Scientific Series

Quantum cellular automata (QCA) are unitary transformations that preserve locality. In one dimension, QCA are known to be fully characterized by a topological chiral index that takes on arbitrary rational numbers [1]. QCA with nonzero indices are anomalous, in the sense that they are not finite-depth quantum circuits of local unitaries, yet they can appear as the edge dynamics of two-dimensional chiral Floquet topological phases [2].

In this seminar, I will focus on the topological aspects of one-dimensional QCA. First, I will talk about how the topological classification of QCA will be enriched by finite unitary symmetries [3]. On top of the cohomology character that applies equally to topological states, I will introduce a new class of topological numbers termed symmetry-protected indices. The latter, which include the chiral index as a special case, are genuinely dynamical topological invariants without state counterparts [4].

In the second part, I will show that the chiral index lower bounds the operator entanglement of QCA [5]. This rigorous bound enforces a linear growth of operator entanglement in the Floquet dynamics governed by nontrivial QCA, ruling out the possibility of many-body localization. In fact, this result gives a rigorous proof to a conjecture in Ref. [2]. Finally, I will present a generalized entanglement membrane theory that captures the large-scale (hydrodynamic) behaviors of typical (chaotic) QCA [6].

References:
[1] D. Gross, V. Nesme, H. Vogts, and R. F. Werner, Commun. Math. Phys. 310, 419 (2012).
[2] H. C. Po, L. Fidkowski, T. Morimoto, A. C. Potter, and A. Vishwanath, Phys. Rev. X 6, 041070 (2016).
[3] Z. Gong, C. Sünderhauf, N. Schuch, and J. I. Cirac, Phys. Rev. Lett. 124, 100402 (2020).
[4] Z. Gong and T. Guaita, arXiv:2106.05044.
[5] Z. Gong, L. Piroli, and J. I. Cirac, Phys. Rev. Lett. 126, 160601 (2021).
[6] Z. Gong, A. Nahum, and L. Piroli, arXiv:2109.07408.

We study the Lyapunov exponent in disordered quantum field theories. Generically the Lyapunov exponent can only be computed in isolated CFTs, and little is known about the way in which chaos grows as we deform the theory away from weak coupling. In this talk we describe families of theories in which the disorder coupling is an exactly marginal deformation, allowing us to follow the Lyapunov exponent from weak to strong coupling. We find surprising behaviors in some cases, including a discontinuous transition into chaos. We also describe a new method allowing for computations in nontrivial CFTs deformed by disorder at leading order in 1/N.

In recent years, weak lensing of the cosmic microwave background (CMB) has emerged as a powerful tool to probe fundamental physics. The prime target of CMB lensing surveys is the lensing potential, which is reconstructed from observed CMB temperature T and polarization E and B fields. In this talk, I will show that the classic Hu-Okamoto (HO02) estimator used for the lensing potential reconstruction is not the absolute optimal lensing estimator that can be constructed out of quadratic combinations of T, E and B fields. Instead, I will derive the global-minimum-variance (GMV) lensing quadratic estimator and show explicitly that the HO02 estimator is suboptimal to the GMV estimator.

Rapidly expanding field of the line intensity mapping (LIM) promises to revolutionise our understanding of the galaxy formation and evolution. Although primarily a tool for galaxy astrophysics, LIM technique can be used as a cosmological probe and I will point out one such application in rest of the talk. I will show that a linear combination of lensing maps from the cosmic microwave background (CMB) and from line intensity maps (LIMs) allows to exactly null the low-redshift contribution to CMB lensing, and extract only the contribution from the Universe from/beyond reionization. This would provide a unique probe of the Dark Ages, complementary with 21 cm. I will quantify the interloper bias (which is a key hurdle to LIM techniques) to LIM lensing for the first time, and derive a "LIM-pair" estimator which nulls it exactly.

In the end, I will show some results for prospects of observing the Doppler boosted CIB emission and its applications.

