Note: For this talk only, please use the link provided in the Perimeter Institute seminar page.
Abstract: Traditionally, quantum many-body theory has focussed on ground states and equilibrium properties of spatially extended systems, such as electrons and spins in crystalline solids. In recent years “noisy intermediate scale quantum computers” (NISQ) have emerged, providing new opportunities for controllable non-equilibrium many-body systems. In such dynamical quantum systems the inexorable growth of non-local quantum entanglement is expected, but monitoring (by making projective measurements) can compete against entanglement growth. In this talk I will overview theoretical work exploring the behavior of “monitored” quantum circuits, which can exhibit a novel quantum dynamical phase transition between a weak measurement phase and a quantum Zeno phase, the former which we characterize in detail. Accessing such physics in the lab is challenged by the need for post-selection, which might be circumnavigated by decoding using active error correction, conditioned on the measurement outcomes, as will be described in systems with Z2 symmetry.
Chair: Tim Hsieh
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
Abstract: 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.
Title: Planckian Metals (talk link)
Many modern materials feature a “Planckian metal”: a phase of electronic quantum matter without quasiparticle excitations, and relaxation in a time of order Planck's constant divided by the absolute temperature. I will review recent progress in understanding such metals using insights from the Sachdev-Ye-Kitaev model of many-particle quantum dynamics. I will also note connections to progress in understanding the quantum nature of black holes.
Abstract: 2+1d U(1) Chern-Simons (CS) gauge theories provide a simple and complete description of all 2+1d Abelian topological phases. In this talk, I will discuss how the theoretical framework can be used to explore 3+1d quantum phases of matter. The 3+1d generalization involves an infinite number of 2+1d U(1) gauge fields, which can be thought of as living in different spatial layers, coupled through CS terms. When the theory is fully gapped, it describes a new kind of fracton topological order, where all excitations are restricted to move in planes. We will discuss how these new examples compare with existing constructions of fracton order. Interestingly, for certain couplings the theory becomes gapless. I will discuss our current understanding of the nature of the gapless theories, with the help of a microscopic realization with coupled wire constructions. I will argue that these models realize stable gapless phases, including in particular new types of compressible quantum liquids in (3+1)d.
Abstract: Local moment formation is a ubiquitous phenomenon in disordered semiconductors, alloys and related systems. They likely play an important role in universal behavior near metal-insulator transitions. Much work has been done in this area starting from the metallic side. We discuss local moment behavior in disordered insulators. Given the lack of analytic tools, we must resort to numerics. Using DMRG, we study disorder and interaction effects in a 1D Hubbard model where all single particle states are localized. For both random fermion hoppings and random chemical potentials, and over some range of half-filling, we find exponential charge and single fermion correlations but power law spin correlations indicative of the random singlet phase. The numerical results can be understood qualitatively by appealing to the U/t >> 1 limit of the Hubbard chain where a remarkably simple picture emerges.
Abstract: When the twist angle of a bilayer graphene is near the ``magic'' value, there are four narrow bands near the neutrality point, each two-fold spin degenerate. These bands are separated from the rest of the bands by energy gaps. In the first part of the talk, the topology of the narrow bands will be discussed, as well as the associated obstructions --or lack there of -- to construction of a complete localized basis [1,3].
In the second part of the talk, I will present a two stage renormalization group treatment [4] which connects the continuum Hamiltonian at length scales shorter than the moire superlattice period to the Hamiltonian for the active narrow bands only, which is valid at distances much longer than the moire period. Via a progressive numerical elimination of remote bands the relative strength of the one-particle-like dispersion and the interactions within the active narrow band Hamiltonian will be determined, thus quantifying the residual correlations and justifying the strong coupling approach in the final step.
In the last part of the talk, the states favored by electron-electron Coulomb interactions within the narrow bands will be discussed. Analytical and DMRG results based on 2D localized Wannier states [2,5], 1D localized hybrid Wannier states [3] and Bloch states [3,4] will be compared. Topological and symmetry constraints on the spectra of charged and neutral excitation[4] for various ground states, as well as non-Abelian braiding of Dirac nodes[3] , will also be presented.
[1] Jian Kang and Oskar Vafek, Phys. Rev. X 8, 031088 (2018).
[2] Jian Kang and Oskar Vafek, Phys. Rev. Lett. 122, 246401 (2019)
[3] Jian Kang and Oskar Vafek, Phys. Rev. B 102, 035161 (2020)
[4] Oskar Vafek and Jian Kang Phys. Rev. Lett. 125, 257602 (2020)
[5] Bin-Bin Chen, Yuan Da Liao, Ziyu Chen, Oskar Vafek, Jian Kang, Wei Li, Zi Yang Meng arXiv:2011.07602
Abstract: In this talk I will begin by introducing symmetry protected topological (SPT) Floquet systems in 1D. I will describe the topological invariants that characterize these systems, and highlight their differences from SPT phases arising in static systems. I will also discuss how the entanglement properties of a many-particle wavefunction depend on these topological invariants. I will then show that the edge modes encountered in free fermion SPTs are remarkably robust to adding interactions, even in disorder-free systems where generic bulk quantities can heat to infinite temperatures due to the periodic driving. This robustness of the edge modes to heating can be understood in the language of strong modes for free fermion SPTs, and almost strong modes for interacting SPTs. I will then outline a tunneling calculation for extracting the long lifetimes of these edge modes by mapping the Heisenberg time-evolution of the edge operator to dynamics of a single particle in Krylov space.
References: arXiv:2011.12310. and arXiv:1912.09634
References:
https://arxiv.org/abs/2006.10073
https://arxiv.org/abs/1912.08848
https://arxiv.org/abs/1912.06150