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Recent experiments4 on solid Helium 4 exhibit antiferromagnets in an external magnetic field, triplet super-solid type features and have led to a flurry of ac- states with spins aligned along the field direction can tivity. In the simplest explanation of observations, a frac- be regarded as hard core bosons. In many other sys- tion of the medium becomes, at low temperatures, a su- tems, interactions between quantum spins may also be perfluid that decouples from the measurement apparatus. mapped onto hard core type bosonic systems.2122 If a However, the required condensate fraction does not sim- solid or glassy phase appears in a classical Brownian sys- ply conform with thermodynamic measurement12. Rit- tem, then a mapping similar to that of BCZ suggests tner and Reppy13 further found that the putative super- supersolidity/superglassiness in the corresponding quan- solid type feature is accutely sensitive to the quench tum spin system. Recently, there has been much work rate for solidifying the liquid. Aoki, Keiderling, and examining supersolidity in such spin systems, e.g.,22. It Kojima discovered rich hysteresis and memory effects14. is highly natural to expect new lattice spin superglass All of these features can arise from glassy characteristics counterparts. alone12,15- precisely as in the superglass phase discussed In transition-metal compounds, the fractional filling of by BCZ. It may indeed well be that a confluence of both the 3d-shells allows for cooperative orbital ordering. This superfluid and glassy features (and their effects on elastic order has been observed in numerous compounds.23 Sim- properties, e.g., screened finite elastic shear penetration ilar to the spin and charge degrees of freedom, we may depths)16 may be at work. There may be new experi- ask whether low temperature Bose condensed glasses of mental consequences of (super-) glassy dynamics such as orbitals may appear: an orbital superglass. The work of this. For instance, such dynamics can manifest disparate BCZ allows to investigate this by knowing the dynamics relaxation times that may be probed for.12 Typical glass of hard core Bose model derived from a classical counter- formers indeed typically exhibit relaxations on two dif- part. Orbital states can be described in terms of a S=1/2 ferent time scales. pseudo-spin.23 We may, in turn, map these pseudo-spins Cold atom systems may provide another realization to hard core bosons21 and then investigate the dynamics of a superglass state. Indeed, a supersolid state of cold of these bosons by mapping the system to that of classical atoms in a confining optical lattice was very recently Brownian particles on a lattice. achieved17. It is natural to expect a superglass analog The mapping employed by BCZ also suggests a new of these cold atomic systems. quantum critical point in related systems. The classi- The super-glass phases that BCZ find and the mapping cal jamming transition24 of hard spheres/disks from a they employ may also have new manifestations elsewhere. jammed system at high density to an unjammed one at We suggest a few of these below. lower densities is a continuous transition with known crit- We may envision lattice extensions of the continuum ical exponents, both static25 and dynamic26. Replicating system investigated by BCZ: a ”lattice superglass”. For the mapping used by BCZ28, we may derive an analog charged bosons (e.g., Cooper pairs) on a lattice, such quantum system harboring a zero temperature transi- a charge superglass would correspond to a superconduc- tion with similar critical exponents. The classical zero tor with glassy dynamics. In a similar vein, a ”lattice temperature critical point (”point J”)24,25 may rear its supersolid” of Cooper pairs would correspond to a su- head anew in the form of quantum critical jamming of perconductor concomitant with well defined crystalline the bosonic systems with dynamical exponents, poten- (i.e., charge density wave) order. Indeed, in some heavy tially as high as z =4.6, as we may ascertain from those fermion compounds as well as in the cuprate and the reported for the classical jamming system26. newly discovered iron arsenide family of high temper- All of the above mentioned examples are free of ature superconductors18 there are some indications of quenched disorder. Glassiness in structural glasses and non-uniform meso-scale spatial electronic structures and the Brownian hard sphere system is not triggered by dis- glassy dynamics. Classical glass formers are known to ex- order. In classical (and quantum) spin glass system, hibit ”dynamical heterogeneities”- a non-uniform distri- sluggish dynamics is triggered by quenched disorder.27 bution of local velocities19. Using the very same mapping Applying the same mapping of BCZ anew on viscous used by BCZ- Quantum dynamical heterogeneities might classical systems with quenched disorder, we may exam- be suggested in their corresponding quantum counter- ine quenched super spin-glass analogs of spin-glass sys- parts. Such heterogeneities with concurrent non-uniform tems. In a similar vein, quantum analogs of classical liq- spatial structures might have realizations in some of the uid crystalline systems (nematic or smectic phases) first aforementioned electronic systems. advanced in29 and further investigated in16 can be de- Other realizations may be manifest as spin super- rived by examining the bosonic analog of classical liquid glasses. Quantum spin systems in a magnetic field,20 crystalline systems. can exhibit a delicate interplay between the formation The work of BCZ provides important steps in an en- of singlet states and the tendency of spins to align with tirely new field. It proves, as a matter of principle, the the field direction. These systems can be mapped onto a existence of a superglass phase in a physical quantum system of bosons with hard core interactions- just as in systems. The ramifications of such a phase may be nu- the system investigated by BCZ. In some spin S=1/2 merous. 3

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