Quantum Matter

I will review recent progress on theory of many-body localization, mostly focusing on properties of the many-body localized phase itself.

I will discuss explicit construction of effective Hamiltonians governing the dynamics of conserved quantities.  The analysis reveals several inequivalent length scales in the system, some of which do not appear to diverge on the approach to the thermalized phase.

Experimental protocols to measure these length scales will also be discussed.

Numerical results suggest that the quantum Hall effect at {\nu} = 5/2 is described by the Pfaffian or anti-Pfaffian state in the absence of disorder and Landau level mixing. Those states are incompatible with the observed transport properties of GaAs heterostructures, where disorder and Landau level mixing are strong. We show that the recent proposal of a PH-Pfaffian topological order by Son is consistent with all experiments. The absence of the particle-hole symmetry at {\nu} =

5/2 is not an obstacle to the existence of the PH-Pfaffian order since the order is robust to symmetry breaking.

Quantum spin ice is a frustrated magnet that displays rich emergent phenomena. For example, the magnetic moments carried by the spins may separate into mobile magnetic charges, producing quantum fractional excitations known as spinons. The spinon moves in a background of disordered spins, and its motion is strongly coupled to the spin background. In this talk, I will demonstrate that the spinon dynamics can be described as a quantum walk with entropy-induced memory. Our numerical simulation shows that the dynamics of spinon exhibits a remarkable renormalization phenomenon: the spinon behaves as a massive free particle at low energy despite its strong coupling at the lattice scale.

The ytterbium pyrochlores, Yb2B2O7, are a family of materials with a remarkable diversity in their low-temperature physics. At the heart of their interesting physics is the proximity of their ground states to numerous competing phases. These proximate phases make the Yb pyrochlores very sensitive to perturbations such as pressure and off-stoichiometry. I will present a study of the effects of chemical pressure on the ytterbium pyrochlores, in which substitution of a non-magnetic constituent alters the lattice size and consequently inflicts an internal pressure on the system. We find that although each of Yb2B2O7 (B = Ge, Ti, Sn) exhibits a distinct dipole ordered state, there is a ubiquitous nature to their spin excitations. Furthermore, these spin excitations are highly unconventional in their own right and may hint at a hidden order parameter.

We introduce a new classical spin liquid on the pyrochlore lattice by extending spin ice with further neighbour interactions. This disorder-free spin model exhibits a form of dynamical heterogeneity with extremely slow relaxation for some spins while others fluctuate quickly down to zero temperature. We thus call this state "spin slush", in analogy to the heterogeneous mixture of solid and liquid water. This behaviour is driven by the structure of the ground state manifold that extends the two-in/two-out ice states to include branching structures built from three-in/one-out, three-out/one-in and all-in/all-out defects. Distinctive liquid-like patterns in the spin correlations serve as a signature of this intermediate range order. Finally, we discuss possible applications to materials as well the effects of quantum tunneling.

In this talk, I will describe a new technique—stochastic resonance magnetic force microscopy (SRMFM)—developed in my group for imaging the vortex dynamics in multiply connected superconducting devices. Unlike existing techniques, which directly image vortices, our technique relies on the mechanism of stochastic resonance to image the fluctuations between different vortex configurations. I will present data, taken using Josephson junction arrays and ring structures, that reveal striking geometric patterns which emerge when the energy of different vortex configurations become degenerate at well-defined positions of a magnetic tip that is scanned above the surface of the device. By analyzing the fluctuation rate as a function of temperature or external field, we obtain detailed information regarding the energy barriers connecting different vortex configurations, as well as energy scales associated with vortex-vortex interactions. The technique also provides a convenient means to manipulate vortices in multiply connected superconducting structures, which may prove useful in certain topological quantum-computing applications.

The kagome lattice in a mineral compound "Herbertsmithite" represents structurally the most ideal kagome Heisenberg antiferromagnet known to date. Herbertsmithite does not undergo a magnetic long-range order or spin freezing at least down to ~J/2000. We will present 17-Oxygen and 2-Deuterium single crystal NMR study of Herbertsmithite. We will demonstrate that the ground state of the kagome plane has a spin gap ~ 0.05J [1], and ~5% excess Cu2+ ions occupying the out-of-plane Zn2+ sites are the only defects [2]. [1] M. Fu et al., Science 350, 655 (2015). [2] T. Imai et al., Phys. Rev. B 84, 020411 (2011).