Quantum spin liquids (QSL) are enigmatic phases of matter characterized by the absence of symmetry breaking and the presence of fractionalized quasiparticles. While theories for QSLs are now in abundance, tracking them down in real materials has turned out to be remarkably tricky. I will focus on two sets of studies on QSLs in three dimensional pyrochlore systems, which have proven to be particularly promising. In the first work, we analyze the newly discovered spin-1 pyrochlore compound NaCaNi2F7 whose properties we find to be described by a nearly idealized Heisenberg Hamiltonian [1]. We study its dynamical structure factor using molecular dynamics simulations, stochastic dynamical theory, and linear spin wave theory, all of which reproduce remarkably well the momentum dependence of the experimental inelastic neutron scattering intensity as well as its energy dependence (with the exception of the lowest energies) [2]. We apply many of the lessons learnt to Ce2Zr2O7 which has been recently shown to exhibit strong signatures of QSL behavior in neutron scattering experiments. Its magnetic properties emerge from interacting cerium ions, whose ground state doublet (with J = 5/2,m_J = ±3/2) arises from strong spin orbit coupling and crystal field effects. With the help of finite temperature Lanczos calculations, we determine the low energy effective spin-1/2 Hamiltonian parameters using which we reproduce all the prominent features of the dynamical spin structure factor. These parameters suggest the realization of a U(1) π-flux QSL phase [3] and they allow us to make predictions for responses in an applied magnetic field that highlight the important role played by octupoles in the disappearance of spectral weight.

*Supported by FSU and NHMFL, funded by NSF/DMR-1644779 and the State of Florida, and NSF DMR-2046570

[1] K. W. Plumb, H. J. Changlani, A. Scheie, S. Zhang, J. W. Krizan, J. A. Rodriguez-Rivera, Yiming Qiu, B. Winn, R. J. Cava & C. L. Broholm, Nature Physics 15, 54–59 (2019)
[2] S. Zhang, H. J. Changlani, K. W. Plumb, O. Tchernyshyov, and R. Moessner, Phys. Rev. Lett. 122, 167203 (2019)
[3] A.Bhardwaj, S.Zhang, H.Yan, R. Moessner, A. H. Nevidomskyy, H. J. Changlani, arXiv:2108.01096 (2021), under review.

Zoom Link: https://pitp.zoom.us/meeting/register/tJcqc-ihqzMvHdW-YBm7mYd_XP9Amhypv5vO

I will connect approaches to classical integrable systems via 4d Chern-Simons theory and via symmetry reductions of the anti-self-dual Yang-Mills equations. In particular, I will consider holomorphic Chern-Simons theory on twistor space, defined using a range of meromorphic (3,0)-forms. On shell these are, in most cases, found to agree with actions for anti-self-dual Yang-Mills theory on space-time. Under symmetry reduction, these space-time actions yield actions for 2d integrable systems. On the other hand, performing the symmetry reduction directly on twistor space reduces the holomorphic Chern-Simons action to 4d Chern-Simons theory.

Zoom Link: https://pitp.zoom.us/j/99193672959?pwd=RUJ3N3h2V3RFK3ZNVVVCK1E3bXJ2Zz09

Many cosmological scenarios beyond the Standard Model lead to the formation of a network of cosmic strings. In this talk, I will review how these models lead in a natural way to the production of a stochastic gravitational wave background and how this signal could account for the recently reported results from the NANOGrav collaboration. Finally, we will explain how future observations could allow us to confirm this interpretation of the NANOGrav data.

In this talk I introduce nonlocal (infinite derivative) field theories. First of all, I discuss how and which principles of quantum field theory are affected when higher-order derivative operators are taken into account in a Lagrangian. In particular, I focus on the issue of unitarity and on how to make higher-derivative theories healthy by means of non-polynomial differential operators. I extend the treatment to the gravity sector and consider nonlocal theories whose graviton propagators are ghost-free, and explore the possibility of regularizing singularities. Next, I discuss some recent progress in proving perturbative unitarity for a very general class of nonlocal field theories. Finally, I will make some remarks on nonlocality and quantum gravity.

We will discuss quantum singular value transformation (QSVT), a simple unifying framework for quantum linear algebra algorithms developed by Gilyén, Low, Su, and Wiebe. QSVT is often applied to try to achieve quantum speedups for machine learning problems. We will see the typical structure of such an application, the barriers to achieving super-polynomial quantum speedup, and the state of the literature that's attempting to bypass these barriers. Along the way, we'll also see an interesting connection between quantum linear algebra and classical sampling and sketching algorithms(explored in the form of "quantum-inspired" classical algorithms).

