Quantum Matter

I will discuss ongoing work on the robustness of symmetry protected topological (SPT) phases in open systems. By studying the evolution of non-local string order parameters, we find that one-dimensional SPT order is destabilized by couplings to the environment satisfying a weak symmetry condition that directly generalizes from closed systems. We introduce a stronger symmetry condition on channels that ensures SPT order is preserved. SPT phases of mixed states and their transformation under noisy channels is also discussed.

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.

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.

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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.

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

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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.

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Critical states of matter are a class of highly entangled quantum matter with various interesting properties and form important bases for emergence of a variety of novel quantum phases. Such states pose serious challenges for the community due to their strongly interacting nature. In this talk, I will discuss our recent progress on tackling critical quantum matter using the method of conformal bootstrap. I will start with introducing several representative examples of critical quantum matter, including the familiar deconfined quantum phase transition, U(1) Dirac spin liquid phase, and the newly proposed Stiefel liquid phase. Next I will focus on the SU(N) deconfined phase transition (i.e. scalar QED), and demonstrate that they can be solved by conformal bootstrap, namely we have obtained their bootstrap kinks and islands.

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In this talk, I will present a general approach to obtain effective field theories for topological crystalline insulators whose low-energy theories are described by massive Dirac fermions. We show that these phases are characterized by the responses to spatially dependent mass parameters with interfaces. These mass interfaces implement the dimensional reduction procedure such that the state of interest is smoothly deformed into a network of defects (dubbed topological crystal), where each defect supports a short-ranged entangled state. Effective field theories are obtained by integrating out the massive Dirac fermions, and various quantized topological terms are uncovered. I will describe how to apply this strategy through a few simple examples and comment on the relation to the topological elasticity theory. 

Twisted bilayer graphene (TBG) realizes an exquisitely tunable, strongly interacting system featuring superconductivity and various correlated insulating states. In this talk I will introduce gate-defined wires in TBG as an enticing platform for Majorana-based fault-tolerant qubits. Our proposal notably relies on “internally” generated superconductivity in TBG – as opposed to “external” superconducting proximity effects commonly employed in Majorana devices – and may operate even at zero magnetic field. I will also describe how electrical measurements of gate-defined wires can reveal the nature of correlated insulators and shed light on the Cooper-pairing mechanism in TBG.

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I will talk on experiments and their interpretation done with Professor Lei Shu and her collaborators at Fudan University, Shanghai, and some tentative theory for the observations.  Thermodynamic and magnetic relaxation measurements in zero and finite magnetic field have been performed in two related almost triangular lattices of S=1/2 spins. One of these compounds is the purest of any of the potential spin-liquid compounds investigated so far. All its measured properties are extra-ordinary and characterized simply by just one parameter, the exchange energy obtained from susceptibility measurements. There are also colossal ultra-low energy singlet excitations. This may be the first characterization of the intrinsic properties of a class of spin-liquids.  An ansatz in which the excitations are calculated from a state of singlet-dimers interacting with excitations from other such singlets can be expressed in terms of Majoranas and gives properties similar to those observed.