admit a local hidden variable model in the standard Bell scenario nevertheless reveal their nonlocal nature in more exotic measurement scenarios. It has recently been shown that by broadcasting the subsystems of a bipartite quantum state, one can activate Bell nonlocality and significantly improve noise tolerance bounds for device-independent and semi-device-independent entanglement certification, with a single copy of the state and local measurements. In this talk I will review the state of the art on activation of nonlocality and existence of local hidden variable models, introduce the broadcasting technique and outline several interesting results and research directions.

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Zoom link  https://pitp.zoom.us/j/91214624839?pwd=dXNUOERLMldScjczemlaSUhFbFNWQT09

With the main purpose of identifying the existence of gravitational radiation at infinity (scri), a novel approach to the asymptotic structure of spacetime is presented, focusing mainly in cases with non-negative cosmological constant. The basic idea is to consider the strength of tidal forces experienced by scri. To that end I will introduce the asymptotic (radiant) super-momentum, a causal vector defined at scri with remarkable properties that, in particular, provides an innovative characterization of gravitational radiation valid for the general case with Λ ≥ 0 (and which has been proven to be equivalent when Λ = 0 to the standard one based on the News tensor). This analysis is also shown to be supported by the initial- (or final-) value Cauchy-type problem defined at scri. The implications are discussed in some detail. The geometric structure of scri, and of its cuts, is clarified. The question of whether or not a News tensor can be defined in the presence of a positive cosmological constant is addressed. Several definitions of asymptotic symmetries are presented. Conserved charges that may detect gravitational radiation are exhibited. Balance laws that might be useful as diagnostic tools to test the accuracy of model waveforms discussed. An interpretation of the Geroch `rho' tensor is found. The whole thing will be complemented with a series of illustrative examples based on exact solutions. In particular we will see that exact solutions with black holes will be radiative if, and only if, they are accelerated.

Zoom link: https://pitp.zoom.us/j/95879544523?pwd=MFl5UEtUZ0hUcU1hNk1SZ2R4MThxUT09