The study of spectral statistics is of importance due to its universality and utility as a robust diagnostic of quantum chaos. For closed many-body quantum chaotic systems, I will present two results: (i) a quantum-classical mapping that connects the Thouless time, which characterizes the onset of RMT of the spectral form factor (SFF); and the spectral gap of a dual classical stochastic system; (ii) a set of Lyapunov exponents which characterize the spectral statistics in the thermodynamic limit. For open quantum systems with complex spectra, I will propose and analyze a generalized SFF, and show that dissipative quantum chaotic systems display a “dip-ramp-plateau” behaviour with a quadratic ramp.

When a generic isolated quantum many-body system is driven out of equilibrium, its local properties are eventually described by the thermal ensemble. This picture can be intuitively explained by saying that, in the thermodynamic limit, the system acts as a bath for its own local subsystems. Despite the undeniable success of this paradigm, for interacting systems most of the evidence in support of it comes from numerical computations in relatively small systems, and there are very few exact results. In the talk, I will present an exact solution for the thermalization dynamics in the "Rule 54" cellular automaton, which can be considered the simplest interacting integrable model. After introducing the model and its tensor-network formulation, I will present the main tool of my analysis: the space-like formulation of the dynamics. Namely, I will recast the time-evolution of finite subsystems in terms of a transfer matrix in space and construct its fixed-points. I will conclude by showing two examples of physical applications: dynamics of local observables and entanglement growth. The talk is based on a recent series of papers: arXiv:2012.12256, arXiv:2104.04511, and arXiv:2104.04513.

Dark matter constitutes 85% of the matter content in the Universe, but its physical nature remains unknown and requires new physics to explain. I will review the status of the recent early-universe and late-universe searches for the identity of dark matter, summarizing the best current limits on scattering between dark matter and baryons, and discussing cosmological limits on the mass of thermal-relic dark matter. I will highlight the interplay between the thermal history of the universe and the formation of structure as complementary probes of dark matter physics, using the example of the 21-cm signal from the Cosmic Dawn. Finally, I will discuss the prospects for unveiling the physics of dark matter in the coming decade.

Kitaev quantum spin liquids (QSLs) are exotic states of matter that are predicted to host Majorana fermions and gauge flux excitations. However, so far all known Kitaev QSL candidates are known to have appreciable non-Kitaev interactions that pushes these systems far from the QSL regime. Co based magnets have been proposed to be perhaps a more ideal platform for realizing Kitaev QSLs. In this talk I will show evidence for a Kitaev interactions in both the quasi-one-dimensional ferromagnet CoNb2O6 as well as the hexagonal magnet BaCo2(AsO4). Although it is usually believed to be the best material realization of a 1D Ising chain, by combining terahertz spectroscopy and calculations we have shown that CoNb2O6 is well described by a model with bond-dependent interactions. We call this model the ‘twisted Kitaev chain’, as these interactions are similar to those of the honeycomb Kitaev spin liquid. The ferromagnetic ground state of CoNb2O6 arises from the compromise between two axes. Owing to this frustration, even at zero field domain walls have quantum motion, which is described by the celebrated Su–Schrieffer–Heeger model of polyacetylene and shows rich behavior as a function of field. Most recently, we have shown also that the honeycomb cobalt-based Kitaev QSL candidate, BaCo2(AsO4)2, has dominant Kitaev interactions. Due to only small non-Kitaev terms a magnetic continuum consistent with Majorana fermions and the existence of a Kitaev QSL can be induced by a small out-of-plane-magnetic field. Our results demonstrate BaCo2(AsO4)2 as a far more ideal version of Kitaev QSL compared with other candidates.

C. M Morris et al. "Hierarchy of bound states in the one-dimensional ferromagnetic Ising chain CoNb2O6 investigated by high-resolution time-domain terahertz spectroscopy.” Phys. Rev. Lett. 112.13 137403 (2014).

C.M. Morris et al. “Duality and domain wall dynamics in a twisted Kitaev chain”, Nature Physics

volume 17, pages 832–836 (2021).

X. Zhang, et al., "In- and out-of-plane field induced quantum spin-liquid states in a more ideal Kitaev material: BaCo2(AsO4)”, https://arxiv.org/abs/2106.13418

Zoom Link: https://pitp.zoom.us/meeting/register/tJcqc-ihqzMvHdW-YBm7mYd_XP9Amhypv5vO