Talks

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