A many-body quantum system on the verge of instability between competing ground states exhibits emergent phenomena. Interacting electrons on triangular lattices are likely subjected to multiple instabilities in the charge and spin degrees of freedom, affording diverse phenomena related to the Mott physics. The molecular conductors are superior model systems for studying the Mott physics because of the designability and controllability of material parameters such as lattice geometry and bandwidth by chemical substitution and/or pressure. In this symposium, I first introduce the fundamentals of organic materials and then present various quantum manifestations that interacting electrons in triangular-lattice organics show under variable correlation on the verge of the Mott metal-insulator transition. The topics include i) the quantum criticality of the Mott transition revealed by the resistivity that obeys quantum-critical scaling, ii) the pseudo-gap-like behavior of the metallic state, which is found to originate from preformed Cooper pairs that persist up to twice as high as Tc, and iii) the spin liquid state that emerges in the Mott insulating state, depending on the lattice geometry. I may touch the recent finding on a doped triangular lattice that exhibits a possible BEC-to-BCS crossover in superconductivity. The work presented here was performed in collaboration with T. Furukawa, H. Oike, J. Ibuka, M. Urai, Y. Suzuki, K. Miyagawa (UTokyo), Y. Shimizu (Nagoya Univ.), M. Ito, H. Taniguchi (Saitama Univ.) and R. Kato (RIKEN)

In recent years, there has been much interest in honeycomb lattice quantum magnets described by Kitaev-Heisenberg Hamiltonian. For example, honeycomb lattice iridates, such as Na2IrO3 and Li2IrO3 have been intensely scrutinized. Recently, we proposed that a 4d honeycomb magnet α-RuCl3 is a promising candidate material in which Kitaev physics could be studied. I will give an overview of the physics of alpha-RuCl3, and talk about recent experimental and theoretical advances.

We have recently demonstrated an experimental platform to isolate 2D materials that are unstable in the ambient environment. I will discuss our recent studies of the charge density wave compound 1T-TaS2 and superconducting 2H-NbSe¬ in the atomically thin limit, made possible using this technique. In TaS2, we uncover a new surface charge density wave transition that is distinct from that in the bulk layers, as well as demonstrate continuous electrical control over this phase transition. In NbSe2, a small perpendicular magnetic field induces a transition to a quantum metallic phase, the resistivity of which obeys a unique field-scaling consistent with that predicted for a Bose metal. These methods and experiments open new doors for the study of other correlated 2D systems in the immediate future.

Beyond their deceptively featureless ground states, spin liquids are particularly remarkable in the exotic nature of their (fractionalised and gauge charged) excitations. Quenched disorder can be instrumental in nucleating or localising defects with unusual properties, revealing otherwise hidden features of these topological many-body states. This talk discusses how to turn the nuisance of disorder into a powerful probe and origin of new collective behaviour.

We numerically investigate the expansion of clouds of hard-core bosons in a 2D square lattice using a matrix-product state based method. This non-equilibrium setup is induced by quenching a trapping potential to zero and is specifically motivated by an experiment with ultracold atoms [1]. As the anisotropy for hopping amplitudes in different spatial directions is varied from 1D to 2D, we observe a crossover from a fast ballistic expansion in the 1D limit to much slower dynamics in the isotropic 2D lattice [2].

 

Introducing a site-dependent disorder potential allows to study many body localization (MBL). In a very recent experiment, the melting of a domain wall gave evidence for an MBL transition in 2D [3]. We study 1D and quasi-1D models, for which the phase diagram in the presence of disorder is known, such as the Anderson insulator, Aubry-Andre model and interacting fermions in 1D and on a two-leg ladder [4]. By considering several observables, we demonstrate that the domain wall melting can indeed yield quantitative information on the transition from an ergodic to the MBL phase as a function of disorder.

 

[1] J. P. Ronzheimer et al., PRL 110, 205301 (2013) [2] J. Hauschild et al., PRA 92, 053629 (2015) [3] J. Choi et al., arXiv:1604.04178 (2016) [4] J. Hauschild et al., in preparation